In this notebook we try to find for any knot in the SnapPy census that has two integer surgeries an almost alternating diagram of the unknot together with a crossing in it such that tangle replacement of that crossing gives the whole interval of alternating surgeries. In other words, we will prove that all these knots are in D.
We start with a list of the integer and half-integer alternating surgeries of the SnapPy census knots. It is of the form [Census knot, branching set of the half-integer slope, branching set of the integer slope 1, branching set of the integer slope 2].
alternating_surgeries=[['m016', 'K8a14', 'K7a2', 'L7a5'],
['m071', 'K10a83', 'K9a8', 'L9a38'],
['m103', 'K10a50', 'K9a21', 'L9a16'],
['m118', 'K9a11', 'L8a8', 'K8a1'],
['m240', 'K10a106', 'K9a34', 'L9a12'],
['m270', 'K10a47', 'K9a16', 'L9a23'],
['m276', 'K10a11', 'L9a27', 'K9a5'],
['o9_00133', 'K14a13432', 'L13a5000', 'K13a633'],
['o9_00168', 'K14a13417', 'K13a4314', 'L13a2992'],
['o9_00797', 'K14a13298', 'K13a2120', 'L13a4286'],
['o9_00815', 'K14a13403', 'L13a4253', 'K13a1883'],
['o9_01680', 'K14a14297', 'K13a2759', 'L13a2083'],
['o9_01765', 'K14a13889', 'K13a2125', 'L13a1850'],
['o9_02340', 'K14a7439', 'K13a2125', 'L13a957'],
['o9_02386', 'K14a6987', 'K13a1944', 'L13a500'],
['o9_02706', 'K14a2247', 'L13a4202', 'K13a2041'],
['o9_02735', 'K14a2615', 'K13a2675', 'L13a4183'],
['o9_03118', 'K14a1536', 'L13a3236', 'K13a299'],
['o9_03149', 'K14a2613', 'K13a1860', 'L13a2812'],
['o9_03288', 'K14a14831', 'L13a4304', 'K13a3453'],
['o9_03412', 'K14a10105', 'K13a2291', 'L13a2528'],
['o9_03526', 'K14a16396', 'K13a4852', 'L13a2127'],
['o9_03932', 'K14a11193', 'K13a2858', 'L13a2843'],
['o9_04313', 'K14a14819', 'L13a4979', 'K13a1458'],
['o9_04431', 'K14a5832', 'K13a2704', 'L13a3104'],
['o9_04435', 'K14a14873', 'L13a4313', 'K13a1220'],
['o9_07943', 'K14a18265', 'K13a4569', 'L13a2937'],
['o9_08042', 'K14a14990', 'L13a3474', 'K13a3452'],
['o9_08776', 'K14a2564', 'K13a1209', 'L13a1062'],
['o9_08852', 'K14a2653', 'K13a1205', 'L13a996'],
['o9_10696', 'K14a18376', 'K13a3915', 'L13a4297'],
['o9_11467', 'K14a3771', 'L13a3188', 'K13a809'],
['o9_11560', 'K14a3245', 'K13a1205', 'L13a1896'],
['o9_12144', 'K14a17264', 'K13a4563', 'L13a2083'],
['o9_12230', 'K14a15078', 'L13a3468', 'K13a2857'],
['o9_12736', 'K14a771', 'L13a3633', 'K13a1390'],
['o9_13056', 'K14a1548', 'K13a1432', 'L13a2954'],
['o9_13508', 'K14a5545', 'L13a3090', 'K13a1042'],
['o9_14018', 'K14a3045', 'K13a759', 'L13a1624'],
['o9_14136', 'K14a5717', 'K13a2317', 'L13a2143'],
['s042', 'K11a167', 'K10a69', 'L10a41'],
['s068', 'K11a80', 'L10a92', 'K10a17'],
['s104', 'K11a264', 'L10a92', 'K10a34'],
['s114', 'K11a71', 'K10a32', 'L10a91'],
['s344', 'K11a149', 'K10a53', 'L10a10'],
['s369', 'K11a69', 'K10a58', 'L10a59'],
['s769', 'K11a70', 'K10a40', 'L10a30'],
['t00110', 'K13a3353', 'K12a1033', 'L12a647'],
['t00146', 'K13a3362', 'L12a1265', 'K12a158'],
['t00423', 'K13a3384', 'L12a1243', 'K12a540'],
['t00434', 'K13a3361', 'L12a1240', 'K12a579'],
['t00873', 'K13a2071', 'K12a306', 'L12a492'],
['t00932', 'K13a1907', 'K12a522', 'L12a595'],
['t01216', 'K13a3907', 'K12a1039', 'L12a187'],
['t01292', 'K13a1805', 'K12a534', 'L12a327'],
['t01409', 'K13a615', 'K12a510', 'L12a932'],
['t01424', 'K13a439', 'L12a883', 'K12a281'],
['t01598', 'K13a680', 'K12a721', 'L12a887'],
['t01646', 'K13a442', 'L12a971', 'K12a98'],
['t01850', 'K13a2519', 'L12a1039', 'K12a591'],
['t01949', 'K13a3826', 'K12a1023', 'L12a1292'],
['t03566', 'K13a1285', 'L12a678', 'K12a420'],
['t03709', 'K13a806', 'K12a376', 'L12a615'],
['t04228', 'K13a221', 'L12a676', 'K12a144'],
['t05239', 'K13a1364', 'K12a368', 'L12a600'],
['t05426', 'K13a821', 'L12a972', 'K12a21'],
['t05578', 'K13a715', 'L12a962', 'K12a258'],
['t05663', 'K13a607', 'L12a1105', 'K12a329'],
['v0082', 'K12a851', 'L11a356', 'K11a58'],
['v0114', 'K12a849', 'K11a309', 'L11a190'],
['v0220', 'K12a282', 'L11a266', 'K11a117'],
['v0223', 'K12a214', 'K11a91', 'L11a247'],
['v0424', 'K12a944', 'K11a191', 'L11a186'],
['v0497', 'K12a509', 'K11a120', 'L11a151'],
['v0709', 'K12a1011', 'K11a310', 'L11a274'],
['v0715', 'K12a138', 'L11a262', 'K11a107'],
['v0741', 'K12a191', 'K11a77', 'L11a268'],
['v0847', 'K12a606', 'L11a271', 'K11a60'],
['v0912', 'K12a1008', 'L11a359', 'K11a139'],
['v1300', 'K12a1219', 'K11a341', 'L11a200'],
['v1628', 'K12a290', 'L11a191', 'K11a60'],
['v1940', 'K12a73', 'L11a155', 'K11a16'],
['v1966', 'K12a184', 'K11a87', 'L11a77'],
['m082', 'K9a32', 'K8a9', 'L8a3'],
['m144', 'K10a97', 'L9a34', 'K9a9'],
['m194', 'K10a97', 'K9a34', 'L9a7'],
['m198', 'K10a118', 'K9a10', 'L9a24'],
['m239', 'K9a28', 'K8a15', 'L8a9'],
['m281', 'K10a66', 'L9a26', 'K9a4'],
['o9_00644', 'K14a16783', 'L13a4960', 'K13a646'],
['o9_01436', 'K14a17856', 'L13a4220', 'K13a666'],
['o9_01496', 'K14a15197', 'L13a1884', 'K13a3215'],
['o9_01584', 'K14a16756', 'L13a339', 'K13a4827'],
['o9_01621', 'K14a16609', 'L13a337', 'K13a4315'],
['o9_01953', 'K14a18519', 'K13a4562', 'L13a2843'],
['o9_01955', 'K14a18499', 'L13a4298', 'K13a1536'],
['o9_02255', 'K14a7592', 'K13a1793', 'L13a597'],
['o9_02350', 'K14a7103', 'K13a1938', 'L13a949'],
['o9_02655', 'K13a1443', 'K12a527', 'L12a882'],
['o9_02696', 'K13a761', 'L12a920', 'K12a497'],
['o9_02772', 'K14a18477', 'K13a1540', 'L13a5041'],
['o9_02786', 'K13a3307', 'K12a1095', 'L12a630'],
['o9_02794', 'K14a12509', 'L13a2115', 'K13a2427'],
['o9_03032', 'K14a11620', 'L13a1210', 'K13a3004'],
['o9_03108', 'K14a19430', 'K13a1585', 'L13a4297'],
['o9_03133', 'K14a16622', 'L13a1959', 'K13a4539'],
['o9_03162', 'K14a10625', 'L13a3384', 'K13a296'],
['o9_03188', 'K14a10099', 'K13a1772', 'L13a2823'],
['o9_03313', 'K14a10266', 'K13a587', 'L13a4340'],
['o9_03586', 'K14a19105', 'K13a1584', 'L13a5059'],
['o9_03622', 'K14a17463', 'L13a1604', 'K13a4311'],
['o9_03802', 'K14a19111', 'L13a1665', 'K13a4833'],
['o9_03833', 'K14a10696', 'L13a768', 'K13a2317'],
['o9_04106', 'K14a12339', 'L13a380', 'K13a2807'],
['o9_04205', 'K14a7694', 'L13a365', 'K13a2110'],
['o9_04245', 'K14a10812', 'L13a1869', 'K13a2857'],
['o9_04269', 'K13a3201', 'K12a1011', 'L12a634'],
['o9_04438', 'K14a8243', 'K13a60', 'L13a2960'],
['o9_05021', 'K14a11003', 'L13a765', 'K13a2832'],
['o9_05177', 'K14a11048', 'L13a763', 'K13a1941'],
['o9_05229', 'K14a12627', 'L13a841', 'K13a2122'],
['o9_05357', 'K14a11003', 'K13a427', 'L13a2981'],
['o9_05426', 'K14a10190', 'K13a817', 'L13a3443'],
['o9_05483', 'K14a9562', 'L13a2133', 'K13a1432'],
['o9_05562', 'K14a10897', 'L13a1595', 'K13a2841'],
['o9_05618', 'K14a9163', 'L13a790', 'K13a2002'],
['o9_05860', 'K14a8262', 'L13a2837', 'K13a523'],
['o9_05970', 'K14a6783', 'K13a18', 'L13a4371'],
['o9_06060', 'K13a1328', 'K12a318', 'L12a226'],
['o9_06128', 'K14a7129', 'L13a2838', 'K13a1818'],
['o9_06154', 'K13a1509', 'L12a835', 'K12a83'],
['o9_06248', 'K14a2949', 'L13a1153', 'K13a788'],
['o9_06301', 'K14a6547', 'K13a332', 'L13a4461'],
['o9_07790', 'K14a17873', 'L13a2991', 'K13a653'],
['o9_07893', 'K13a3150', 'L12a29', 'K12a501'],
['o9_07945', 'K13a1843', 'L12a26', 'K12a499'],
['o9_08006', 'K14a11327', 'K13a1044', 'L13a2240'],
['o9_08224', 'K13a3634', 'K12a1178', 'L12a1239'],
['o9_08302', 'K13a3547', 'L12a1298', 'K12a219'],
['o9_08477', 'K14a17811', 'K13a4871', 'L13a699'],
['o9_08647', 'K14a8937', 'L13a947', 'K13a2288'],
['o9_08765', 'K13a3671', 'L12a987', 'K12a258'],
['o9_08771', 'K14a6761', 'L13a574', 'K13a1772'],
['o9_08828', 'K14a16699', 'L13a2834', 'K13a3097'],
['o9_08831', 'K13a3803', 'K12a977', 'L12a595'],
['o9_08875', 'K14a11069', 'K13a803', 'L13a3161'],
['o9_09213', 'K14a7691', 'K13a176', 'L13a4238'],
['o9_09465', 'K14a7568', 'K13a1850', 'L13a2859'],
['o9_09808', 'K14a10354', 'L13a3286', 'K13a565'],
['o9_11248', 'K14a17871', 'L13a2940', 'K13a3593'],
['o9_11570', 'K14a16575', 'K13a2804', 'L13a2937'],
['o9_11685', 'K13a4143', 'K12a1169', 'L12a872'],
['o9_11795', 'K13a4228', 'K12a952', 'L12a326'],
['o9_11845', 'K13a3487', 'K12a1238', 'L12a1323'],
['o9_11999', 'K14a11475', 'L13a572', 'K13a2834'],
['o9_12412', 'K13a2257', 'K12a660', 'L12a870'],
['o9_12459', 'K13a2345', 'K12a440', 'L12a868'],
['o9_12519', 'K13a2254', 'K12a365', 'L12a1261'],
['o9_12693', 'K14a19195', 'L13a4353', 'K13a4273'],
['o9_12757', 'K14a10775', 'L13a4367', 'K13a2705'],
['o9_12873', 'K14a5793', 'L13a3024', 'K13a1749'],
['o9_12892', 'K13a4426', 'L12a998', 'K12a524'],
['o9_12919', 'K13a3486', 'K12a1236', 'L12a962'],
['o9_12971', 'K13a2347', 'L12a558', 'K12a303'],
['o9_13052', 'K14a12642', 'K13a1413', 'L13a3219'],
['o9_13125', 'K13a1834', 'L12a841', 'K12a579'],
['o9_13182', 'K13a4754', 'K12a1262', 'L12a492'],
['o9_13188', 'K14a12639', 'L13a674', 'K13a3102'],
['o9_13400', 'K14a17456', 'L13a4477', 'K13a3456'],
['o9_13403', 'K13a2904', 'K12a262', 'L12a932'],
['o9_13433', 'K13a1734', 'L12a920', 'K12a497'],
['o9_13537', 'K13a1664', 'L12a912', 'K12a215'],
['o9_13604', 'K14a12420', 'L13a1604', 'K13a878'],
['o9_13639', 'K13a4371', 'L12a689', 'K12a145'],
['o9_13649', 'K13a2011', 'L12a1313', 'K12a81'],
['o9_13666', 'K14a19167', 'L13a1663', 'K13a4825'],
['o9_13720', 'K14a7490', 'L13a318', 'K13a2004'],
['o9_13952', 'K14a10121', 'L13a3554', 'K13a1295'],
['o9_14079', 'K14a4414', 'K13a937', 'L13a4350'],
['o9_14364', 'K13a3952', 'K12a1047', 'L12a62'],
['o9_14376', 'K14a6097', 'L13a1116', 'K13a1572'],
['o9_14495', 'K13a2218', 'K12a617', 'L12a66'],
['o9_14599', 'K14a12304', 'K13a1248', 'L13a2383'],
['o9_14716', 'K14a18651', 'K13a3243', 'L13a4977'],
