#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_003 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(242,3492,11568,13860,5544) ### ### H_*=(Z,0,0,0,Z) ### ### PL 4-sphere ### ### ### ### ### ### references: ### ### ### ### Frank H. Lutz and Mimi Tsuruga. ### ### Constructing complicated spheres. ### ### arXiv:1302.6856[math.CO], 2013. ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [0,1,2,5,161],[0,1,2,35,191],[0,1,2,158,161],[0,1,2,158,191], [0,1,4,5,161],[0,1,4,82,160],[0,1,4,160,161],[0,1,34,35,191], [0,1,34,70,148],[0,1,34,70,226],[0,1,34,112,148],[0,1,34,190,191], [0,1,34,190,226],[0,1,69,70,148],[0,1,69,70,226],[0,1,69,147,148], [0,1,69,147,225],[0,1,69,225,226],[0,1,79,82,160],[0,1,79,112,148], [0,1,79,147,148],[0,1,79,147,225],[0,1,157,158,161],[0,1,157,158,191], [0,1,79,157,160],[0,1,157,160,161],[0,1,157,190,191],[0,1,157,190,226], [0,1,79,157,225],[0,1,157,225,226],[0,2,5,26,104],[0,2,5,26,182], [2,5,26,104,182],[0,2,5,83,104],[2,5,83,104,182],[0,2,5,161,182], [2,5,83,161,182],[0,2,26,29,107],[0,2,26,29,185],[2,26,29,107,185], [0,2,26,104,107],[2,26,104,107,185],[0,2,26,182,185],[2,26,104,182,185], [0,2,29,73,151],[0,2,29,73,229],[0,2,29,107,151],[0,2,29,185,229], [0,2,35,73,151],[0,2,35,73,229],[0,2,35,113,151],[0,2,35,191,229], [0,2,80,83,104],[2,80,83,104,182],[2,80,83,161,182],[0,2,80,104,107], [2,80,104,107,185],[2,80,104,182,185],[0,2,80,107,151],[0,2,80,113,151], [0,2,158,161,182],[2,80,158,161,182],[0,2,158,182,185],[2,80,158,182,185], [0,2,158,185,229],[0,2,158,191,229],[0,3,4,5,161],[0,3,4,82,160], [0,3,4,160,161],[0,3,5,26,104],[0,3,5,26,182],[0,3,5,83,104], [0,3,5,161,182],[0,3,24,26,104],[0,3,24,26,182],[0,3,24,102,104], [0,3,24,102,180],[0,3,24,180,182],[0,3,81,82,160],[0,3,81,83,104], [0,3,81,102,104],[0,3,81,102,180],[0,3,81,159,160],[0,3,159,160,161], [0,3,159,161,182],[0,3,81,159,180],[0,3,159,180,182],[0,24,26,29,107], [0,24,26,29,185],[0,24,26,104,107],[0,24,26,182,185],[0,24,27,29,107], [0,24,27,29,185],[0,24,27,105,107],[0,24,27,105,183],[0,24,27,183,185], [0,24,102,104,107],[0,24,102,105,107],[0,24,102,105,183],[0,24,180,182,185], [0,24,102,180,183],[0,24,180,183,185],[0,27,29,73,151],[0,27,29,73,229], [0,27,29,107,151],[0,27,29,185,229],[0,27,66,70,148],[0,27,66,70,226], [0,27,66,73,151],[0,27,66,73,229],[0,27,66,144,148],[0,27,66,144,151], [0,27,66,222,226],[0,27,66,222,229],[0,27,69,70,148],[0,27,69,70,226], [0,27,69,147,148],[0,27,69,147,225],[0,27,69,225,226],[0,27,105,107,151], [0,27,105,144,148],[0,27,105,144,151],[0,27,105,147,148],[0,27,105,147,225], [0,27,183,185,229],[0,27,183,222,226],[0,27,183,222,229],[0,27,105,183,225], [0,27,183,225,226],[0,33,34,35,191],[0,33,34,70,148],[0,33,34,70,226], [0,33,34,112,148