#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_003 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(320,4854,16236,19500,7800) ### ### 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],[0,1,4,82,238],[0,1,4,160,161],[0,1,4,160,238], [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],[0,1,69,147,303],[0,1,69,225,226],[0,1,69,225,303], [0,1,79,82,238],[0,1,79,112,148],[0,1,79,147,148],[0,1,79,147,303], [0,1,79,235,238],[0,1,79,235,303],[0,1,157,158,161],[0,1,157,158,191], [0,1,157,160,161],[0,1,157,160,238],[0,1,157,190,191],[0,1,157,190,226], [0,1,157,225,226],[0,1,157,225,303],[0,1,157,235,238],[0,1,157,235,303], [0,2,5,26,104],[2,5,26,104,260],[0,2,5,26,182],[2,5,26,182,260], [0,2,5,83,104],[2,5,83,104,260],[2,5,83,239,260],[0,2,5,161,182], [2,5,161,182,260],[2,5,161,239,260],[0,2,26,29,107],[2,26,29,107,263], [0,2,26,29,185],[2,26,29,185,263],[0,2,26,104,107],[2,26,104,107,263], [2,26,104,260,263],[0,2,26,182,185],[2,26,182,185,263],[2,26,182,260,263], [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],[2,80,83,104,260],[2,80,83,239,260],[0,2,80,104,107], [2,80,104,107,263],[2,80,104,260,263],[0,2,80,107,151],[0,2,80,113,151], [2,80,236,239,260],[2,80,236,260,263],[0,2,158,161,182],[2,158,161,182,260], [2,158,161,239,260],[0,2,158,182,185],[2,158,182,185,263],[2,158,182,260,263], [0,2,158,185,229],[0,2,158,191,229],[2,158,236,239,260],[2,158,236,260,263], [0,3,4,5,161],[0,3,4,82,238],[0,3,4,160,161],[0,3,4,160,238], [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],[0,3,24,102,258], [0,3,24,180,182],[0,3,24,180,258],[0,3,81,82,238],[0,3,81,83,104], [0,3,81,102,104],[0,3,81,102,258],[0,3,81,237,238],[0,3,81,237,258], [0,3,159,160,161],[0,3,159,160,238],[0,3,159,161,182],[0,3,159,180,182], [0,3,159,180,258],[0,3,159,237,238],[0,3,159,237,258],[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],[0,24,27,105,261],[0,24,27,183,185], [0,24,27,183,261],[0,24,102,104,107],[0,24,102,105,107],[0,24,102,105,261], [0,24,102,258,261],[0,24,180,182,185],[0,24,180,183,185],[0,24,180,183,261], [0,24,180,258,261],[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], [0,27,69,147,303],[0,27,69,225,226],[0,27,69,225,303],[0,27,105,107,151], [0,27,105,144,148],[0,27,105,144,151],[0,27,105,147,148],[0,27,105,147,303], [0,27,105,261,303],[0,27,183,185,229],[0,27,183,222,226],[0,27,183,222,229], [0,27,183,225,226],[0,27,183,225,303],[0,27,183,261,303],[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],[78,79,80,83,239],[78,79,80,113,269], [78,79,80,236,239],[78,79,80,236,269],[78,79,82,83,239],[0,78,79,82,238], [78,79,82,238,239],[78,79,112,113,269],[0,78,79,112,148],[78,79,112,148,304], [78,79,112,268,269],[78,79,112,268,304],[0,78,79,147,148],[78,79,147,148,304], [0,78,79,147,303],[78,79,147,303,304],[78,79,235,236,239],[78,79,235,236,269], [0,78,79,235,238],[78,79,235,238,239],[78,79,235,268,269],[78,79,235,268,304], [0,78,79,235,303],[78,79,235,303,304],[0,78,80,83,104],[78,80,83,104,260], [78,80,83,239,260],[0,78,80,104,107],[78,80,104,107,263],[78,80,104,260,263], [0,78,80,107,151],[78,80,107,151