['o9_14831', 'K12a864', 'L11a51', 'K11a174'],
['o9_14974', 'K14a11401', 'K13a1545', 'L13a3322'],
['o9_15506', 'K13a1178', 'K12a349', 'L12a176'],
['o9_15633', 'K13a2658', 'L12a921', 'K12a17'],
['o9_15997', 'K14a10710', 'L13a707', 'K13a2033'],
['o9_16065', 'K14a7006', 'L13a2968', 'K13a581'],
['o9_16141', 'K14a5782', 'K13a148', 'L13a2527'],
['o9_16157', 'K14a5900', 'L13a1842', 'K13a1470'],
['o9_16181', 'K14a8736', 'K13a811', 'L13a2226'],
['o9_16319', 'K14a4566', 'K13a719', 'L13a3098'],
['o9_16356', 'K14a18894', 'L13a2089', 'K13a1469'],
['o9_16527', 'K14a18817', 'L13a1858', 'K13a3098'],
['o9_16642', 'K14a3526', 'L13a354', 'K13a769'],
['o9_16748', 'K13a1775', 'L12a473', 'K12a220'],
['o9_16920', 'K12a631', 'L11a54', 'K11a11'],
['o9_17450', 'K13a2563', 'L12a821', 'K12a275'],
['o9_18007', 'K13a2363', 'L12a536', 'K12a583'],
['o9_18209', 'K14a10774', 'K13a575', 'L13a4200'],
['o9_18633', 'K13a3082', 'K12a779', 'L12a184'],
['o9_18813', 'K12a696', 'L11a198', 'K11a32'],
['o9_19130', 'K12a857', 'L11a102', 'K11a34'],
['o9_20219', 'K13a3718', 'K12a849', 'L12a331'],
['o9_21893', 'K12a1199', 'L11a282', 'K11a309'],
['o9_21918', 'K12a1228', 'L11a173', 'K11a108'],
['o9_22129', 'K14a19388', 'L13a1662', 'K13a4863'],
['o9_22477', 'K12a1231', 'L11a255', 'K11a110'],
['o9_22607', 'K14a19195', 'L13a1949', 'K13a4839'],
['o9_22663', 'K12a316', 'L11a104', 'K11a100'],
['o9_22698', 'K13a1395', 'K12a353', 'L12a367'],
['o9_22925', 'K12a309', 'K11a232', 'L11a157'],
['o9_23023', 'K13a713', 'L12a456', 'K12a99'],
['o9_23263', 'K14a17804', 'L13a4177', 'K13a3593'],
['o9_23660', 'K14a11215', 'K13a1744', 'L13a1894'],
['o9_23955', 'K14a19194', 'K13a3269', 'L13a4275'],
['o9_23961', 'K14a12666', 'L13a1655', 'K13a3136'],
['o9_23977', 'K13a3677', 'K12a989', 'L12a626'],
['o9_24149', 'K14a19179', 'L13a3083', 'K13a4830'],
['o9_24183', 'K14a3347', 'K13a888', 'L13a1362'],
['o9_24534', 'K14a18856', 'L13a3661', 'K13a4275'],
['o9_24592', 'K12a1271', 'L11a255', 'K11a33'],
['o9_24886', 'K14a7920', 'L13a353', 'K13a1227'],
['o9_24889', 'K14a12495', 'L13a2793', 'K13a3134'],
['o9_25595', 'K14a19452', 'L13a1946', 'K13a4831'],
['o9_26604', 'K12a793', 'L11a182', 'K11a27'],
['o9_26791', 'K13a2340', 'K12a321', 'L12a1036'],
['o9_27155', 'K13a1194', 'L12a923', 'K12a385'],
['o9_27261', 'K13a2311', 'K12a635', 'L12a188'],
['o9_27392', 'K14a3943', 'L13a3545', 'K13a238'],
['o9_27480', 'K14a7535', 'L13a3645', 'K13a578'],
['o9_27737', 'K14a12587', 'L13a1963', 'K13a3111'],
['o9_28113', 'K14a11153', 'L13a803', 'K13a2882'],
['o9_28153', 'K13a1374', 'L12a1133', 'K12a21'],
['o9_28529', 'K14a3324', 'K13a780', 'L13a2219'],
['o9_28592', 'K14a7952', 'K13a1156', 'L13a3322'],
['o9_28746', 'K13a2505', 'L12a1097', 'K12a82'],
['o9_28810', 'K13a1132', 'K12a403', 'L12a1072'],
['o9_29246', 'K14a5848', 'K13a1903', 'L13a710'],
['o9_29436', 'K14a10851', 'L13a1612', 'K13a842'],
['o9_29529', 'K12a359', 'L11a3', 'K11a72'],
['o9_30375', 'K13a1092', 'K12a284', 'L12a516'],
['o9_30721', 'K12a467', 'L11a69', 'K11a157'],
['o9_30790', 'K14a7870', 'K13a9', 'L13a4191'],
['o9_31165', 'K14a10885', 'L13a1668', 'K13a912'],
['o9_32257', 'K12a993', 'L11a313', 'K11a257'],
['o9_33526', 'K11a287', 'K10a72', 'L10a69'],
['o9_33585', 'K12a340', 'K11a130', 'L11a30'],
['o9_34403', 'K12a1198', 'K11a137', 'L11a50'],
['o9_35320', 'K12a1217', 'K11a312', 'L11a149'],
['o9_35549', 'K14a3551', 'K13a164', 'L13a4597'],
['o9_35682', 'K12a1081', 'K11a295', 'L11a89'],
['o9_35736', 'K14a6098', 'L13a2540', 'K13a914'],
['o9_35772', 'K12a966', 'K11a320', 'L11a109'],
['o9_37941', 'K12a1005', 'K11a115', 'L11a102'],
['o9_39394', 'K12a765', 'K11a217', 'L11a220'],
['s086', 'K11a345', 'K10a60', 'L10a67'],
['s294', 'K10a77', 'L9a22', 'K9a15'],
['s301', 'K11a146', 'L10a72', 'K10a9'],
['s308', 'K11a122', 'L10a19', 'K10a42'],
['s336', 'K10a85', 'K9a31', 'L9a27'],
['s346', 'K11a160', 'K10a52', 'L10a29'],
['s367', 'K11a168', 'L10a64', 'K10a37'],
['s407', 'K11a189', 'K10a30', 'L10a60'],
['s582', 'K11a280', 'L10a40', 'K10a82'],
['s665', 'K11a114', 'L10a13', 'K10a30'],
['s684', 'K10a36', 'L9a3', 'K9a13'],
['s800', 'K11a209', 'K10a8', 'L10a87'],
['t00324', 'K13a4578', 'K12a723', 'L12a896'],
['t00729', 'K13a3026', 'L12a410', 'K12a591'],
['t00787', 'K13a2738', 'L12a872', 'K12a118'],
['t00826', 'K13a2435', 'L12a100', 'K12a652'],
['t00855', 'K13a1915', 'L12a97', 'K12a540'],
['t01033', 'K13a4277', 'L12a1058', 'K12a420'],
['t01037', 'K13a4271', 'L12a530', 'K12a1028'],
['t01125', 'K13a3911', 'K12a649', 'L12a339'],
['t01268', 'K13a1896', 'K12a522', 'L12a221'],
['t01318', 'K12a807', 'L11a257', 'K11a183'],
['t01368', 'K12a358', 'K11a81', 'L11a247'],
['t01422', 'K12a858', 'K11a323', 'L11a196'],
['t01440', 'K13a2587', 'L12a629', 'K12a619'],
['t01636', 'K13a3939', 'K12a729', 'L12a888'],
['t01690', 'K13a2743', 'L12a882', 'K12a95'],
['t01757', 'K13a2915', 'L12a269', 'K12a752'],
['t01834', 'K13a2739', 'K12a62', 'L12a1323'],
['t01863', 'K13a3748', 'K12a520', 'L12a889'],
['t02099', 'K12a821', 'L11a255', 'K11a257'],
['t02104', 'K12a670', 'L11a234', 'K11a121'],
['t02238', 'K13a2380', 'L12a240', 'K12a238'],
['t02378', 'K13a1806', 'K12a247', 'L12a1299'],
['t02398', 'K13a1983', 'L12a239', 'K12a524'],
['t02404', 'K12a415', 'K11a150', 'L11a62'],
['t02470', 'K13a2082', 'K12a112', 'L12a888'],
['t02537', 'K13a2460', 'L12a599', 'K12a445'],
['t02567', 'K13a2737', 'K12a240', 'L12a964'],
['t02639', 'K13a794', 'K12a229', 'L12a256'],
['t03607', 'K13a1605', 'K12a436', 'L12a350'],
['t03713', 'K12a360', 'L11a328', 'K11a11'],
['t03781', 'K13a3991', 'K12a1243', 'L12a289'],
['t03864', 'K12a202', 'K11a215', 'L11a268'],
['t03956', 'K12a919', 'L11a377', 'K11a7'],
['t03979', 'K12a865', 'L11a144', 'K11a183'],
['t04003', 'K12a455', 'K11a158', 'L11a77'],
['t04019', 'K13a4402', 'K12a843', 'L12a646'],
['t04102', 'K12a407', 'L11a239', 'K11a31'],
['t04180', 'K13a2187', 'L12a524', 'K12a511'],
['t04244', 'K13a1016', 'L12a93', 'K12a226'],
['t04382', 'K13a2731', 'L12a90', 'K12a727'],
['t04721', 'K13a4582', 'L12a250', 'K12a1136'],
['t05118', 'K13a1626', 'K12a175', 'L12a702'],
['t05390', 'K12a1268', 'K11a296', 'L11a151'],
['t05425', 'K12a656', 'L11a212', 'K11a117'],
['t05538', 'K12a559', 'L11a148', 'K11a175'],
['t05564', 'K13a2522', 'L12a202', 'K12a684'],
['t05658', 'K12a631', 'K11a167', 'L11a262'],
['t05674', 'K13a1655', 'L12a501', 'K12a749'],
['t05695', 'K13a2869', 'K12a93', 'L12a1029'],
['t06001', 'K13a2963', 'L12a523', 'K12a764'],
['t06440', 'K13a2202', 'L12a497', 'K12a568'],
['t06463', 'K13a1008', 'K12a79', 'L12a516'],
['t06525', 'K12a695', 'K11a80', 'L11a159'],
['t06570', 'K13a2495', 'L12a602', 'K12a194'],
['t06605', 'K13a885', 'L12a342', 'K12a263'],
['t07348', 'K11a233', 'K10a12', 'L10a61'],
['t08111', 'K11a283', 'K10a106', 'L10a60'],
['t08201', 'K11a233', 'L10a84', 'K10a38'],
['t08267', 'K12a209', 'K11a80', 'L11a55'],
['t08403', 'K12a346', 'L11a148', 'K11a85'],
['t09016', 'K12a426', 'K11a52', 'L11a78'],
['t09267', 'K13a1011', 'L12a529', 'K12a577'],
['t09313', 'K13a1035', 'K12a129', 'L12a718'],
['t09455', 'K13a1649', 'K12a355', 'L12a926'],
['t09580', 'K12a637', 'K11a148', 'L11a266'],
['t09704', 'K13a1282', 'K12a271', 'L12a292'],
['t09852', 'K11a289', 'K10a106', 'L10a29'],
['t09954', 'K11a351', 'L10a55', 'K10a87'],
['t10230', 'K11a289', 'K10a97', 'L10a28'],
['t10462', 'K12a588', 'L11a321', 'K11a1'],
['t10643', 'K13a1714', 'L12a363', 'K12a648'],
['t10681', 'K13a1574', 'K12a271', 'L12a709'],
['t10985', 'K13a1963', 'K12a57', 'L12a1286'],
['t11852', 'K11a326', 'K10a45', 'L10a49'],
['v0165', 'K12a1063', 'L11a355', 'K11a62'],
['v0330', 'K12a1176', 'K11a65', 'L11a274'],
['v0398', 'K12a799', 'K11a118', 'L11a94'],
['v0407', 'K12a1060', 'L11a36', 'K11a357'],
['v0434', 'K12a635', 'L11a35', 'K11a204'],
['v0554', 'K12a1235', 'K11a154', 'L11a383'],
['v0570', 'K12a1245', 'K11a340', 'L11a154'],
['v0573', 'K12a1239', 'K11a153', 'L11a296'],
['v0707', 'K11a256', 'K10a101', 'L10a65'],
['v0740', 'K12a781', 'L11a194', 'K11a133'],
['v0759', 'K12a646', 'L11a85', 'K11a207'],
['v0765', 'K12a751', 'L11a43', 'K11a201'],
['v0939', 'K11a255', 'K10a91', 'L10a28'],
['v0945', 'K12a614', 'L11a84', 'K11a94'],
['v1077', 'K12a287', 'L11a160', 'K11a35'],
['v1109', 'K12a470', 'L11a113', 'K11a134'],
['v1392', 'K11a282', 'K10a119', 'L10a90'],
['v1547', 'K11a290', 'L10a80', 'K10a35'],
['v1620', 'K12a1169', 'K11a361', 'L11a75'],
['v1690', 'K11a101', 'L10a106', 'K10a3'],
['v1709', 'K11a73', 'L10a4', 'K10a25'],
['v1716', 'K11a300', 'K10a98', 'L10a25'],
['v1718', 'K12a1182', 'L11a189', 'K11a63'],
['v1728', 'K11a272', 'K10a95', 'L10a57'],
['v1810', 'K12a308', 'K11a22', 'L11a284'],
['v1832', 'K11a136', 'L10a55', 'K10a31'],
['v1839', 'K12a261', 'L11a57', 'K11a96'],
['v1921', 'K12a1048', 'L11a153', 'K11a236'],
['v1980', 'K10a88', 'L9a9', 'K9a12'],
['v1986', 'K12a770', 'L11a26', 'K11a236'],
['v2024', 'K12a766', 'K11a10', 'L11a155'],
['v2090', 'K12a310', 'K11a78', 'L11a157'],
['v2215', 'K11a138', 'K10a39', 'L10a91'],
['v2325', 'K12a608', 'L11a315', 'K11a186'],
['v2759', 'K12a1169', 'K11a260', 'L11a259'],
['v2930', 'K12a1258', 'L11a164', 'K11a356'],
['v3354', 'K12a604', 'L11a39', 'K11a202']]
The following is the code to construct the almost alternating diagrams of the unknot. Together with the function that verify its correctness.
import snappy
def smoothings(link):
'''
Given a link L with a diagram D, this function returns a list of SnaPy link diagrams: For any crossing c in D
we get the orientable smoothing of D together with the original crossing in the PD code marked.