],[0,33,34,190,191],[0,33,34,190,226],[0,33,35,73,151], [0,33,35,73,229],[0,33,35,113,151],[0,33,35,191,229],[0,33,66,70,148], [0,33,66,70,226],[0,33,66,73,151],[0,33,66,73,229],[0,33,66,144,148], [0,33,66,144,151],[0,33,66,222,226],[0,33,66,222,229],[0,33,111,112,148], [0,33,111,113,151],[0,33,111,144,148],[0,33,111,144,151],[0,33,189,190,191], [0,33,189,190,226],[0,33,189,191,229],[0,33,189,222,226],[0,33,189,222,229], [78,79,80,83,161],[78,79,80,113,191],[78,79,80,158,161],[78,79,80,158,191], [78,79,82,83,161],[0,78,79,82,160],[78,79,82,160,161],[78,79,112,113,191], [0,78,79,112,148],[78,79,112,148,226],[78,79,112,190,191],[78,79,112,190,226], [0,78,79,147,148],[78,79,147,148,226],[0,78,79,147,225],[78,79,147,225,226], [78,79,157,158,161],[78,79,157,158,191],[0,78,79,157,160],[78,79,157,160,161], [78,79,157,190,191],[78,79,157,190,226],[0,78,79,157,225],[78,79,157,225,226], [0,78,80,83,104],[78,80,83,104,182],[78,80,83,161,182],[0,78,80,104,107], [78,80,104,107,185],[78,80,104,182,185],[0,78,80,107,151],[78,80,107,151,229], [78,80,107,185,229],[0,78,80,113,151],[78,80,113,151,229],[78,80,113,191,229], [78,80,158,161,182],[78,80,158,182,185],[78,80,158,185,229],[78,80,158,191,229], [78,81,82,83,161],[0,78,81,82,160],[78,81,82,160,161],[0,78,81,83,104], [78,81,83,104,182],[78,81,83,161,182],[0,78,81,102,104],[78,81,102,104,182], [0,78,81,102,180],[78,81,102,180,182],[0,78,81,159,160],[78,81,159,160,161], [78,81,159,161,182],[0,78,81,159,180],[78,81,159,180,182],[0,78,102,104,107], [78,102,104,107,185],[78,102,104,182,185],[0,78,102,105,107],[78,102,105,107,185], [0,78,102,105,183],[78,102,105,183,185],[78,102,180,182,185],[0,78,102,180,183], [78,102,180,183,185],[0,78,105,107,151],[78,105,107,151,229],[78,105,107,185,229], [0,78,105,144,148],[78,105,144,148,226],[0,78,105,144,151],[78,105,144,151,229], [78,105,144,222,226],[78,105,144,222,229],[0,78,105,147,148],[78,105,147,148,226], [0,78,105,147,225],[78,105,147,225,226],[78,105,183,185,229],[78,105,183,222,226], [78,105,183,222,229],[0,78,105,183,225],[78,105,183,225,226],[78,111,112,113,191], [0,78,111,112,148],[78,111,112,148,226],[78,111,112,190,191],[78,111,112,190,226], [0,78,111,113,151],[78,111,113,151,229],[78,111,113,191,229],[0,78,111,144,148], [78,111,144,148,226],[0,78,111,144,151],[78,111,144,151,229],[78,111,144,222,226], [78,111,144,222,229],[78,111,189,190,191],[78,111,189,190,226],[78,111,189,191,229], [78,111,189,222,226],[78,111,189,222,229],[0,156,157,158,161],[78,156,157,158,161], [0,156,157,158,191],[78,156,157,158,191],[0,78,156,157,160],[0,156,157,160,161], [78,156,157,160,161],[0,156,157,190,191],[78,156,157,190,191],[0,156,157,190,226], [78,156,157,190,226],[0,78,156,157,225],[0,156,157,225