,307],[78,80,107,263,307],[0,78,80,113,151], [78,80,113,151,307],[78,80,113,269,307],[78,80,236,239,260],[78,80,236,260,263], [78,80,236,263,307],[78,80,236,269,307],[78,81,82,83,239],[0,78,81,82,238], [78,81,82,238,239],[0,78,81,83,104],[78,81,83,104,260],[78,81,83,239,260], [0,78,81,102,104],[78,81,102,104,260],[0,78,81,102,258],[78,81,102,258,260], [0,78,81,237,238],[78,81,237,238,239],[78,81,237,239,260],[0,78,81,237,258], [78,81,237,258,260],[0,78,102,104,107],[78,102,104,107,263],[78,102,104,260,263], [0,78,102,105,107],[78,102,105,107,263],[0,78,102,105,261],[78,102,105,261,263], [78,102,258,260,263],[0,78,102,258,261],[78,102,258,261,263],[0,78,105,107,151], [78,105,107,151,307],[78,105,107,263,307],[0,78,105,144,148],[78,105,144,148,304], [0,78,105,144,151],[78,105,144,151,307],[78,105,144,300,304],[78,105,144,300,307], [0,78,105,147,148],[78,105,147,148,304],[0,78,105,147,303],[78,105,147,303,304], [78,105,261,263,307],[78,105,261,300,304],[78,105,261,300,307],[0,78,105,261,303], [78,105,261,303,304],[78,111,112,113,269],[0,78,111,112,148],[78,111,112,148,304], [78,111,112,268,269],[78,111,112,268,304],[0,78,111,113,151],[78,111,113,151,307], [78,111,113,269,307],[0,78,111,144,148],[78,111,144,148,304],[0,78,111,144,151], [78,111,144,151,307],[78,111,144,300,304],[78,111,144,300,307],[78,111,267,268,269], [78,111,267,268,304],[78,111,267,269,307],[78,111,267,300,304],[78,111,267,300,307], [78,234,235,236,239],[78,234,235,236,269],[0,78,234,235,238],[78,234,235,238,239], [78,234,235,268,269],[78,234,235,268,304],[0,78,234,235,303],[78,234,235,303,304], [78,234,236,239,260],[78,234,236,260,263],[78,234,236,263,307],[78,234,236,269,307], [0,78,234,237,238],[78,234,237,238,239],[78,234,237,239,260],[0,78,234,237,258], [78,234,237,258,260],[78,234,258,260,263],[0,78,234,258,261],[78,234,258,261,263], [78,234,261,263,307],[78,234,261,300,304],[78,234,261,300,307],[0,78,234,261,303], [78,234,261,303,304],[78,234,267,268,269],[78,234,267,268,304],[78,234,267,269,307], [78,234,267,300,304],[78,234,267,300,307],[0,156,157,158,161],[156,157,158,161,239], [0,156,157,158,191],[156,157,158,191,269],[156,157,158,236,239],[156,157,158,236,269], [0,156,157,160,161],[156,157,160,161,239],[0,156,157,160,238],[156,157,160,238,239], [0,156,157,190,191],[156,157,190,191,269],[0,156,157,190,226],[156,157,190,226,304], [156,157,190,268,269],[156,157,190,268,304],[0,156,157,225,226],[156,157,225,226,304], [0,156,157,225,303],[156,157,225,303,304],[156,157,235,236,239],[156,157,235,236,269], [0,156,157,235,238],[156,157,235,238,239],[156,157,235,268,269],[156,157,235,268,304], [0,156,157,235,303],[156,157,235,303,304],[0,156,158,161,182],[156,158,161,182,260], [156,158,161,239,260],[0,156,158,182,185],[156,158,182,185,263],[156,158,182,260,263], [0,156,158,185,229],[156,158,185,229,307],[156,158,185,263,307],[0,156,158,191,229], [156,158,191,229,307],[156,158,191,269,307],[156,158,236,239,260],[156,158,236,260,263], [156,158,236,263,307],[156,158,236,269,307],[0,156,159,160,161],[156,159,160,161,239], [0,156,159,160,238],[156,159,160,238,239],