'''
L=snappy.Manifold(link)
PD=L.link().PD_code()
SMOOTHINGS=[]
for cros in PD:
(a,b,c,d)=cros
PDcopy=PD.copy()
PDcopy.remove(cros) #Remove the crossing
PD_new=[]
if b<d:
dic = {d:a, c:b,} #Replace d by a and c by b.
for x in PDcopy:
x=[dic.get(n, n) for n in x]
[v,w,y,z]=x
PD_new.append((v,w,y,z))
if b>d:
dic = {b:a, d:c,} #Replace b by a and c by d.
for x in PDcopy:
x=[dic.get(n, n) for n in x]
[v,w,y,z]=x
PD_new.append((v,w,y,z))
K=snappy.Link(PD_new).exterior()
SMOOTHINGS.append([K,cros])
return SMOOTHINGS
def change_crossing(link,crossing):
'''
Given a SnapPy link with a given diagram D and a crossing marked in its PD code. Then it returns the
SnapPy diagram that we get by changing that crossing together with the new crossing marked.
'''
(a,b,c,d)=crossing
L=snappy.Manifold(link)
PD=L.link().PD_code()
for cros in PD:
if cros==crossing:
PD.remove(cros)
if b<d:
PD.append((b,c,d,a)) #Change the crossing
return [snappy.Link(PD),(b,c,d,a)]
if d<b:
PD.append((d,a,b,c)) #Change the crossing
return [snappy.Link(PD),(d,a,b,c)]
return False
def better_is_isometric_to(X,Y,index):
"""
Returns True if X and Y are isometric.
Returns False if X and Y have different homologies.
The higher the index the harder SnapPy tries.
"""
w='unclear'
if X.homology()!=Y.homology():
w=False
if w=='unclear':
for i in (0,index):
try:
w=X.is_isometric_to(Y)
except RuntimeError:
pass
except snappy.SnapPeaFatalError:
pass
if w==True:
break
if w==False:
w='unclear'
X.randomize()
Y.randomize()
i=i+1
return w
def is_unknot(link,index=100):
'''
Returns True if the given link is the unknot and False if it is not clear or False.
'''
L=link.exterior()
if L.num_cusps()!=1:
return False
RandomizeCount=0
while L.fundamental_group().num_generators()!=1 and RandomizeCount<index:
L.randomize
RandomizeCount=RandomizeCount+1
if L.fundamental_group().num_generators()!=1:
return False
if L.fundamental_group().num_relators()!=0:
return False
return True
def get_tangle_exterior_of_crossing(link,crossing,index=100):
'''
Given a SnapPy link diagram D and a crossing marked in its PD code. Then it returns the
tangle complement of that crossing as a SnapPy manifold.
'''
(a,b,c,d)=crossing
B=link.copy()
PD=B.PD_code()
X=[]
for cros in PD:
X=X+[x for x in cros]
m=max(X) #The maximal value of the PD code.
PD_new=PD.copy()
PD_new.remove(crossing)
#We introduce a circle C around that crossing.
PD_new=PD_new+[(a,m+5,m+1,m+8),(m+5,b,m+6,m+2),(m+6,c,m+7,m+3),(m+4,m+7,d,m+8),(m+1,m+2,m+3,m+4)]
E=snappy.Link(PD_new).exterior() #The exterior of that new link.
for i in range(E.num_cusps()-1):
E.dehn_fill((2,0),i)
#We take the DBC along B. The Conway sphere around the crossing will lift to an torus T.
#The torus T will bound on one side the tangle exterior and on the other side a pair of pants times S1,
#where the other two tori boundary components are given by the lifts of C.
for C in E.covers(2):
if C.cusp_info('filling').count((0,0))==2:
if (2,0) not in C.cusp_info('filling'):
#Next we cut C along T to get the tangle exterior.
#The code looks a bit akward since the SnapPy function .split() is not deterministic.
RandomizeCount=0
while RandomizeCount<index:
try:
for S in C.splitting_surfaces():
for T in C.split(S):
if T.num_cusps()==1:
return T
C.randomize()
RandomizeCount=RandomizeCount+1
except ValueError:
C.randomize()
RandomizeCount=RandomizeCount+1
return False
def has_intervall_of_alternating_surgeries(knot,half,int1,int2,index=100):
'''
Takes a SnapPy Census knot K together with its half-integer alternating
branching set and the nearby integer alternating branching sets and builds the
almost alternating diagram D of the unknot together with its alternation crossing c.
Performing tangle replacement of that crossing gives the interval of alternating surgeries.
The fourth and fifth return values are True, if D is verified to represent an unknot and if
the exterior of the crossing c lifts to the exterior of K.
'''
B1=snappy.Manifold(int1)
B2=snappy.Manifold(int2)
for S in smoothings(half):
if better_is_isometric_to(S[0],B1,index)==True or better_is_isometric_to(S[0],B2,index)==True:
[U,cros]=change_crossing(half,S[1])
w=False
Count=0
while w!=True and Count<index:
T=get_tangle_exterior_of_crossing(U,cros)
w=better_is_isometric_to(T,snappy.Manifold(knot),index)
return [knot,U,cros,is_unknot(U,index),w]
### U will be the almost alternating diagram of the unknot.
import time
start_time = time.time()
PD_CODES_OF_ALMOST_ALTERNATING_DIAGRAMS=[]
for [knot,half,int1,int2] in alternating_surgeries:
RESULT=has_intervall_of_alternating_surgeries(knot,half,int1,int2)
print(RESULT)
PD_CODES_OF_ALMOST_ALTERNATING_DIAGRAMS.append([RESULT[0],RESULT[1].PD_code(),RESULT[2]])
print("--- Time taken: %s seconds ---" % (time.time() - start_time))
['m016', <Link: 1 comp; 8 cross>, (4, 12, 5, 11), True, True] ['m071', <Link: 1 comp; 10 cross>, (6, 15, 7, 16), True, True] ['m103', <Link: 1 comp; 10 cross>, (6, 13, 7, 14), True, True] ['m118', <Link: 1 comp; 9 cross>, (4, 14, 5, 13), True, True] ['m240', <Link: 1 comp; 10 cross>, (16, 1, 17, 2), True, True] ['m270', <Link: 1 comp; 10 cross>, (12, 0, 13, 19), True, True] ['m276', <Link: 1 comp; 10 cross>, (4, 11, 5, 12), True, True] ['o9_00133', <Link: 1 comp; 14 cross>, (6, 19, 7, 20), True, True] ['o9_00168', <Link: 1 comp; 14 cross>, (6, 16, 7, 15), True, True] ['o9_00797', <Link: 1 comp; 14 cross>, (4, 16, 5, 15), True, True] ['o9_00815', <Link: 1 comp; 14 cross>, (4, 17, 5, 18), True, True] ['o9_01680', <Link: 1 comp; 14 cross>, (2, 9, 3, 10), True, True] ['o9_01765', <Link: 1 comp; 14 cross>, (2, 9, 3, 10), True, True] ['o9_02340', <Link: 1 comp; 14 cross>, (16, 21, 17, 22), True, True] ['o9_02386', <Link: 1 comp; 14 cross>, (22, 18, 23, 17), True, True] ['o9_02706', <Link: 1 comp; 14 cross>, (4, 15, 5, 16), True, True] ['o9_02735', <Link: 1 comp; 14 cross>, (4, 18, 5, 17), True, True] ['o9_03118', <Link: 1 comp; 14 cross>, (6, 16, 7, 15), True, True] ['o9_03149', <Link: 1 comp; 14 cross>, (6, 15, 7, 16), True, True] ['o9_03288', <Link: 1 comp; 14 cross>, (14, 2, 15, 1), True, True] ['o9_03412', <Link: 1 comp; 14 cross>, (24, 5, 25, 6), True, True] ['o9_03526', <Link: 1 comp; 14 cross>, (22, 1, 23, 2), True, True] ['o9_03932', <Link: 1 comp; 14 cross>, (18, 0, 19, 27), True, True] ['o9_04313', <Link: 1 comp; 14 cross>, (16, 2, 17, 1), True, True] ['o9_04431', <Link: 1 comp; 14 cross>, (6, 17, 7, 18), True, True] ['o9_04435', <Link: 1 comp; 14 cross>, (6, 17, 7, 18), True, True] ['o9_07943', <Link: 1 comp; 14 cross>, (10, 20, 11, 19), True, True] ['o9_08042', <Link: 1 comp; 14 cross>, (6, 17, 7, 18), True, True] ['o9_08776', <Link: 1 comp; 14 cross>, (6, 11, 7, 12), True, True] ['o9_08852', <Link: 1 comp; 14 cross>, (6, 11, 7, 12), True, True] ['o9_10696', <Link: 1 comp; 14 cross>, (22, 5, 23, 6), True, True] ['o9_11467', <Link: 1 comp; 14 cross>, (16, 6, 17, 5), True, True] ['o9_11560', <Link: 1 comp; 14 cross>, (16, 8, 17, 7), True, True] ['o9_12144', <Link: 1 comp; 14 cross>, (22, 1, 23, 2), True, True] ['o9_12230', <Link: 1 comp; 14 cross>, (18, 0, 19, 27), True, True] ['o9_12736', <Link: 1 comp; 14 cross>, (6, 16, 7, 15), True, True] ['o9_13056', <Link: 1 comp; 14 cross>, (4, 13, 5, 14), True, True] ['o9_13508', <Link: 1 comp; 14 cross>, (16, 0, 17, 27), True, True] ['o9_14018', <Link: 1 comp; 14 cross>, (14, 8, 15, 7), True, True] ['o9_14136', <Link: 1 comp; 14 cross>, (6, 15, 7, 16), True, True] ['s042', <Link: 1 comp; 11 cross>, (6, 15, 7, 16), True, True] ['s068', <Link: 1 comp; 11 cross>, (18, 7, 19, 8), True, True] ['s104', <Link: 1 comp; 11 cross>, (4, 15, 5, 16), True, True] ['s114', <Link: 1 comp; 11 cross>, (16, 5, 17, 6), True, True] ['s344', <Link: 1 comp; 11 cross>, (16, 21, 17, 0), True, True] ['s369', <Link: 1 comp; 11 cross>, (6, 13, 7, 14), True, True] ['s769', <Link: 1 comp; 11 cross>, (6, 11, 7, 12), True, True] ['t00110', <Link: 1 comp; 13 cross>, (6, 14, 7, 13), True, True] ['t00146', <Link: 1 comp; 13 cross>, (6, 17, 7, 18), True, True] ['t00423', <Link: 1 comp; 13 cross>, (4, 17, 5, 18), True, True] ['t00434', <Link: 1 comp; 13 cross>, (4, 16, 5, 15), True, True] ['t00873', <Link: 1 comp; 13 cross>, (16, 23, 17, 24), True, True] ['t00932', <Link: 1 comp; 13 cross>, (22, 16, 23, 15), True, True] ['t01216', <Link: 1 comp; 13 cross>, (20, 25, 21, 0), True, True] ['t01292', <Link: 1 comp; 13 cross>, (14, 19, 15, 20), True, True] ['t01409', <Link: 1 comp; 13 cross>, (4, 16, 5, 15), True, True] ['t01424', <Link: 1 comp; 13 cross>, (4, 13, 5, 14), True, True] ['t01598', <Link: 1 comp; 13 cross>, (6, 15, 7, 16), True, True] ['t01646', <Link: 1 comp; 13 cross>, (6, 16, 7, 15), True, True] ['t01850', <Link: 1 comp; 13 cross>, (4, 20, 5, 19), True, True] ['t01949', <Link: 1 comp; 13 cross>, (14, 4, 15, 3), True, True] ['t03566', <Link: 1 comp; 13 cross>, (4, 15, 5, 16), True, True] ['t03709', <Link: 1 comp; 13 cross>, (22, 5, 23, 6), True, True] ['t04228', <Link: 1 comp; 13 cross>, (4, 11, 5, 12), True, True] ['t05239', <Link: 1 comp; 13 cross>, (16, 25, 17, 0), True, True] ['t05426', <Link: 1 comp; 13 cross>, (14, 6, 15, 5), True, True] ['t05578', <Link: 1 comp; 13 cross>, (12, 21, 13, 22), True, True] ['t05663', <Link: 1 comp; 13 cross>, (4, 16, 5, 15), True, True] ['v0082', <Link: 1 comp; 12 cross>, (6, 17, 7, 18), True, True] ['v0114', <Link: 1 comp; 12 cross>, (6, 14, 7, 13), True, True] ['v0220', <Link: 1 comp; 12 cross>, (18, 5, 19, 6), True, True] ['v0223', <Link: 1 comp; 12 cross>, (18, 7, 19, 8), True, True] ['v0424', <Link: 1 comp; 12 cross>, (2, 9, 3, 10), True, True] ['v0497', <Link: 1 comp; 12 cross>, (14, 21, 15, 22), True, True] ['v0709', <Link: 1 