,226],[78,156,157,225,226], [0,156,158,161,182],[78,156,158,161,182],[0,156,158,182,185],[78,156,158,182,185], [0,156,158,185,229],[78,156,158,185,229],[0,156,158,191,229],[78,156,158,191,229], [0,78,156,159,160],[0,156,159,160,161],[78,156,159,160,161],[0,156,159,161,182], [78,156,159,161,182],[0,78,156,159,180],[0,156,159,180,182],[78,156,159,180,182], [0,156,180,182,185],[78,156,180,182,185],[0,78,156,180,183],[0,156,180,183,185], [78,156,180,183,185],[0,156,183,185,229],[78,156,183,185,229],[0,156,183,222,226], [78,156,183,222,226],[0,156,183,222,229],[78,156,183,222,229],[0,78,156,183,225], [0,156,183,225,226],[78,156,183,225,226],[0,156,189,190,191],[78,156,189,190,191], [0,156,189,190,226],[78,156,189,190,226],[0,156,189,191,229],[78,156,189,191,229], [0,156,189,222,226],[78,156,189,222,226],[0,156,189,222,229],[78,156,189,222,229], [1,2,5,41,119],[1,2,5,41,197],[2,5,41,119,197],[1,2,5,83,119], [2,5,83,119,197],[1,2,5,161,197],[2,5,83,161,197],[1,2,35,73,151], [1,2,35,73,229],[1,2,35,113,151],[1,2,35,191,229],[1,2,38,41,119], [1,2,38,41,197],[2,38,41,119,197],[1,2,38,76,154],[1,2,38,76,232], [1,2,38,116,119],[2,38,116,119,197],[1,2,38,116,154],[1,2,38,194,197], [2,38,116,194,197],[1,2,38,194,232],[1,2,72,73,151],[1,2,72,73,229], [1,2,72,76,154],[1,2,72,76,232],[1,2,72,150,151],[1,2,72,150,154], [1,2,72,228,229],[1,2,72,228,232],[1,2,80,83,119],[2,80,83,119,197], [2,80,83,161,197],[1,2,80,113,151],[1,2,80,116,119],[2,80,116,119,197], [1,2,80,116,154],[2,80,116,194,197],[1,2,80,150,151],[1,2,80,150,154], [1,2,158,161,197],[2,80,158,161,197],[1,2,158,191,229],[1,2,158,194,197], [2,80,158,194,197],[1,2,158,194,232],[1,2,158,228,229],[1,2,158,228,232], [1,4,5,41,119],[1,4,5,41,197],[1,4,5,83,119],[1,4,5,161,197], [1,4,39,41,119],[1,4,39,41,197],[1,4,39,117,119],[1,4,39,117,195], [1,4,39,195,197],[1,4,82,83,119],[1,4,82,117,119],[1,4,82,117,195], [1,4,160,161,197],[1,4,82,160,195],[1,4,160,195,197],[1,34,35,73,151], [1,34,35,73,229],[1,34,35,113,151],[1,34,35,191,229],[1,34,67,70,148], [1,34,67,70,226],[1,34,67,73,151],[1,34,67,73,229],[1,34,67,145,148], [1,34,67,145,151],[1,34,67,223,226],[1,34,67,223,229],[1,34,112,113,151], [1,34,112,145,148],[1,34,112,145,151],[1,34,190,191,229],[1,34,190,223,226], [1,34,190,223,229],[1,36,38,41,119],[1,36,38,41,197],[1,36,38,76,154], [1,36,38,76,232],[1,36,38,116,119],[1,36,38,116,154],[1,36,38,194,197], [1,36,38,194,232],[1,36,39,41,119],[1,36,39,41,197],[1,36,39,117,119], [1,36,39,117,195],[1,36,39,195,197],[1,36,67,70,148],[1,36,67,70,226], [1,36,67,73,151],[1,36,67,73,229],[1,36,67,145,148],[1,36,67,145,151], [1,36,67,223,226],[1,36,67,223,229],[1,36,69,70,148],[1,36,69,70,226], [1,36,69,147,148],[1,36,69,147,225],[1,36,69,225