[0,156,159,161,182],[156,159,161,182,260], [156,159,161,239,260],[0,156,159,180,182],[156,159,180,182,260],[0,156,159,180,258], [156,159,180,258,260],[0,156,159,237,238],[156,159,237,238,239],[156,159,237,239,260], [0,156,159,237,258],[156,159,237,258,260],[0,156,180,182,185],[156,180,182,185,263], [156,180,182,260,263],[0,156,180,183,185],[156,180,183,185,263],[0,156,180,183,261], [156,180,183,261,263],[156,180,258,260,263],[0,156,180,258,261],[156,180,258,261,263], [0,156,183,185,229],[156,183,185,229,307],[156,183,185,263,307],[0,156,183,222,226], [156,183,222,226,304],[0,156,183,222,229],[156,183,222,229,307],[156,183,222,300,304], [156,183,222,300,307],[0,156,183,225,226],[156,183,225,226,304],[0,156,183,225,303], [156,183,225,303,304],[156,183,261,263,307],[156,183,261,300,304],[156,183,261,300,307], [0,156,183,261,303],[156,183,261,303,304],[0,156,189,190,191],[156,189,190,191,269], [0,156,189,190,226],[156,189,190,226,304],[156,189,190,268,269],[156,189,190,268,304], [0,156,189,191,229],[156,189,191,229,307],[156,189,191,269,307],[0,156,189,222,226], [156,189,222,226,304],[0,156,189,222,229],[156,189,222,229,307],[156,189,222,300,304], [156,189,222,300,307],[156,189,267,268,269],[156,189,267,268,304],[156,189,267,269,307], [156,189,267,300,304],[156,189,267,300,307],[156,234,235,236,239],[156,234,235,236,269], [0,156,234,235,238],[156,234,235,238,239],[156,234,235,268,269],[156,234,235,268,304], [0,156,234,235,303],[156,234,235,303,304],[156,234,236,239,260],[156,234,236,260,263], [156,234,236,263,307],[156,234,236,269,307],[0,156,234,237,238],[156,234,237,238,239], [156,234,237,239,260],[0,156,234,237,258],[156,234,237,258,260],[156,234,258,260,263], [0,156,234,258,261],[156,234,258,261,263],[156,234,261,263,307],[156,234,261,300,304], [156,234,261,300,307],[0,156,234,261,303],[156,234,261,303,304],[156,234,267,268,269], [156,234,267,268,304],[156,234,267,269,307],[156,234,267,300,304],[156,234,267,300,307], [1,2,5,41,119],[2,5,41,119,275],[1,2,5,41,197],[2,5,41,197,275], [1,2,5,83,119],[2,5,83,119,275],[2,5,83,239,275],[1,2,5,161,197], [2,5,161,197,275],[2,5,161,239,275],[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],[2,38,41,119,275], [1,2,38,41,197],[2,38,41,197,275],[1,2,38,76,154],[1,2,38,76,232], [1,2,38,116,119],[2,38,116,119,275],[1,2,38,116,154],[2,38,116,272,275], [1,2,38,194,197],[2,38,194,197,275],[1,2,38,194,232],[2,38,194,272,275], [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],[2,80,83,119,275],[2,80,83,239,275],[1,2,80,113,151], [1,2,80,116,119],[2,80,116,119,275],[1,2,80,116,154],[2,80,116,272,275], [1,2,80,150,151],[1,2,80,150,154],[2,80,236,239,275],[2,80,236,272,275], [1,2,158,161,197],[2,158,161,197,275],[2,158,161,239,275],[1,2,158,191,229], [1,2,158,194,197],[2,158,194,197,275],[1,2,158,194,232],[2,158,194,272,275], [1,2,158,228,229],[1,2,158,228,232],[2,158,236,239,275],[2,158,236,272,275], [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],[1,4,39,117,273], [1,4,39,195,197],[1,4,39,195,273],[1,4,82,83,119],[1,4,82,117,119], [1,4,82,117,273],[1,4,82,238,273],[1,4,160,161,