comp; 12 cross>, (18, 3, 19, 4), True, True] ['v0715', <Link: 1 comp; 12 cross>, (4, 13, 5, 14), True, True] ['v0741', <Link: 1 comp; 12 cross>, (4, 16, 5, 15), True, True] ['v0847', <Link: 1 comp; 12 cross>, (4, 15, 5, 16), True, True] ['v0912', <Link: 1 comp; 12 cross>, (14, 2, 15, 1), True, True] ['v1300', <Link: 1 comp; 12 cross>, (10, 18, 11, 17), True, True] ['v1628', <Link: 1 comp; 12 cross>, (4, 13, 5, 14), True, True] ['v1940', <Link: 1 comp; 12 cross>, (4, 11, 5, 12), True, True] ['v1966', <Link: 1 comp; 12 cross>, (6, 11, 7, 12), True, True] ['m082', <Link: 1 comp; 9 cross>, (12, 8, 13, 7), True, True] ['m144', <Link: 1 comp; 10 cross>, (4, 14, 5, 13), True, True] ['m194', <Link: 1 comp; 10 cross>, (0, 5, 1, 6), True, True] ['m198', <Link: 1 comp; 10 cross>, (6, 14, 7, 13), True, True] ['m239', <Link: 1 comp; 9 cross>, (12, 3, 13, 4), True, True] ['m281', <Link: 1 comp; 10 cross>, (4, 16, 5, 15), True, True] ['o9_00644', <Link: 1 comp; 14 cross>, (4, 18, 5, 17), True, True] ['o9_01436', <Link: 1 comp; 14 cross>, (6, 18, 7, 17), True, True] ['o9_01496', <Link: 1 comp; 14 cross>, (6, 13, 7, 14), True, True] ['o9_01584', <Link: 1 comp; 14 cross>, (0, 5, 1, 6), True, True] ['o9_01621', <Link: 1 comp; 14 cross>, (20, 26, 21, 25), True, True] ['o9_01953', <Link: 1 comp; 14 cross>, (20, 2, 21, 1), True, True] ['o9_01955', <Link: 1 comp; 14 cross>, (8, 20, 9, 19), True, True] ['o9_02255', <Link: 1 comp; 14 cross>, (22, 18, 23, 17), True, True] ['o9_02350', <Link: 1 comp; 14 cross>, (20, 15, 21, 16), True, True] ['o9_02655', <Link: 1 comp; 13 cross>, (4, 17, 5, 18), True, True] ['o9_02696', <Link: 1 comp; 13 cross>, (20, 5, 21, 6), True, True] ['o9_02772', <Link: 1 comp; 14 cross>, (8, 21, 9, 22), True, True] ['o9_02786', <Link: 1 comp; 13 cross>, (6, 23, 7, 24), True, True] ['o9_02794', <Link: 1 comp; 14 cross>, (20, 14, 21, 13), True, True] ['o9_03032', <Link: 1 comp; 14 cross>, (8, 19, 9, 20), True, True] ['o9_03108', <Link: 1 comp; 14 cross>, (16, 0, 17, 27), True, True] ['o9_03133', <Link: 1 comp; 14 cross>, (10, 19, 11, 20), True, True] ['o9_03162', <Link: 1 comp; 14 cross>, (6, 21, 7, 22), True, True] ['o9_03188', <Link: 1 comp; 14 cross>, (22, 7, 23, 8), True, True] ['o9_03313', <Link: 1 comp; 14 cross>, (6, 19, 7, 20), True, True] ['o9_03586', <Link: 1 comp; 14 cross>, (6, 20, 7, 19), True, True] ['o9_03622', <Link: 1 comp; 14 cross>, (26, 8, 27, 7), True, True] ['o9_03802', <Link: 1 comp; 14 cross>, (0, 7, 1, 8), True, True] ['o9_03833', <Link: 1 comp; 14 cross>, (26, 6, 27, 5), True, True] ['o9_04106', <Link: 1 comp; 14 cross>, (26, 6, 27, 5), True, True] ['o9_04205', <Link: 1 comp; 14 cross>, (26, 6, 27, 5), True, True] ['o9_04245', <Link: 1 comp; 14 cross>, (26, 15, 27, 16), True, True] ['o9_04269', <Link: 1 comp; 13 cross>, (20, 2, 21, 1), True, True] ['o9_04438', <Link: 1 comp; 14 cross>, (26, 10, 27, 9), True, True] ['o9_05021', <Link: 1 comp; 14 cross>, (10, 17, 11, 18), True, True] ['o9_05177', <Link: 1 comp; 14 cross>, (16, 9, 17, 10), True, True] ['o9_05229', <Link: 1 comp; 14 cross>, (18, 9, 19, 10), True, True] ['o9_05357', <Link: 1 comp; 14 cross>, (26, 10, 27, 9), True, True] ['o9_05426', <Link: 1 comp; 14 cross>, (20, 6, 21, 5), True, True] ['o9_05483', <Link: 1 comp; 14 cross>, (22, 13, 23, 14), True, True] ['o9_05562', <Link: 1 comp; 14 cross>, (18, 26, 19, 25), True, True] ['o9_05618', <Link: 1 comp; 14 cross>, (14, 25, 15, 26), True, True] ['o9_05860', <Link: 1 comp; 14 cross>, (26, 15, 27, 16), True, True] ['o9_05970', <Link: 1 comp; 14 cross>, (6, 17, 7, 18), True, True] ['o9_06060', <Link: 1 comp; 13 cross>, (18, 0, 19, 25), True, True] ['o9_06128', <Link: 1 comp; 14 cross>, (26, 16, 27, 15), True, True] ['o9_06154', <Link: 1 comp; 13 cross>, (12, 6, 13, 5), True, True] ['o9_06248', <Link: 1 comp; 14 cross>, (26, 18, 27, 17), True, True] ['o9_06301', <Link: 1 comp; 14 cross>, (18, 5, 19, 6), True, True] ['o9_07790', <Link: 1 comp; 14 cross>, (16, 7, 17, 8), True, True] ['o9_07893', <Link: 1 comp; 13 cross>, (0, 5, 1, 6), True, True] ['o9_07945', <Link: 1 comp; 13 cross>, (14, 20, 15, 19), True, True] ['o9_08006', <Link: 1 comp; 14 cross>, (6, 18, 7, 17), True, True] ['o9_08224', <Link: 1 comp; 13 cross>, (4, 18, 5, 17), True, True] ['o9_08302', <Link: 1 comp; 13 cross>, (4, 15, 5, 16), True, True] ['o9_08477', <Link: 1 comp; 14 cross>, (0, 5, 1, 6), True, True] ['o9_08647', <Link: 1 comp; 14 cross>, (18, 14, 19, 13), True, True] ['o9_08765', <Link: 1 comp; 13 cross>, (20, 12, 21, 11), True, True] ['o9_08771', <Link: 1 comp; 14 cross>, (14, 20, 15, 19), True, True] ['o9_08828', <Link: 1 comp; 14 cross>, (18, 0, 19, 27), True, True] ['o9_08831', <Link: 1 comp; 13 cross>, (18, 11, 19, 12), True, True] ['o9_08875', <Link: 1 comp; 14 cross>, (4, 19, 5, 20), True, True] ['o9_09213', <Link: 1 comp; 14 cross>, (4, 15, 5, 16), True, True] ['o9_09465', <Link: 1 comp; 14 cross>, (16, 27, 17, 0), True, True] ['o9_09808', <Link: 1 comp; 14 cross>, (10, 23, 11, 24), True, True] ['o9_11248', <Link: 1 comp; 14 cross>, (8, 18, 9, 17), True, True] ['o9_11570', <Link: 1 comp; 14 cross>, (18, 0, 19, 27), True, True] ['o9_11685', <Link: 1 comp; 13 cross>, (4, 20, 5, 19), True, True] ['o9_11795', <Link: 1 comp; 13 cross>, (0, 5, 1, 6), True, True] ['o9_11845', <Link: 1 comp; 13 cross>, (16, 3, 17, 4), True, True] ['o9_11999', <Link: 1 comp; 14 cross>, (22, 18, 23, 17), True, True] ['o9_12412', <Link: 1 comp; 13 cross>, (24, 13, 25, 14), True, True] ['o9_12459', <Link: 1 comp; 13 cross>, (4, 17, 5, 18), True, True] ['o9_12519', <Link: 1 comp; 13 cross>, (4, 18, 5, 17), True, True] ['o9_12693', <Link: 1 comp; 14 cross>, (2, 13, 3, 14), True, True] ['o9_12757', <Link: 1 comp; 14 cross>, (16, 0, 17, 27), True, True] ['o9_12873', <Link: 1 comp; 14 cross>, (4, 20, 5, 19), True, True] ['o9_12892', <Link: 1 comp; 13 cross>, (18, 1, 19, 2), True, True] ['o9_12919', <Link: 1 comp; 13 cross>, (18, 2, 19, 1), True, True] ['o9_12971', <Link: 1 comp; 13 cross>, (20, 14, 21, 13), True, True] ['o9_13052', <Link: 1 comp; 14 cross>, (4, 22, 5, 21), True, True] ['o9_13125', <Link: 1 comp; 13 cross>, (18, 10, 19, 9), True, True] ['o9_13182', <Link: 1 comp; 13 cross>, (12, 20, 13, 19), True, True] ['o9_13188', <Link: 1 comp; 14 cross>, (22, 27, 23, 0), True, True] ['o9_13400', <Link: 1 comp; 14 cross>, (6, 22, 7, 21), True, True] ['o9_13403', <Link: 1 comp; 13 cross>, (10, 21, 11, 22), True, True] ['o9_13433', <Link: 1 comp; 13 cross>, (20, 5, 21, 6), True, True] ['o9_13537', <Link: 1 comp; 13 cross>, (6, 21, 7, 22), True, True] ['o9_13604', <Link: 1 comp; 14 cross>, (8, 27, 9, 0), True, True] ['o9_13639', <Link: 1 comp; 13 cross>, (22, 16, 23, 15), True, True] ['o9_13649', <Link: 1 comp; 13 cross>, (18, 5, 19, 6), True, True] ['o9_13666', <Link: 1 comp; 14 cross>, (0, 7, 1, 8), True, True] ['o9_13720', <Link: 1 comp; 14 cross>, (26, 22, 27, 21), True, True] ['o9_13952', <Link: 1 comp; 14 cross>, (16, 25, 17, 26), True, True] ['o9_14079', <Link: 1 comp; 14 cross>, (4, 15, 5, 16), True, True] ['o9_14364', <Link: 1 comp; 13 cross>, (18, 14, 19, 13), True, True] ['o9_14376', <Link: 1 comp; 14 cross>, (12, 18, 13, 17), True, True] ['o9_14495', <Link: 1 comp; 13 cross>, (24, 20, 25, 19), True, True] ['o9_14599', <Link: 1 comp; 14 cross>, (18, 9, 19, 10), True, True] ['o9_14716', <Link: 1 comp; 14 cross>, (6, 20, 7, 19), True, True] ['o9_14831', <Link: 1 comp; 12 cross>, (2, 8, 3, 7), True, True] ['o9_14974', <Link: 1 comp; 14 cross>, (10, 23, 11, 24), True, True] ['o9_15506', <Link: 1 comp; 13 cross>, (24, 18, 25, 17), True, True] ['o9_15633', <Link: 1 comp; 13 cross>, (8, 23, 9, 24), True, True] ['o9_15997', <Link: 1 comp; 14 cross>, (10, 16, 11, 15), True, True] ['o9_16065', <Link: 1 comp; 14 cross>, (10, 21, 11, 22), True, True] ['o9_16141', <Link: 1 comp; 14 cross>, (26, 8, 27, 7), True, True] ['o9_16157', <Link: 1 comp; 14 cross>, (18, 12, 19, 11), True, True] ['o9_16181', <Link: 1 comp; 14 cross>, (6, 16, 7, 15), True, True] ['o9_16319', <Link: 1 comp; 14 cross>, (16, 27, 17, 0), True, True] ['o9_16356', <Link: 1 comp; 14 cross>, (0, 7, 1, 8), True, True] ['o9_16527', <Link: 1 comp; 14 cross>, (0, 7, 1, 8), True, True] ['o9_16642', <Link: 1 comp; 14 cross>, (26, 6, 27, 5), True, True] ['o9_16748', <Link: 1 comp; 13 cross>, (14, 22, 15, 21), True, True] ['o9_16920', <Link: 1 comp; 12 cross>, (16, 22, 17, 21), True, True] ['o9_17450', <Link: 1 comp; 13 cross>, (24, 8, 25, 7), True, True] ['o9_18007', <Link: 1 comp; 13 cross>, (18, 25, 19, 0), True, True] ['o9_18209', <Link: 1 comp; 14 cross>, (4, 17, 5, 18), True, True] ['o9_18633', <Link: 1 comp; 13 cross>, (22, 17, 23, 18), True, True] ['o9_18813', <Link: 1 comp; 12 cross>, (22, 8, 23, 7), True, True] ['o9_19130', <Link: 1 comp; 12 cross>, (2, 8, 3, 7), True, True] ['o9_20219', <Link: 1 comp; 13 cross>, (0, 5, 1, 6), True, True] ['o9_21893', <Link: 1 comp; 12 cross>, (2, 18, 3, 17), True, True] ['o9_21918', <Link: 1 comp; 12 cross>, (0, 7, 1, 8), True, True] ['o9_22129', <Link: 1 comp; 14 cross>, (0, 7, 1, 8), True, True] ['o9_22477', <Link: 1 comp; 12 cross>, (16, 2, 17, 1), True, True] ['o9_22607', <Link: 1 comp; 14 cross>, (24, 4, 25, 3), True, True] ['o9_22663', <Link: 1 comp; 12 cross>, (12, 17, 13, 18), True, True] ['o9_22698', <Link: 1 comp; 13 cross>, (10, 16, 11, 15), True, True] ['o9_22925', <Link: 1 comp; 12 cross>, (8, 16, 9, 15), True, True] ['o9_23023', <Link: 1 comp; 13 cross>, (6, 14, 7, 13), True, True] ['o9_23263', <Link: 1 comp; 14 cross>, (6, 18, 7, 17), True, True] ['o9_23660', <Link: 1 comp; 14 cross>, (16, 9, 17, 10), True, True] ['o9_23955', <Link: 1 comp; 14 cross>, (2, 14, 3, 