,226],[1,36,72,73,151], [1,36,72,73,229],[1,36,72,76,154],[1,36,72,76,232],[1,36,72,150,151], [1,36,72,150,154],[1,36,72,228,229],[1,36,72,228,232],[1,36,114,116,119], [1,36,114,116,154],[1,36,114,117,119],[1,36,114,117,195],[1,36,114,145,148], [1,36,114,145,151],[1,36,114,147,148],[1,36,114,147,225],[1,36,114,150,151], [1,36,114,150,154],[1,36,192,194,197],[1,36,192,194,232],[1,36,114,192,195], [1,36,192,195,197],[1,36,192,223,226],[1,36,192,223,229],[1,36,114,192,225], [1,36,192,225,226],[1,36,192,228,229],[1,36,192,228,232],[1,79,80,83,119], [79,80,83,119,197],[79,80,83,161,197],[1,79,80,113,151],[79,80,113,151,229], [79,80,113,191,229],[1,79,80,116,119],[79,80,116,119,197],[1,79,80,116,154], [79,80,116,154,232],[79,80,116,194,197],[79,80,116,194,232],[1,79,80,150,151], [79,80,150,151,229],[1,79,80,150,154],[79,80,150,154,232],[79,80,150,228,229], [79,80,150,228,232],[79,80,158,161,197],[79,80,158,191,229],[79,80,158,194,197], [79,80,158,194,232],[79,80,158,228,229],[79,80,158,228,232],[1,79,82,83,119], [79,82,83,119,197],[79,82,83,161,197],[1,79,82,117,119],[79,82,117,119,197], [1,79,82,117,195],[79,82,117,195,197],[79,82,160,161,197],[1,79,82,160,195], [79,82,160,195,197],[1,79,112,113,151],[79,112,113,151,229],[79,112,113,191,229], [1,79,112,145,148],[79,112,145,148,226],[1,79,112,145,151],[79,112,145,151,229], [79,112,145,223,226],[79,112,145,223,229],[79,112,190,191,229],[79,112,190,223,226], [79,112,190,223,229],[1,79,114,116,119],[79,114,116,119,197],[1,79,114,116,154], [79,114,116,154,232],[79,114,116,194,197],[79,114,116,194,232],[1,79,114,117,119], [79,114,117,119,197],[1,79,114,117,195],[79,114,117,195,197],[1,79,114,145,148], [79,114,145,148,226],[1,79,114,145,151],[79,114,145,151,229],[79,114,145,223,226], [79,114,145,223,229],[1,79,114,147,148],[79,114,147,148,226],[1,79,114,147,225], [79,114,147,225,226],[1,79,114,150,151],[79,114,150,151,229],[1,79,114,150,154], [79,114,150,154,232],[79,114,150,228,229],[79,114,150,228,232],[79,114,192,194,197], [79,114,192,194,232],[1,79,114,192,195],[79,114,192,195,197],[79,114,192,223,226], [79,114,192,223,229],[1,79,114,192,225],[79,114,192,225,226],[79,114,192,228,229], [79,114,192,228,232],[1,157,158,161,197],[79,157,158,161,197],[1,157,158,191,229], [79,157,158,191,229],[1,157,158,194,197],[79,157,158,194,197],[1,157,158,194,232], [79,157,158,194,232],[1,157,158,228,229],[79,157,158,228,229],[1,157,158,228,232], [79,157,158,228,232],[1,157,160,161,197],[79,157,160,161,197],[1,79,157,160,195], [1,157,160,195,197],[79,157,160,195,197],[1,157,190,191,229],[79,157,190,191,229], [1,157,190,223,226],[79,157,190,223,226],[1,157,190,223,229],[79,157,190,223,229], [1,157,192,194,197],[79,157,192,194,197],[1,157,192,194,232