197],[1,4,160,195,197], [1,4,160,195,273],[1,4,160,238,273],[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],[1,36,39,117,273], [1,36,39,195,197],[1,36,39,195,273],[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],[1,36,69,147,303],[1,36,69,225,226],[1,36,69,225,303], [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],[1,36,114,117,273], [1,36,114,145,148],[1,36,114,145,151],[1,36,114,147,148],[1,36,114,147,303], [1,36,114,150,151],[1,36,114,150,154],[1,36,114,270,273],[1,36,114,270,303], [1,36,192,194,197],[1,36,192,194,232],[1,36,192,195,197],[1,36,192,195,273], [1,36,192,223,226],[1,36,192,223,229],[1,36,192,225,226],[1,36,192,225,303], [1,36,192,228,229],[1,36,192,228,232],[1,36,192,270,273],[1,36,192,270,303], [1,79,80,83,119],[79,80,83,119,275],[79,80,83,239,275],[1,79,80,113,151], [79,80,113,151,307],[79,80,113,269,307],[1,79,80,116,119],[79,80,116,119,275], [1,79,80,116,154],[79,80,116,154,310],[79,80,116,272,275],[79,80,116,272,310], [1,79,80,150,151],[79,80,150,151,307],[1,79,80,150,154],[79,80,150,154,310], [79,80,150,306,307],[79,80,150,306,310],[79,80,236,239,275],[79,80,236,269,307], [79,80,236,272,275],[79,80,236,272,310],[79,80,236,306,307],[79,80,236,306,310], [1,79,82,83,119],[79,82,83,119,275],[79,82,83,239,275],[1,79,82,117,119], [79,82,117,119,275],[1,79,82,117,273],[79,82,117,273,275],[79,82,238,239,275], [1,79,82,238,273],[79,82,238,273,275],[1,79,112,113,151],[79,112,113,151,307], [79,112,113,269,307],[1,79,112,145,148],[79,112,145,148,304],[1,79,112,145,151], [79,112,145,151,307],[79,112,145,301,304],[79,112,145,301,307],[79,112,268,269,307], [79,112,268,301,304],[79,112,268,301,307],[1,79,114,116,119],[79,114,116,119,275], [1,79,114,116,154],[79,114,116,154,310],[79,114,116,272,275],[79,114,116,272,310], [1,79,114,117,119],[79,114,117,119,275],[1,79,114,117,273],[79,114,117,273,275], [1,79,114,145,148],[79,114,145,148,304],[1,79,114,145,151],[79,114,145,151,307], [79,114,145,301,304],[79,114,145,301,307],[1,79,114,147,148],[79,114,147,148,304], [1,79,114,147,303],[79,114,147,303,304],[1,79,114,150,151],[79,114,150,151,307], [1,79,114,150,154],[79,114,150,154,310],[79,114,150,306,307],[79,114,150,306,310], [79,114,270,272,275],[79,114,270,272,310],[1,79,114,270,273],[79,114,270,273,275], [79,114,270,301,304],[79,114,270,301,307],[1,79,114,270,303],[79,114,270,303,304], [79,114,270,306,307],[79,114,270,306,310],[79,235,236,239,275],[79,235,236,269,307], [79,235,236,272,275],[79,235,236,272,310],[79,235,236,306,307],[79,235,236,306,310], [79,235,238,239,275],[1,79,235,238,273],[79,235,238,273,275],[79,235,268,269,307], [79,235,268,301,304],[79,235,268,301,307],[79,235,270,272,275],[79,235,270,272,310], [1,79,235,270,273],[79,235,270,273,275],[79,235,270,301,304],[79,235,270,301,307], [1,79,235,270,303],[79,235,270,303,304],[79,235,270,306,307],[79,235,270,306,310], [1,157,158,161,197],[157,158,161,197,275],[157,158,161,239,275],[1,157,158,191,229], [157,158,191,229,307],[157,158,191,269,307],[1,157,158,194,197],[157,158,194,197,275], 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