13), True, True] ['o9_23961', <Link: 1 comp; 14 cross>, (18, 26, 19, 25), True, True] ['o9_23977', <Link: 1 comp; 13 cross>, (6, 23, 7, 24), True, True] ['o9_24149', <Link: 1 comp; 14 cross>, (22, 4, 23, 3), True, True] ['o9_24183', <Link: 1 comp; 14 cross>, (26, 19, 27, 20), True, True] ['o9_24534', <Link: 1 comp; 14 cross>, (2, 12, 3, 11), True, True] ['o9_24592', <Link: 1 comp; 12 cross>, (14, 0, 15, 23), True, True] ['o9_24886', <Link: 1 comp; 14 cross>, (6, 27, 7, 0), True, True] ['o9_24889', <Link: 1 comp; 14 cross>, (16, 26, 17, 25), True, True] ['o9_25595', <Link: 1 comp; 14 cross>, (0, 7, 1, 8), True, True] ['o9_26604', <Link: 1 comp; 12 cross>, (4, 20, 5, 19), True, True] ['o9_26791', <Link: 1 comp; 13 cross>, (4, 17, 5, 18), True, True] ['o9_27155', <Link: 1 comp; 13 cross>, (20, 12, 21, 11), True, True] ['o9_27261', <Link: 1 comp; 13 cross>, (24, 19, 25, 20), True, True] ['o9_27392', <Link: 1 comp; 14 cross>, (4, 13, 5, 14), True, True] ['o9_27480', <Link: 1 comp; 14 cross>, (4, 15, 5, 16), True, True] ['o9_27737', <Link: 1 comp; 14 cross>, (24, 17, 25, 18), True, True] ['o9_28113', <Link: 1 comp; 14 cross>, (20, 27, 21, 0), True, True] ['o9_28153', <Link: 1 comp; 13 cross>, (18, 7, 19, 8), True, True] ['o9_28529', <Link: 1 comp; 14 cross>, (12, 25, 13, 26), True, True] ['o9_28592', <Link: 1 comp; 14 cross>, (4, 18, 5, 17), True, True] ['o9_28746', <Link: 1 comp; 13 cross>, (4, 20, 5, 19), True, True] ['o9_28810', <Link: 1 comp; 13 cross>, (18, 5, 19, 6), True, True] ['o9_29246', <Link: 1 comp; 14 cross>, (8, 13, 9, 14), True, True] ['o9_29436', <Link: 1 comp; 14 cross>, (26, 8, 27, 7), True, True] ['o9_29529', <Link: 1 comp; 12 cross>, (16, 12, 17, 11), True, True] ['o9_30375', <Link: 1 comp; 13 cross>, (6, 22, 7, 21), True, True] ['o9_30721', <Link: 1 comp; 12 cross>, (18, 14, 19, 13), True, True] ['o9_30790', <Link: 1 comp; 14 cross>, (4, 16, 5, 15), True, True] ['o9_31165', <Link: 1 comp; 14 cross>, (26, 8, 27, 7), True, True] ['o9_32257', <Link: 1 comp; 12 cross>, (4, 19, 5, 20), True, True] ['o9_33526', <Link: 1 comp; 11 cross>, (18, 11, 19, 12), True, True] ['o9_33585', <Link: 1 comp; 12 cross>, (20, 15, 21, 16), True, True] ['o9_34403', <Link: 1 comp; 12 cross>, (0, 5, 1, 6), True, True] ['o9_35320', <Link: 1 comp; 12 cross>, (20, 4, 21, 3), True, True] ['o9_35549', <Link: 1 comp; 14 cross>, (20, 7, 21, 8), True, True] ['o9_35682', <Link: 1 comp; 12 cross>, (0, 5, 1, 6), True, True] ['o9_35736', <Link: 1 comp; 14 cross>, (24, 12, 25, 11), True, True] ['o9_35772', <Link: 1 comp; 12 cross>, (8, 14, 9, 13), True, True] ['o9_37941', <Link: 1 comp; 12 cross>, (0, 5, 1, 6), True, True] ['o9_39394', <Link: 1 comp; 12 cross>, (18, 10, 19, 9), True, True] ['s086', <Link: 1 comp; 11 cross>, (16, 1, 17, 2), True, True] ['s294', <Link: 1 comp; 10 cross>, (16, 4, 17, 3), True, True] ['s301', <Link: 1 comp; 11 cross>, (20, 8, 21, 7), True, True] ['s308', <Link: 1 comp; 11 cross>, (20, 6, 21, 5), True, True] ['s336', <Link: 1 comp; 10 cross>, (6, 17, 7, 18), True, True] ['s346', <Link: 1 comp; 11 cross>, (16, 11, 17, 12), True, True] ['s367', <Link: 1 comp; 11 cross>, (4, 18, 5, 17), True, True] ['s407', <Link: 1 comp; 11 cross>, (18, 6, 19, 5), True, True] ['s582', <Link: 1 comp; 11 cross>, (0, 5, 1, 6), True, True] ['s665', <Link: 1 comp; 11 cross>, (10, 15, 11, 16), True, True] ['s684', <Link: 1 comp; 10 cross>, (10, 15, 11, 16), True, True] ['s800', <Link: 1 comp; 11 cross>, (4, 15, 5, 16), True, True] ['t00324', <Link: 1 comp; 13 cross>, (18, 1, 19, 2), True, True] ['t00729', <Link: 1 comp; 13 cross>, (6, 25, 7, 0), True, True] ['t00787', <Link: 1 comp; 13 cross>, (18, 9, 19, 10), True, True] ['t00826', <Link: 1 comp; 13 cross>, (18, 24, 19, 23), True, True] ['t00855', <Link: 1 comp; 13 cross>, (16, 21, 17, 22), True, True] ['t01033', <Link: 1 comp; 13 cross>, (24, 10, 25, 9), True, True] ['t01037', <Link: 1 comp; 13 cross>, (24, 8, 25, 7), True, True] ['t01125', <Link: 1 comp; 13 cross>, (20, 15, 21, 16), True, True] ['t01268', <Link: 1 comp; 13 cross>, (20, 16, 21, 15), True, True] ['t01318', <Link: 1 comp; 12 cross>, (18, 4, 19, 3), True, True] ['t01368', <Link: 1 comp; 12 cross>, (4, 15, 5, 16), True, True] ['t01422', <Link: 1 comp; 12 cross>, (6, 21, 7, 22), True, True] ['t01440', <Link: 1 comp; 13 cross>, (4, 22, 5, 21), True, True] ['t01636', <Link: 1 comp; 13 cross>, (16, 2, 17, 1), True, True] ['t01690', <Link: 1 comp; 13 cross>, (6, 19, 7, 20), True, True] ['t01757', <Link: 1 comp; 13 cross>, (24, 6, 25, 5), True, True] ['t01834', <Link: 1 comp; 13 cross>, (6, 18, 7, 17), True, True] ['t01863', <Link: 1 comp; 13 cross>, (4, 19, 5, 20), True, True] ['t02099', <Link: 1 comp; 12 cross>, (16, 1, 17, 2), True, True] ['t02104', <Link: 1 comp; 12 cross>, (8, 17, 9, 18), True, True] ['t02238', <Link: 1 comp; 13 cross>, (6, 25, 7, 0), True, True] ['t02378', <Link: 1 comp; 13 cross>, (18, 5, 19, 6), True, True] ['t02398', <Link: 1 comp; 13 cross>, (24, 16, 25, 15), True, True] ['t02404', <Link: 1 comp; 12 cross>, (18, 0, 19, 23), True, True] ['t02470', <Link: 1 comp; 13 cross>, (24, 13, 25, 14), True, True] ['t02537', <Link: 1 comp; 13 cross>, (24, 17, 25, 18), True, True] ['t02567', <Link: 1 comp; 13 cross>, (20, 6, 21, 5), True, True] ['t02639', <Link: 1 comp; 13 cross>, (24, 18, 25, 17), True, True] ['t03607', <Link: 1 comp; 13 cross>, (12, 18, 13, 17), True, True] ['t03713', <Link: 1 comp; 12 cross>, (18, 5, 19, 6), True, True] ['t03781', <Link: 1 comp; 13 cross>, (0, 5, 1, 6), True, True] ['t03864', <Link: 1 comp; 12 cross>, (18, 7, 19, 8), True, True] ['t03956', <Link: 1 comp; 12 cross>, (6, 18, 7, 17), True, True] ['t03979', <Link: 1 comp; 12 cross>, (10, 4, 11, 3), True, True] ['t04003', <Link: 1 comp; 12 cross>, (22, 6, 23, 5), True, True] ['t04019', <Link: 1 comp; 13 cross>, (16, 10, 17, 9), True, True] ['t04102', <Link: 1 comp; 12 cross>, (22, 8, 23, 7), True, True] ['t04180', <Link: 1 comp; 13 cross>, (18, 25, 19, 0), True, True] ['t04244', <Link: 1 comp; 13 cross>, (20, 25, 21, 0), True, True] ['t04382', <Link: 1 comp; 13 cross>, (16, 22, 17, 21), True, True] ['t04721', <Link: 1 comp; 13 cross>, (0, 5, 1, 6), True, True] ['t05118', <Link: 1 comp; 13 cross>, (14, 0, 15, 25), True, True] ['t05390', <Link: 1 comp; 12 cross>, (0, 7, 1, 8), True, True] ['t05425', <Link: 1 comp; 12 cross>, (12, 20, 13, 19), True, True] ['t05538', <Link: 1 comp; 12 cross>, (16, 23, 17, 0), True, True] ['t05564', <Link: 1 comp; 13 cross>, (20, 25, 21, 0), True, True] ['t05658', <Link: 1 comp; 12 cross>, (8, 20, 9, 19), True, True] ['t05674', <Link: 1 comp; 13 cross>, (8, 15, 9, 16), True, True] ['t05695', <Link: 1 comp; 13 cross>, (4, 17, 5, 18), True, True] ['t06001', <Link: 1 comp; 13 cross>, (18, 0, 19, 25), True, True] ['t06440', <Link: 1 comp; 13 cross>, (24, 18, 25, 17), True, True] ['t06463', <Link: 1 comp; 13 cross>, (14, 25, 15, 0), True, True] ['t06525', <Link: 1 comp; 12 cross>, (8, 15, 9, 16), True, True] ['t06570', <Link: 1 comp; 13 cross>, (24, 17, 25, 18), True, True] ['t06605', <Link: 1 comp; 13 cross>, (12, 20, 13, 19), True, True] ['t07348', <Link: 1 comp; 11 cross>, (14, 8, 15, 7), True, True] ['t08111', <Link: 1 comp; 11 cross>, (20, 8, 21, 7), True, True] ['t08201', <Link: 1 comp; 11 cross>, (6, 19, 7, 20), True, True] ['t08267', <Link: 1 comp; 12 cross>, (12, 17, 13, 18), True, True] ['t08403', <Link: 1 comp; 12 cross>, (10, 17, 11, 18), True, True] ['t09016', <Link: 1 comp; 12 cross>, (22, 6, 23, 5), True, True] ['t09267', <Link: 1 comp; 13 cross>, (22, 6, 23, 5), True, True] ['t09313', <Link: 1 comp; 13 cross>, (10, 24, 11, 23), True, True] ['t09455', <Link: 1 comp; 13 cross>, (22, 8, 23, 7), True, True] ['t09580', <Link: 1 comp; 12 cross>, (4, 18, 5, 17), True, True] ['t09704', <Link: 1 comp; 13 cross>, (24, 18, 25, 17), True, True] ['t09852', <Link: 1 comp; 11 cross>, (0, 5, 1, 6), True, True] ['t09954', <Link: 1 comp; 11 cross>, (2, 17, 3, 18), True, True] ['t10230', <Link: 1 comp; 11 cross>, (12, 8, 13, 7), True, True] ['t10462', <Link: 1 comp; 12 cross>, (4, 15, 5, 16), True, True] ['t10643', <Link: 1 comp; 13 cross>, (8, 13, 9, 14), True, True] ['t10681', <Link: 1 comp; 13 cross>, (22, 12, 23, 11), True, True] ['t10985', <Link: 1 comp; 13 cross>, (10, 23, 11, 24), True, True] ['t11852', <Link: 1 comp; 11 cross>, (20, 16, 21, 15), True, True] ['v0165', <Link: 1 comp; 12 cross>, (4, 16, 5, 15), True, True] ['v0330', <Link: 1 comp; 12 cross>, (6, 16, 7, 15), True, True] ['v0398', <Link: 1 comp; 12 cross>, (6, 23, 7, 0), True, True] ['v0407', <Link: 1 comp; 12 cross>, (0, 5, 1, 6), True, True] ['v0434', <Link: 1 comp; 12 cross>, (16, 22, 17, 21), True, True] ['v0554', <Link: 1 comp; 12 cross>, (8, 19, 9, 20), True, True] ['v0570', <Link: 1 comp; 12 cross>, (18, 2, 19, 1), True, True] ['v0573', <Link: 1 comp; 12 cross>, (8, 18, 9, 17), True, True] ['v0707', <Link: 1 comp; 11 cross>, (6, 19, 7, 20), True, True] ['v0740', <Link: 1 comp; 12 cross>, (18, 12, 19, 11), True, True] ['v0759', <Link: 1 comp; 12 cross>, (8, 15, 9, 16), True, True] ['v0765', <Link: 1 comp; 12 cross>, (22, 6, 23, 5), True, True] ['v0939', <Link: 1 comp; 11 cross>, (18, 2, 19, 1), True, True] ['v0945', <Link: 1 comp; 12 cross>, (22, 13, 23, 14), True, True] ['v1077', <Link: 1 comp; 12 cross>, (22, 8, 23, 7), True, True] ['v1109', <Link: 1 comp; 12 cross>, (22, 15, 23, 16), True, True] ['v1392', <Link: 1 comp; 11 cross>, (4, 16, 5, 15), True, True] ['v1547', <Link: 1 comp; 11 cross>, (18, 12, 19, 11), True, True] ['v1620', <Link: 1 comp; 12 cross>, (0, 5, 1, 6), True, True] ['v1690', <Link: 1 comp; 11 cross>, (16, 5, 17, 6), True, True] ['v1709', <Link: 1 comp; 11 cross>, (12, 18, 13, 17), True, True] ['v1716', <Link: 1 comp; 11 cross>, (16, 11, 17, 12), True, True] ['v1718', <Link: 1 comp; 12 cross>, (14, 7, 15, 8), True, True] ['v1728', <Link: 1 comp; 11 cross>, (16, 2, 17, 1), True, True] ['v1810', <Link: 1 comp; 12 cross>, (4, 13, 5, 14), True, True] ['v1832', <Link: 1 comp; 11 cross>, (18, 12, 19, 11), True, True] ['v1839', <Link: 1 comp; 12 cross>, (12, 18, 13, 17), True, True] ['v1921', <Link: 1 comp; 12 cross>, (16, 0, 17, 23), True, True] ['v1980', <Link: 1 comp; 10 cross>, (0, 5, 1, 6), True, True] ['v1986', <Link: 1 comp; 12 cross>, (18, 23, 19, 0), True, True] ['v2024', <Link: 1 comp; 12 cross>, (8, 23, 9, 0), True, True] ['v2090', <Link: 1 comp; 12 cross>, (14, 23, 15, 0), True, True] ['v2215', <Link: 1 comp; 11 cross>, (4, 16, 5, 15), True, True] ['v2325', <Link: 1 comp; 12 cross>, (14, 0, 15, 23), True, True] ['v2759', <Link: 1 comp; 12 cross>, (6, 16, 7, 15), True, True] ['v2930', <Link: 1 comp; 12 cross>, (20, 4, 21, 3), True, True] ['v3354', <Link: 1 comp; 12 cross>, (16, 23, 17, 0), True, True] --- Time taken: 43.48233938217163 seconds ---