],[79,157,192,194,232], [1,79,157,192,195],[1,157,192,195,197],[79,157,192,195,197],[1,157,192,223,226], [79,157,192,223,226],[1,157,192,223,229],[79,157,192,223,229],[1,79,157,192,225], [1,157,192,225,226],[79,157,192,225,226],[1,157,192,228,229],[79,157,192,228,229], [1,157,192,228,232],[79,157,192,228,232],[2,29,72,73,151],[2,29,72,73,229], [2,29,72,76,154],[2,29,72,76,232],[2,29,72,150,151],[2,29,72,150,154], [2,29,72,228,229],[2,29,72,228,232],[2,29,74,76,154],[2,29,74,76,232], [2,29,74,152,154],[2,29,74,152,230],[2,29,74,230,232],[2,29,107,150,151], [2,29,107,150,154],[2,29,107,152,154],[2,29,107,152,230],[2,29,185,228,229], [2,29,185,228,232],[2,29,107,185,230],[2,29,185,230,232],[2,38,74,76,154], [2,38,74,76,232],[2,38,74,152,154],[2,38,74,152,230],[2,38,74,230,232], [2,38,116,152,154],[2,38,116,152,230],[2,38,116,194,230],[2,38,194,230,232], [2,80,107,150,151],[80,107,150,151,229],[2,80,107,150,154],[80,107,150,154,232], [80,107,150,228,229],[80,107,150,228,232],[2,80,107,152,154],[80,107,152,154,232], [2,80,107,152,230],[80,107,152,230,232],[80,107,185,228,229],[80,107,185,228,232], [2,80,107,185,230],[80,107,185,230,232],[2,80,116,152,154],[80,116,152,154,232], [2,80,116,152,230],[80,116,152,230,232],[2,80,116,194,230],[80,116,194,230,232], [2,158,185,228,229],[80,158,185,228,229],[2,158,185,228,232],[80,158,185,228,232], [2,80,158,185,230],[2,158,185,230,232],[80,158,185,230,232],[2,80,158,194,230], [2,158,194,230,232],[80,158,194,230,232],[3,4,5,8,164],[3,4,5,161,164], [3,4,7,8,164],[3,4,7,70,148],[3,4,7,70,226],[3,4,7,85,148], [3,4,7,163,164],[3,4,7,163,226],[3,4,69,70,148],[3,4,69,70,226], [3,4,69,147,148],[3,4,69,147,225],[3,4,69,225,226],[3,4,82,85,148], 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[58,61,62,140,238],[57,58,61,139,238],[58,61,139,140,238],[58,136,137,140,238], [57,58,136,139,238],[58,136,139,140,238],[57,60,62,140,238],[57,60,61,139,238], [57,60,138,139,238],[57,60,138,140,238],[57,135,137,140,238],[135,136,137,140,238], [57,135,136,139,238],[135,136,139,140,238],[57,135,138,139,238],[57,135,138,140,238], [135,138,139,140,238],[60,62,65,143,238],[61,62,65,143,238],[60,62,140,143,238], [61,62,140,143,238],[61,64,65,143,238],[60,61,64,142,238],[61,64,142,143,238], [61,139,140,143,238],[60,61,139,142,238],[61,139,142,143,238],[60,63,65,143,238], [60,63,64,142,238],[60,63,141,142,238],[60,63,141,143,238],[60,138,140,143,238], [138,139,140,143,238],[60,138,139,142,238],[138,139,142,143,238],[60,138,141,142,238], [60,138,141,143,238],[138,141,142,143,238],[36,37,38,41,239],[37,38,41,238,239], [36,37,38,65,239],[37,38,65,238,239],[36,37,40,41,239],[36,37,40,238,239], [37,40,41,238,239],[36,37,64,65,239],[36,37,64,238,239],[37,64,65,238,239], [36,39,40,41,239],[36,39,40,238,239],[36,63,64,65,239],[36,63,64,238,239], [39,40,41,44,239],[40,41,44,238,239],[39,40,43,44,239],[39,40,43,238,239], [40,43,44,238,239],[39,42,43,44,239],[39,42,43,238,239],[42,43,44,47,239], [43,44,47,238,239],[42,43,46,47,239],[42,43,46,238,239],[43,46,47,238,239], [42,45,46,47,239],[42,45,46,238,239],[45,46,47,50,239],[46,47,50,238,239], [45,46,49,50,239],[45,46,49,238,239],[46,49,50,238,239],[45,48,49,50,239], [45,48,49,238,239],[48,49,50,53,239],[49,50,53,238,239],[48,49,52,53,239], [48,49,52,238,239],[49,52,53,238,239],[48,51,52,53,239],[48,51,52,238,239], [51,52,53,56,239],[52,53,56,238,239],[51,52,55,56,239],[51,52,55,238,239], [52,55,56,238,239],[51,54,55,56,239],[51,54,55,238,239],[54,55,56,59,239], [55,56,59,238,239],[54,55,58,59,239],[54,55,58,238,239],[55,58,59,238,239], [54,57,58,59,239],[54,57,58,238,239],[57,58,59,62,239],[58,59,62,238,239], [57,58,61,62,239],[57,58,61,238,239],[58,61,62,238,239],[57,60,61,62,239], [57,60,61,238,239],[60,61,62,65,239],[61,62,65,238,239],[60,61,64,65,239], [60,61,64,238,239],[61,64,65,238,239],[60,63,64,65,239],[60,63,64,238,239], [36,38,41,238,240],[36,38,41,239,240],[38,41,238,239,240],[36,38,65,238,240], [36,38,65,239,240],[38,65,238,239,240],[36,39,41,238,240],[36,39,41,239,240], [36,63,65,238,240],[36,63,65,239,240],[39,41,44,238,240],[39,41,44,239,240], [41,44,238,239,240],[39,42,44,238,240],[39,42,44,239,240],[42,44,47,238,240], [42,44,47,239,240],[44,47,238,239,240],[42,45,47,238,240],[42,45,47,239,240], [45,47,50,238,240],[45,47,50,239,240],[47,50,238,239,240],[45,48,50,238,240], [45,48,50,239,240],[48,50,53,238,240],[48,50,53,239,240],[50,53,238,239,240], [48,51,53,238,240],[48,51,53,239,240],[51,53,56,238,240],[51,53,56,239,240], [53,56,238,239,240],[51,54,56,238,240],[51,54,56,239,240],[54,56,59,238,240], [54,56,59,239,240],[56,59,238,239,240],[54,57,59,238,240],[54,57,59,239,240], [57,59,62,238,240],[57,59,62,239,240],[59,62,238,239,240],[57,60,62,238,240], [57,60,62,239,240],[60,62,65,238,240],[60,62,65,239,240],[62,65,238,239,240], [60,63,65,238,240],[60,63,65,239,240],[36,39,238,239,241],[36,39,238,240,241], [36,39,239,240,241],[36,63,238,239,241],[36,63,238,240,241],[36,63,239,240,241], [39,42,238,239,241],[39,42,238,240,241],[39,42,239,240,241],[42,45,238,239,241], [42,45,238,240,241],[42,45,239,240,241],[45,48,238,239,241],[45,48,238,240,241], [45,48,239,240,241],[48,51,238,239,241],[48,51,238,240,241],[48,51,239,240,241], [51,54,238,239,241],[51,54,238,240,241],[51,54,239,240,241],[54,57,238,239,241], [54,57,238,240,241],[54,57,239,240,241],[57,60,238,239,241],[57,60,238,240,241], [57,60,239,240,241],[60,63,238,239,241],[60,63,238,240,241],[60,63,239,240,241] ];