len(PD_CODES_OF_ALMOST_ALTERNATING_DIAGRAMS)
381
PD_CODES_OF_ALMOST_ALTERNATING_DIAGRAMS
[['m016', [(5, 1, 6, 0), (1, 12, 2, 13), (7, 2, 8, 3), (3, 8, 4, 9), (13, 7, 14, 6), (9, 15, 10, 14), (15, 11, 0, 10), (4, 12, 5, 11)], (4, 12, 5, 11)], ['m071', [(5, 1, 6, 0), (1, 14, 2, 15), (7, 2, 8, 3), (3, 8, 4, 9), (13, 4, 14, 5), (9, 17, 10, 16), (17, 11, 18, 10), (11, 19, 12, 18), (19, 13, 0, 12), (6, 15, 7, 16)], (6, 15, 7, 16)], ['m103', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (15, 4, 16, 5), (5, 18, 6, 19), (7, 11, 8, 10), (11, 17, 12, 16), (17, 13, 18, 12), (19, 14, 0, 15), (6, 13, 7, 14)], (6, 13, 7, 14)], ['m118', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (5, 16, 6, 17), (11, 7, 12, 6), (9, 15, 10, 14), (15, 11, 16, 10), (17, 12, 0, 13), (4, 14, 5, 13)], (4, 14, 5, 13)], ['m240', [(5, 1, 6, 0), (9, 2, 10, 3), (3, 12, 4, 13), (19, 5, 0, 4), (13, 6, 14, 7), (7, 14, 8, 15), (15, 8, 16, 9), (17, 11, 18, 10), (11, 19, 12, 18), (16, 1, 17, 2)], (16, 1, 17, 2)], ['m270', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (13, 4, 14, 5), (5, 18, 6, 19), (17, 6, 18, 7), (7, 14, 8, 15), (15, 10, 16, 11), (11, 16, 12, 17), (12, 0, 13, 19)], (12, 0, 13, 19)], ['m276', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (5, 18, 6, 19), (13, 6, 14, 7), (9, 17, 10, 16), (15, 11, 16, 10), (19, 13, 0, 12), (17, 14, 18, 15), (4, 11, 5, 12)], (4, 11, 5, 12)], ['o9_00133', [(5, 1, 6, 0), (1, 18, 2, 19), (7, 2, 8, 3), (3, 8, 4, 9), (17, 4, 18, 5), (9, 21, 10, 20), (21, 11, 22, 10), (11, 27, 12, 26), (25, 13, 26, 12), (13, 25, 14, 24), (23, 15, 24, 14), (15, 23, 16, 22), (27, 17, 0, 16), (6, 19, 7, 20)], (6, 19, 7, 20)], ['o9_00168', [(5, 1, 6, 0), (1, 17, 2, 16), (7, 2, 8, 3), (3, 8, 4, 9), (17, 5, 18, 4), (9, 24, 10, 25), (23, 10, 24, 11), (11, 22, 12, 23), (21, 12, 22, 13), (13, 20, 14, 21), (25, 14, 26, 15), (27, 18, 0, 19), (19, 26, 20, 27), (6, 16, 7, 15)], (6, 16, 7, 15)], ['o9_00797', [(5, 1, 6, 0), (1, 16, 2, 17), (7, 2, 8, 3), (3, 8, 4, 9), (17, 7, 18, 6), (9, 25, 10, 24), (23, 11, 24, 10), (11, 23, 12, 22), (21, 13, 22, 12), (13, 19, 14, 18), (27, 15, 0, 14), (19, 26, 20, 27), (25, 20, 26, 21), (4, 16, 5, 15)], (4, 16, 5, 15)], ['o9_00815', [(5, 1, 6, 0), (1, 17, 2, 16), (7, 2, 8, 3), (3, 8, 4, 9), (15, 6, 16, 7), (9, 27, 10, 26), (19, 11, 20, 10), (11, 24, 12, 25), (23, 12, 24, 13), (13, 22, 14, 23), (21, 14, 22, 15), (27, 18, 0, 19), (25, 21, 26, 20), (4, 17, 5, 18)], (4, 17, 5, 18)], ['o9_01680', [(5, 1, 6, 0), (1, 7, 2, 6), (3, 17, 4, 16), (19, 5, 20, 4), (7, 19, 8, 18), (17, 9, 18, 8), (21, 10, 22, 11), (11, 22, 12, 23), (23, 12, 24, 13), (13, 26, 14, 27), (25, 14, 26, 15), (15, 24, 16, 25), (27, 20, 0, 21), (2, 9, 3, 10)], (2, 9, 3, 10)], ['o9_01765', [(5, 1, 6, 0), (1, 7, 2, 6), (3, 18, 4, 19), (15, 4, 16, 5), (7, 16, 8, 17), (17, 8, 18, 9), (19, 11, 20, 10), (11, 25, 12, 24), (23, 13, 24, 12), (13, 23, 14, 22), (25, 15, 26, 14), (27, 21, 0, 20), (21, 27, 22, 26), (2, 9, 3, 10)], (2, 9, 3, 10)], ['o9_02340', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (15, 4, 16, 5), (5, 22, 6, 23), (17, 7, 18, 6), (7, 19, 8, 18), (23, 8, 24, 9), (9, 26, 10, 27), (13, 11, 14, 10), (27, 14, 0, 15), (19, 25, 20, 24), (25, 21, 26, 20), (16, 21, 17, 22)], (16, 21, 17, 22)], ['o9_02386', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (13, 5, 14, 4), (5, 24, 6, 25), (19, 7, 20, 6), (7, 19, 8, 18), (23, 8, 24, 9), (9, 16, 10, 17), (15, 10, 16, 11), (27, 15, 0, 14), (25, 20, 26, 21), (21, 26, 22, 27), (22, 18, 23, 17)], (22, 18, 23, 17)], ['o9_02706', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (5, 26, 6, 27), (17, 6, 18, 7), (9, 25, 10, 24), (19, 11, 20, 10), (11, 23, 12, 22), (21, 13, 22, 12), (13, 21, 14, 20), (23, 15, 24, 14), (27, 17, 0, 16), (25, 18, 26, 19), (4, 15, 5, 16)], (4, 15, 5, 16)], ['o9_02735', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (5, 26, 6, 27), (15, 7, 16, 6), (9, 25, 10, 24), (19, 10, 20, 11), (11, 22, 12, 23), (21, 12, 22, 13), (13, 20, 14, 21), (25, 15, 26, 14), (27, 16, 0, 17), (23, 18, 24, 19), (4, 18, 5, 17)], (4, 18, 5, 17)], ['o9_03118', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (13, 5, 14, 4), (5, 26, 6, 27), (9, 23, 10, 22), (21, 11, 22, 10), (11, 19, 12, 18), (17, 13, 18, 12), (27, 15, 0, 14), (25, 16, 26, 17), (19, 24, 20, 25), (23, 20, 24, 21), (6, 16, 7, 15)], (6, 16, 7, 15)], ['o9_03149', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (17, 4, 18, 5), (5, 26, 6, 27), (9, 25, 10, 24), (19, 11, 20, 10), (11, 22, 12, 23), (21, 12, 22, 13), (13, 19, 14, 18), (25, 15, 26, 14), (27, 16, 0, 17), (23, 21, 24, 20), (6, 15, 7, 16)], (6, 15, 7, 16)], ['o9_03288', [(5, 1, 6, 0), (9, 2, 10, 3), (3, 19, 4, 18), (27, 5, 0, 4), (17, 7, 18, 6), (7, 17, 8, 16), (15, 9, 16, 8), (21, 10, 22, 11), (11, 22, 12, 23), (23, 12, 24, 13), (13, 24, 14, 25), (19, 26, 20, 27), (25, 20, 26, 21), (14, 2, 15, 1)], (14, 2, 15, 1)], ['o9_03412', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (15, 5, 16, 4), (17, 6, 18, 7), (7, 18, 8, 19), (19, 8, 20, 9), (9, 22, 10, 23), (27, 11, 0, 10), (11, 15, 12, 14), (23, 16, 24, 17), (25, 21, 26, 20), (21, 27, 22, 26), (24, 5, 25, 6)], (24, 5, 25, 6)], ['o9_03526', [(5, 1, 6, 0), (11, 2, 12, 3), (3, 16, 4, 17), (27, 5, 0, 4), (17, 6, 18, 7), (7, 18, 8, 19), (19, 8, 20, 9), (9, 20, 10, 21), (21, 10, 22, 11), (23, 13, 24, 12), (13, 25, 14, 24), (25, 15, 26, 14), (15, 27, 16, 26), (22, 1, 23, 2)], (22, 1, 23, 2)], ['o9_03932', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (19, 4, 20, 5), (5, 26, 6, 27), (25, 6, 26, 7), (7, 24, 8, 25), (23, 8, 24, 9), (9, 20, 10, 21), (15, 11, 16, 10), (11, 15, 12, 14), (21, 16, 22, 17), (17, 22, 18, 23), (18, 0, 19, 27)], (18, 0, 19, 27)], ['o9_04313', [(5, 1, 6, 0), (9, 2, 10, 3), (3, 19, 4, 18), (25, 5, 26, 4), (27, 7, 0, 6), (7, 27, 8, 26), (17, 9, 18, 8), (19, 10, 20, 11), (11, 24, 12, 25), (21, 12, 22, 13), (13, 22, 14, 23), (23, 14, 24, 15), (15, 20, 16, 21), (16, 2, 17, 1)], (16, 2, 17, 1)], ['o9_04431', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (19, 4, 20, 5), (5, 24, 6, 25), (7, 13, 8, 12), (27, 10, 0, 11), (11, 26, 12, 27), (13, 23, 14, 22), (21, 15, 22, 14), (15, 21, 16, 20), (23, 17, 24, 16), (25, 18, 26, 19), (6, 17, 7, 18)], (6, 17, 7, 18)], ['o9_04435', [(5, 1, 6, 0), (1, 12, 2, 13), (11, 2, 12, 3), (3, 10, 4, 11), (9, 4, 10, 5), (7, 26, 8, 27), (19, 8, 20, 9), (13, 25, 14, 24), (23, 15, 24, 14), (15, 23, 16, 22), (21, 17, 22, 16), (27, 19, 0, 18), (25, 20, 26, 21), (6, 17, 7, 18)], (6, 17, 7, 18)], ['o9_07943', [(7, 1, 8, 0), (1, 9, 2, 8), (9, 3, 10, 2), (3, 21, 4, 20), (11, 4, 12, 5), (5, 12, 6, 13), (21, 7, 22, 6), (13, 22, 14, 23), (23, 14, 24, 15), (15, 26, 16, 27), (25, 16, 26, 17), (17, 24, 18, 25), (27, 18, 0, 19), (10, 20, 11, 19)], (10, 20, 11, 19)], ['o9_08042', [(5, 1, 6, 0), (1, 13, 2, 12), (11, 3, 12, 2), (3, 11, 4, 10), (13, 5, 14, 4), (7, 24, 8, 25), (21, 8, 22, 9), (9, 15, 10, 14), (15, 22, 16, 23), (23, 16, 24, 17), (25, 19, 26, 18), (19, 27, 20, 26), (27, 21, 0, 20), (6, 17, 7, 18)], (6, 17, 7, 18)], ['o9_08776', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (17, 4, 18, 5), (5, 20, 6, 21), (9, 19, 10, 18), (19, 11, 20, 10), (21, 12, 22, 13), (13, 27, 14, 26), (23, 15, 24, 14), (15, 25, 16, 24), (25, 17, 26, 16), (27, 22, 0, 23), (6, 11, 7, 12)], (6, 11, 7, 12)], ['o9_08852', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (19, 5, 20, 4), (5, 17, 6, 16), (9, 18, 10, 19), (17, 10, 18, 11), (21, 13, 22, 12), (13, 27, 14, 26), (23, 14, 24, 15), (15, 24, 16, 25), (27, 21, 0, 20), (25, 22, 26, 23), (6, 11, 7, 12)], (6, 11, 7, 12)], ['o9_10696', [(7, 1, 8, 0), (1, 9, 2, 8), (9, 3, 10, 2), (3, 18, 4, 19), (13, 4, 14, 5), (27, 7, 0, 6), (19, 11, 20, 10), (11, 21, 12, 20), (21, 13, 22, 12), (23, 14, 24, 15), (15, 24, 16, 25), (25, 16, 26, 17), (17, 26, 18, 27), (22, 5, 23, 6)], (22, 5, 23, 6)], ['o9_11467', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (13, 4, 14, 5), (19, 6, 20, 7), (7, 22, 8, 23), (11, 9, 12, 8), (27, 12, 0, 13), (21, 14, 22, 15), (15, 20, 16, 21), (17, 25, 18, 24), (25, 19, 26, 18), (23, 27, 24, 26), (16, 6, 17, 5)], (16, 6, 17, 5)], ['o9_11560', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (11, 5, 12, 4), (5, 22, 6, 23), (19, 6, 20, 7), (13, 8, 14, 9), (27, 13, 0, 12), (21, 15, 22, 14), (15, 21, 16, 20), (17, 24, 18, 25), (25, 18, 26, 19), (23, 26, 24, 27), (16, 8, 17, 7)], (16, 8, 17, 7)], ['o9_12144', [(5, 1, 6, 0), (13, 2, 14, 3), (3, 16, 4, 17), (25, 5, 26, 4), (27, 7, 0, 6), (7, 27, 8, 26), (17, 8, 18, 9), (9, 20, 10, 21), (19, 10, 20, 11), (11, 18, 12, 19), (21, 12, 22, 13), (23, 15, 24, 14), (15, 25, 16, 24), (22, 1, 23, 2)], (22, 1, 23, 2)], ['o9_12230', [(5, 1, 6, 0), (1, 13, 2, 12), (11, 3, 12, 2), (3, 11, 4, 10), (13, 5, 14, 4), (19, 6, 20, 7), (7, 26, 8, 27), (25, 8, 26, 9), (9, 20, 10, 21), (21, 14, 22, 15), (15, 24, 16, 25), (23, 16, 24, 17), (17, 22, 18, 23), (18, 0, 19, 27)], (18, 0, 19, 27)], ['o9_12736', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (11, 5, 12, 4), (5, 24, 6, 25), (9, 21, 10, 20), (19, 11, 20, 10), (27, 13, 0, 12), (13, 27, 14, 26), (25, 15, 26, 14), (23, 16, 24, 17), (17, 22, 18, 23), (21, 18, 22, 19), (6, 16, 7, 15)], (6, 16, 7, 15)], ['o9_13056', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (5, 24, 6, 25), (17, 6, 18, 7), (9, 18, 10, 19), (19, 10, 20, 11), (11, 23, 12, 22), (21, 13, 22, 12), (25, 15, 26, 14), (15, 27, 16, 26), (27, 17, 0, 16), (23, 20, 24, 21), (4, 13, 5, 14)], (4, 13, 5, 14)], ['o9_13508', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (17, 4, 18, 5), (5, 26, 6, 27), (25, 6, 26, 7), (7, 18, 8, 19), (11, 9, 12, 8), (21, 13, 22, 12), (13, 23, 14, 22), (23, 15, 24, 14), (15, 21, 16, 20), (19, 24, 20, 25), (16, 0, 17, 27)], (16, 0, 17, 27)], ['o9_14018', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (11, 4, 12, 5), (5, 20, 6, 21), (17, 6, 18, 7), (27, 10, 0, 11), (19, 13, 20, 12), (13, 19, 14, 18), (15, 25, 16, 24), (23, 17, 24, 16), (21, 26, 22, 27), (25, 22, 26, 23), (14, 8, 15, 7)], (14, 8, 15, 7)], ['o9_14136', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (19, 4, 20, 5), (5, 24, 6, 25), (7, 11, 8, 10), (11, 21, 12, 20), (21, 13, 22, 12), (13, 23, 14, 22), (23, 15, 24, 14), (25, 16, 26, 17), (17, 26, 18, 27), (27, 18, 0, 19), (6, 15, 7, 16)], (6, 15, 7, 16)], ['s042', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (17, 4, 18, 5), (5, 20, 6, 21), (7, 13, 8, 12), (11, 9, 12, 8), (13, 19, 14, 18), (19, 15, 20, 14), (21, 16, 0, 17), (6, 15, 7, 16)], (6, 15, 7, 16)], ['s068', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (11, 5, 12, 4), (5, 16, 6, 17), (13, 6, 14, 7), (21, 9, 0, 8), (17, 13, 18, 12), (19, 14, 20, 15), (15, 20, 16, 21), (18, 7, 19, 8)], (18, 7, 19, 8)], ['s104', [(5, 1, 6, 0), (1, 15, 2, 14), (7, 2, 8, 3), (3, 8, 4, 9), (13, 6, 14, 7), (9, 21, 10, 20), (17, 11, 18, 10), (11, 19, 12, 18), (19, 13, 20, 12), (21, 16, 0, 17), (4, 15, 5, 16)], (4, 15, 5, 16)], ['s114', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (11, 4, 12, 5), (13, 7, 14, 6), (7, 18, 8, 19), (21, 10, 0, 11), (17, 12, 18, 13), (19, 15, 20, 14), (15, 21, 16, 20), (16, 5, 17, 6)], (16, 5, 17, 6)], ['s344', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (15, 5, 16, 4), (5, 20, 6, 21), (19, 6, 20, 7), (7, 15, 8, 14), (11, 9, 12, 8), (17, 13, 18, 12), (13, 19, 14, 18), (16, 21, 17, 0)], (16, 21, 17, 0)], ['s369', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (15, 4, 16, 5), (5, 20, 6, 21), (9, 19, 10, 18), (17, 11, 18, 10), (11, 17, 12, 16), (19, 13, 20, 12), (21, 14, 0, 15), (6, 13, 7, 14)], (6, 13, 7, 14)], ['s769', [(3, 1, 4, 0), (1, 8, 2, 9), (7, 2, 8, 3), (17, 5, 18, 4), (5, 15, 6, 14), (9, 16, 10, 17), (15, 10, 16, 11), (19, 13, 20, 12), (13, 21, 14, 20), (21, 19, 0, 18), (6, 11, 7, 12)], (6, 11, 7, 12)], ['t00110', [(5, 1, 6, 0), (1, 15, 2, 14), (7, 2, 8, 3), (3, 8, 4, 9), (15, 5, 16, 4), (9, 23, 10, 22), (21, 11, 22, 10), (11, 21, 12, 20), (19, 13, 20, 12), (25, 16, 0, 17), (17, 24, 18, 25), (23, 18, 24, 19), (6, 14, 7, 13)], (6, 14, 7, 13)], ['t00146', [(5, 1, 6, 0), (1, 16, 2, 17), (7, 2, 8, 3), (3, 8, 4, 9), (15, 4, 16, 5), (9, 19, 10, 18), (19, 11, 20, 10), (11, 24, 12, 25), (23, 12, 24, 13), (13, 22, 14, 23), (21, 14, 22, 15), (25, 21, 0, 20), (6, 17, 7, 18)], (6, 17, 7, 18)], ['t00423', [(5, 1, 6, 0), (1, 17, 2, 16), (7, 2, 8, 3), (3, 8, 4, 9), (15, 6, 16, 7), (9, 25, 10, 24), (19, 11, 20, 10), (11, 23, 12, 22), (21, 13, 22, 12), (13, 21, 14, 20), (23, 15, 24, 14), (25, 18, 0, 19), (4, 17, 5, 18)], (4, 17, 5, 18)], ['t00434', [(5, 1, 6, 0), (1, 16, 2, 17), (7, 2, 8, 3), (3, 8, 4, 9), (17, 7, 18, 6), (9, 25, 10, 24), (19, 10, 20, 11), (11, 22, 12, 23), (21, 12, 22, 13), (13, 20, 14, 21), (25, 15, 0, 14), (23, 18, 24, 19), (4, 16, 5, 15)], (4, 16, 5, 15)], ['t00873', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (15, 5, 16, 4), (5, 22, 6, 23), (17, 6, 18, 7), (7, 18, 8, 19), (21, 8, 22, 9), (9, 15, 10, 14), (13, 11, 14, 10), (19, 25, 20, 24), (25, 21, 0, 20), (16, 23, 17, 24)], (16, 23, 17, 24)], ['t00932', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (13, 5, 14, 4), (5, 20, 6, 21), (17, 6, 18, 7), (7, 16, 8, 17), (21, 8, 22, 9), (9, 15, 10, 14), (25, 11, 0, 10), (23, 18, 24, 19), (19, 24, 20, 25), (22, 16, 23, 15)], (22, 16, 23, 15)], ['t01216', [(5, 1, 6, 0), (1, 14, 2, 15), (11, 2, 12, 3), (3, 12, 4, 13), (13, 4, 14, 5), (19, 7, 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14, 2, 15), (13, 2, 14, 3), (5, 24, 6, 25), (23, 6, 24, 7), (7, 17, 8, 16), (15, 9, 16, 8), (9, 22, 10, 23), (21, 10, 22, 11), (11, 20, 12, 21), (19, 12, 20, 13), (25, 19, 0, 18), (4, 17, 5, 18)], (4, 17, 5, 18)], ['t06001', [(3, 1, 4, 0), (1, 14, 2, 15), (13, 2, 14, 3), (19, 4, 20, 5), (5, 24, 6, 25), (23, 6, 24, 7), (7, 22, 8, 23), (17, 9, 18, 8), (9, 17, 10, 16), (21, 10, 22, 11), (11, 20, 12, 21), (15, 13, 16, 12), (18, 0, 19, 25)], (18, 0, 19, 25)], ['t06440', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (15, 5, 16, 4), (5, 17, 6, 16), (25, 7, 0, 6), (7, 20, 8, 21), (19, 8, 20, 9), (9, 18, 10, 19), (21, 10, 22, 11), (13, 22, 14, 23), (23, 14, 24, 15), (24, 18, 25, 17)], (24, 18, 25, 17)], ['t06463', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (13, 5, 14, 4), (5, 24, 6, 25), (17, 7, 18, 6), (7, 19, 8, 18), (15, 8, 16, 9), (11, 23, 12, 22), (21, 13, 22, 12), (19, 17, 20, 16), (23, 20, 24, 21), (14, 25, 15, 0)], (14, 25, 15, 0)], ['t06525', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (9, 4, 10, 5), (5, 20, 6, 21), (17, 6, 18, 7), (7, 23, 8, 22), (19, 11, 20, 10), (11, 19, 12, 18), (23, 14, 0, 15), (21, 17, 22, 16), (8, 15, 9, 16)], (8, 15, 9, 16)], ['t06570', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (19, 4, 20, 5), (5, 20, 6, 21), (21, 6, 22, 7), (7, 18, 8, 19), (25, 9, 0, 8), (9, 17, 10, 16), (15, 11, 16, 10), (13, 23, 14, 22), (23, 15, 24, 14), (24, 17, 25, 18)], (24, 17, 25, 18)], ['t06605', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (11, 5, 12, 4), (5, 22, 6, 23), (21, 6, 22, 7), (7, 16, 8, 17), (15, 8, 16, 9), (13, 24, 14, 25), (17, 15, 18, 14), (25, 18, 0, 19), (23, 21, 24, 20), (12, 20, 13, 19)], (12, 20, 13, 19)], ['t07348', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (9, 4, 10, 5), (5, 17, 6, 16), (19, 7, 20, 6), (21, 8, 0, 9), (17, 10, 18, 11), (11, 18, 12, 19), (15, 21, 16, 20), (14, 8, 15, 7)], (14, 8, 15, 7)], ['t08111', [(5, 1, 6, 0), (1, 10, 2, 11), (9, 2, 10, 3), (3, 16, 4, 17), (15, 4, 16, 5), (13, 7, 14, 6), (17, 8, 18, 9), (11, 18, 12, 19), (19, 12, 20, 13), (21, 15, 0, 14), (20, 8, 21, 7)], (20, 8, 21, 7)], ['t08201', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (9, 4, 10, 5), (5, 17, 6, 16), (7, 14, 8, 15), (21, 8, 0, 9), (17, 10, 18, 11), (11, 18, 12, 19), (15, 21, 16, 20), (6, 19, 7, 20)], (6, 19, 7, 20)], ['t08267', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (11, 5, 12, 4), (5, 16, 6, 17), (13, 6, 14, 7), (7, 22, 8, 23), (19, 8, 20, 9), (21, 15, 22, 14), (15, 21, 16, 20), (23, 19, 0, 18), (12, 17, 13, 18)], (12, 17, 13, 18)], ['t08403', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (15, 5, 16, 4), (5, 22, 6, 23), (11, 6, 12, 7), (7, 19, 8, 18), (19, 12, 20, 13), (13, 20, 14, 21), (21, 14, 22, 15), (23, 17, 0, 16), (10, 17, 11, 18)], (10, 17, 11, 18)], ['t09016', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (17, 4, 18, 5), (11, 6, 12, 7), (7, 14, 8, 15), (15, 10, 16, 11), (19, 13, 20, 12), (13, 21, 14, 20), (23, 16, 0, 17), (21, 19, 22, 18), (22, 6, 23, 5)], (22, 6, 23, 5)], ['t09267', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (13, 5, 14, 4), (17, 6, 18, 7), (7, 18, 8, 19), (19, 8, 20, 9), (11, 20, 12, 21), (21, 12, 22, 13), (23, 15, 24, 14), (15, 25, 16, 24), (25, 17, 0, 16), (22, 6, 23, 5)], (22, 6, 23, 5)], ['t09313', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (13, 5, 14, 4), (5, 13, 6, 12), (19, 6, 20, 7), (7, 20, 8, 21), (11, 16, 12, 17), (25, 15, 0, 14), (15, 25, 16, 24), (17, 22, 18, 23), (21, 18, 22, 19), (10, 24, 11, 23)], (10, 24, 11, 23)], ['t09455', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (19, 4, 20, 5), (5, 18, 6, 19), (17, 6, 18, 7), (13, 9, 14, 8), (11, 21, 12, 20), (21, 13, 22, 12), (23, 14, 24, 15), (15, 24, 16, 25), (25, 16, 0, 17), (22, 8, 23, 7)], (22, 8, 23, 7)], ['t09580', [(3, 1, 4, 0), (1, 11, 2, 10), (11, 3, 12, 2), (5, 22, 6, 23), (15, 7, 16, 6), (7, 15, 8, 14), (21, 8, 22, 9), (9, 18, 10, 19), (19, 12, 20, 13), (13, 20, 14, 21), (23, 16, 0, 17), (4, 18, 5, 17)], (4, 18, 5, 17)], ['t09704', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (15, 5, 16, 4), (5, 15, 6, 14), (19, 6, 20, 7), (7, 20, 8, 21), (25, 10, 0, 11), (11, 16, 12, 17), (23, 13, 24, 12), (13, 23, 14, 22), (21, 18, 22, 19), (24, 18, 25, 17)], (24, 18, 25, 17)], ['t09852', [(1, 16, 2, 17), (9, 3, 10, 2), (3, 9, 4, 8), (15, 4, 16, 5), (19, 7, 20, 6), (7, 12, 8, 13), (17, 10, 18, 11), (11, 18, 12, 19), (13, 21, 14, 20), (21, 15, 0, 14), (0, 5, 1, 6)], (0, 5, 1, 6)], ['t09954', [(5, 1, 6, 0), (1, 12, 2, 13), (3, 11, 4, 10), (15, 4, 16, 5), (13, 7, 14, 6), (7, 18, 8, 19), (19, 8, 20, 9), (9, 20, 10, 21), (11, 17, 12, 16), (21, 15, 0, 14), (2, 17, 3, 18)], (2, 17, 3, 18)], ['t10230', [(5, 1, 6, 0), (1, 16, 2, 17), (9, 3, 10, 2), (3, 9, 4, 8), (15, 4, 16, 5), (19, 7, 20, 6), (17, 10, 18, 11), (11, 18, 12, 19), (13, 21, 14, 20), (21, 15, 0, 14), (12, 8, 13, 7)], (12, 8, 13, 7)], ['t10462', [(3, 1, 4, 0), (1, 11, 2, 10), (11, 3, 12, 2), (5, 22, 6, 23), (17, 6, 18, 7), (7, 18, 8, 19), (21, 8, 22, 9), (9, 15, 10, 14), (19, 13, 20, 12), (13, 21, 14, 20), (23, 17, 0, 16), (4, 15, 5, 16)], (4, 15, 5, 16)], ['t10643', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (21, 5, 22, 4), (5, 21, 6, 20), (19, 7, 20, 6), (7, 17, 8, 16), (11, 18, 12, 19), (17, 12, 18, 13), (23, 15, 24, 14), (15, 25, 16, 24), (25, 23, 0, 22), (8, 13, 9, 14)], (8, 13, 9, 14)], ['t10681', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (19, 4, 20, 5), (5, 20, 6, 21), (13, 6, 14, 7), (7, 14, 8, 15), (25, 10, 0, 11), (17, 12, 18, 13), (15, 25, 16, 24), (23, 17, 24, 16), (21, 18, 22, 19), (22, 12, 23, 11)], (22, 12, 23, 11)], ['t10985', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (13, 5, 14, 4), (5, 20, 6, 21), (21, 6, 22, 7), (7, 15, 8, 14), (15, 9, 16, 8), (9, 19, 10, 18), (25, 17, 0, 16), (17, 25, 18, 24), (19, 22, 20, 23), (10, 23, 11, 24)], (10, 23, 11, 24)], ['t11852', [(5, 1, 6, 0), (1, 18, 2, 19), (11, 3, 12, 2), (3, 11, 4, 10), (17, 4, 18, 5), (13, 7, 14, 6), (7, 15, 8, 14), (21, 9, 0, 8), (9, 16, 10, 17), (19, 12, 20, 13), (20, 16, 21, 15)], (20, 16, 21, 15)], ['v0165', [(5, 1, 6, 0), (1, 16, 2, 17), (11, 2, 12, 3), (3, 12, 4, 13), (21, 7, 22, 6), (7, 21, 8, 20), (19, 9, 20, 8), (9, 19, 10, 18), (17, 11, 18, 10), (13, 23, 14, 22), (23, 15, 0, 14), (4, 16, 5, 15)], (4, 16, 5, 15)], ['v0330', [(5, 1, 6, 0), (1, 17, 2, 16), (17, 3, 18, 2), (3, 13, 4, 12), (13, 5, 14, 4), (7, 18, 8, 19), (19, 8, 20, 9), (9, 20, 10, 21), (21, 10, 22, 11), (11, 22, 12, 23), (23, 14, 0, 15), (6, 16, 7, 15)], (6, 16, 7, 15)], ['v0398', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (19, 4, 20, 5), (5, 18, 6, 19), (7, 17, 8, 16), (21, 8, 22, 9), (9, 20, 10, 21), (15, 11, 16, 10), (11, 15, 12, 14), (17, 23, 18, 22), (6, 23, 7, 0)], (6, 23, 7, 0)], ['v0407', [(1, 16, 2, 17), (11, 2, 12, 3), (3, 12, 4, 13), (15, 4, 16, 5), (19, 7, 20, 6), (7, 21, 8, 20), (21, 9, 22, 8), (9, 19, 10, 18), (17, 11, 18, 10), (13, 23, 14, 22), (23, 15, 0, 14), (0, 5, 1, 6)], (0, 5, 1, 6)], ['v0434', [(3, 1, 4, 0), (1, 11, 2, 10), (11, 3, 12, 2), (17, 4, 18, 5), (5, 20, 6, 21), (15, 7, 16, 6), (7, 15, 8, 14), (19, 8, 20, 9), (9, 18, 10, 19), (23, 12, 0, 13), (13, 22, 14, 23), (16, 22, 17, 21)], (16, 22, 17, 21)], ['v0554', [(7, 1, 8, 0), (1, 18, 2, 19), (9, 2, 10, 3), (3, 10, 4, 11), (15, 4, 16, 5), (5, 16, 6, 17), (17, 6, 18, 7), (11, 21, 12, 20), (21, 13, 22, 12), (13, 23, 14, 22), (23, 15, 0, 14), (8, 19, 9, 20)], (8, 19, 9, 20)], ['v0570', [(7, 1, 8, 0), (9, 2, 10, 3), (3, 10, 4, 11), (17, 4, 18, 5), (5, 16, 6, 17), (15, 6, 16, 7), (19, 9, 20, 8), (11, 23, 12, 22), (21, 13, 22, 12), (13, 21, 14, 20), (23, 15, 0, 14), (18, 2, 19, 1)], (18, 2, 19, 1)], ['v0573', [(7, 1, 8, 0), (1, 19, 2, 18), (9, 2, 10, 3), (3, 14, 4, 15), (15, 4, 16, 5), (5, 16, 6, 17), (23, 7, 0, 6), (19, 11, 20, 10), (11, 23, 12, 22), (21, 13, 22, 12), (13, 21, 14, 20), (8, 18, 9, 17)], (8, 18, 9, 17)], ['v0707', [(5, 1, 6, 0), (1, 18, 2, 19), (7, 2, 8, 3), (3, 15, 4, 14), (11, 5, 12, 4), (17, 8, 18, 9), (9, 16, 10, 17), (15, 10, 16, 11), (21, 12, 0, 13), (13, 20, 14, 21), (6, 19, 7, 20)], (6, 19, 7, 20)], ['v0740', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (17, 4, 18, 5), (5, 16, 6, 17), (23, 7, 0, 6), (7, 23, 8, 22), (21, 9, 22, 8), (9, 21, 10, 20), (15, 10, 16, 11), (19, 14, 20, 15), (18, 12, 19, 11)], (18, 12, 19, 11)], ['v0759', [(3, 1, 4, 0), (1, 11, 2, 10), (11, 3, 12, 2), (17, 4, 18, 5), (5, 18, 6, 19), (19, 6, 20, 7), (7, 22, 8, 23), (9, 13, 10, 12), (13, 21, 14, 20), (21, 15, 22, 14), (23, 16, 0, 17), (8, 15, 9, 16)], (8, 15, 9, 16)], ['v0765', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (17, 4, 18, 5), (15, 7, 16, 6), (7, 15, 8, 14), (21, 8, 22, 9), (9, 20, 10, 21), (19, 10, 20, 11), (11, 18, 12, 19), (23, 16, 0, 17), (22, 6, 23, 5)], (22, 6, 23, 5)], ['v0939', [(5, 1, 6, 0), (7, 2, 8, 3), (3, 15, 4, 14), (11, 5, 12, 4), (19, 7, 20, 6), (15, 8, 16, 9), (9, 16, 10, 17), (17, 10, 18, 11), (21, 12, 0, 13), (13, 20, 14, 21), (18, 2, 19, 1)], (18, 2, 19, 1)], ['v0945', [(3, 1, 4, 0), (1, 11, 2, 10), (11, 3, 12, 2), (15, 4, 16, 5), (5, 14, 6, 15), (23, 7, 0, 6), (7, 13, 8, 12), (19, 8, 20, 9), (9, 18, 10, 19), (21, 17, 22, 16), (17, 21, 18, 20), (22, 13, 23, 14)], (22, 13, 23, 14)], ['v1077', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (13, 5, 14, 4), (5, 16, 6, 17), (15, 6, 16, 7), (19, 8, 20, 9), (11, 20, 12, 21), (21, 12, 22, 13), (17, 15, 18, 14), (23, 19, 0, 18), (22, 8, 23, 7)], (22, 8, 23, 7)], ['v1109', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (19, 5, 20, 4), (5, 19, 6, 18), (13, 6, 14, 7), (7, 14, 8, 15), (23, 10, 0, 11), (11, 17, 12, 16), (21, 13, 22, 12), (17, 20, 18, 21), (22, 15, 23, 16)], (22, 15, 23, 16)], ['v1392', [(5, 1, 6, 0), (1, 16, 2, 17), (9, 3, 10, 2), (3, 9, 4, 8), (13, 7, 14, 6), (7, 20, 8, 21), (17, 10, 18, 11), (11, 18, 12, 19), (19, 12, 20, 13), (21, 15, 0, 14), (4, 16, 5, 15)], (4, 16, 5, 15)], ['v1547', [(5, 1, 6, 0), (1, 10, 2, 11), (9, 2, 10, 3), (3, 16, 4, 17), (15, 4, 16, 5), (19, 7, 20, 6), (7, 12, 8, 13), (17, 8, 18, 9), (13, 21, 14, 20), (21, 15, 0, 14), (18, 12, 19, 11)], (18, 12, 19, 11)], ['v1620', [(1, 17, 2, 16), (17, 3, 18, 2), (3, 11, 4, 10), (11, 5, 12, 4), (15, 6, 16, 7), (7, 20, 8, 21), (19, 8, 20, 9), (9, 18, 10, 19), (21, 12, 22, 13), (13, 22, 14, 23), (23, 14, 0, 15), (0, 5, 1, 6)], (0, 5, 1, 6)], ['v1690', [(3, 1, 4, 0), (1, 9, 2, 8), (9, 3, 10, 2), (13, 5, 14, 4), (11, 6, 12, 7), (7, 18, 8, 19), (19, 10, 20, 11), (17, 13, 18, 12), (21, 15, 0, 14), (15, 21, 16, 20), (16, 5, 17, 6)], (16, 5, 17, 6)], ['v1709', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (11, 5, 12, 4), (5, 19, 6, 18), (13, 6, 14, 7), (7, 20, 8, 21), (15, 9, 16, 8), (19, 15, 20, 14), (21, 16, 0, 17), (12, 18, 13, 17)], (12, 18, 13, 17)], ['v1716', [(5, 1, 6, 0), (1, 9, 2, 8), (9, 3, 10, 2), (3, 18, 4, 19), (17, 4, 18, 5), (13, 6, 14, 7), (7, 14, 8, 15), (19, 11, 20, 10), (21, 12, 0, 13), (15, 20, 16, 21), (16, 11, 17, 12)], (16, 11, 17, 12)], ['v1718', [(5, 1, 6, 0), (1, 17, 2, 16), (17, 3, 18, 2), (3, 13, 4, 12), (13, 5, 14, 4), (23, 7, 0, 6), (19, 8, 20, 9), (9, 20, 10, 21), (21, 10, 22, 11), (11, 18, 12, 19), (15, 23, 16, 22), (14, 7, 15, 8)], (14, 7, 15, 8)], ['v1728', [(5, 1, 6, 0), (9, 2, 10, 3), (3, 15, 4, 14), (11, 5, 12, 4), (21, 7, 0, 6), (7, 21, 8, 20), (17, 9, 18, 8), (15, 10, 16, 11), (19, 12, 20, 13), (13, 18, 14, 19), (16, 2, 17, 1)], (16, 2, 17, 1)], ['v1810', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (5, 22, 6, 23), (17, 6, 18, 7), (7, 16, 8, 17), (15, 8, 16, 9), (11, 21, 12, 20), (19, 13, 20, 12), (23, 15, 0, 14), (21, 18, 22, 19), (4, 13, 5, 14)], (4, 13, 5, 14)], ['v1832', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (15, 5, 16, 4), (5, 20, 6, 21), (13, 6, 14, 7), (7, 12, 8, 13), (17, 8, 18, 9), (19, 14, 20, 15), (21, 17, 0, 16), (18, 12, 19, 11)], (18, 12, 19, 11)], ['v1839', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (11, 5, 12, 4), (5, 20, 6, 21), (19, 6, 20, 7), (7, 15, 8, 14), (15, 9, 16, 8), (13, 22, 14, 23), (23, 16, 0, 17), (21, 19, 22, 18), (12, 18, 13, 17)], (12, 18, 13, 17)], ['v1921', [(5, 1, 6, 0), (1, 11, 2, 10), (11, 3, 12, 2), (3, 15, 4, 14), (15, 5, 16, 4), (17, 6, 18, 7), (7, 20, 8, 21), (19, 8, 20, 9), (9, 18, 10, 19), (21, 12, 22, 13), (13, 22, 14, 23), (16, 0, 17, 23)], (16, 0, 17, 23)], ['v1980', [(1, 15, 2, 14), (7, 2, 8, 3), (3, 10, 4, 11), (17, 5, 18, 4), (13, 6, 14, 7), (15, 9, 16, 8), (9, 17, 10, 16), (11, 18, 12, 19), (19, 12, 0, 13), (0, 5, 1, 6)], (0, 5, 1, 6)], ['v1986', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (17, 5, 18, 4), (5, 22, 6, 23), (21, 6, 22, 7), (7, 17, 8, 16), (15, 9, 16, 8), (9, 20, 10, 21), (19, 10, 20, 11), (11, 15, 12, 14), (18, 23, 19, 0)], (18, 23, 19, 0)], ['v2024', [(3, 1, 4, 0), (1, 13, 2, 12), (13, 3, 14, 2), (17, 4, 18, 5), (5, 18, 6, 19), (19, 6, 20, 7), (7, 16, 8, 17), (9, 15, 10, 14), (21, 10, 22, 11), (11, 20, 12, 21), (15, 23, 16, 22), (8, 23, 9, 0)], (8, 23, 9, 0)], ['v2090', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (13, 5, 14, 4), (5, 22, 6, 23), (17, 7, 18, 6), (7, 19, 8, 18), (15, 8, 16, 9), (11, 20, 12, 21), (21, 12, 22, 13), (19, 17, 20, 16), (14, 23, 15, 0)], (14, 23, 15, 0)], ['v2215', [(3, 1, 4, 0), (1, 10, 2, 11), (9, 2, 10, 3), (5, 20, 6, 21), (13, 7, 14, 6), (7, 19, 8, 18), (17, 9, 18, 8), (11, 17, 12, 16), (19, 13, 20, 12), (21, 14, 0, 15), (4, 16, 5, 15)], (4, 16, 5, 15)], ['v2325', [(3, 1, 4, 0), (1, 11, 2, 10), (11, 3, 12, 2), (15, 4, 16, 5), (5, 22, 6, 23), (21, 6, 22, 7), (7, 18, 8, 19), (17, 8, 18, 9), (9, 16, 10, 17), (19, 12, 20, 13), (13, 20, 14, 21), (14, 0, 15, 23)], (14, 0, 15, 23)], ['v2759', [(5, 1, 6, 0), (1, 17, 2, 16), (17, 3, 18, 2), (3, 11, 4, 10), (11, 5, 12, 4), (7, 20, 8, 21), (19, 8, 20, 9), (9, 18, 10, 19), (21, 12, 22, 13), (13, 22, 14, 23), (23, 14, 0, 15), (6, 16, 7, 15)], (6, 16, 7, 15)], ['v2930', [(7, 1, 8, 0), (1, 9, 2, 8), (11, 3, 12, 2), (15, 4, 16, 5), (5, 16, 6, 17), (17, 6, 18, 7), (9, 18, 10, 19), (19, 10, 20, 11), (21, 13, 22, 12), (13, 23, 14, 22), (23, 15, 0, 14), (20, 4, 21, 3)], (20, 4, 21, 3)], ['v3354', [(3, 1, 4, 0), (1, 12, 2, 13), (11, 2, 12, 3), (15, 5, 16, 4), (5, 22, 6, 23), (21, 6, 22, 7), (7, 15, 8, 14), (13, 9, 14, 8), (9, 19, 10, 18), (19, 11, 20, 10), (17, 21, 18, 20), (16, 23, 17, 0)], (16, 23, 17, 0)]]
Thus we have found a correct almost alternating diagram of the unknot. This finishes the classification of the set of alternating slopes for any knot in the SnapPy censu.