#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_006 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(350,5040,16680,19980,7992) ### ### 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:=[ [0,1,2,5,233],[0,1,2,35,263],[0,1,2,230,233],[0,1,2,230,263], [0,1,4,5,233],[0,1,4,118,232],[0,1,4,232,233],[0,1,34,35,263], [0,1,34,106,220],[0,1,34,106,334],[0,1,34,148,220],[0,1,34,262,263], [0,1,34,262,334],[0,1,105,106,220],[0,1,105,106,334],[0,1,105,219,220], [0,1,105,219,333],[0,1,105,333,334],[0,1,115,118,232],[0,1,115,148,220], [0,1,115,219,220],[0,1,115,219,333],[0,1,229,230,233],[0,1,229,230,263], [0,1,115,229,232],[0,1,229,232,233],[0,1,229,262,263],[0,1,229,262,334], [0,1,115,229,333],[0,1,229,333,334],[0,2,5,26,140],[0,2,5,26,254], [2,5,26,140,254],[0,2,5,119,140],[2,5,119,140,254],[0,2,5,233,254], [2,5,119,233,254],[0,2,26,29,143],[0,2,26,29,257],[2,26,29,143,257], [0,2,26,140,143],[2,26,140,143,257],[0,2,26,254,257],[2,26,140,254,257], [0,2,29,109,223],[0,2,29,109,337],[0,2,29,143,223],[0,2,29,257,337], [0,2,35,109,223],[0,2,35,109,337],[0,2,35,149,223],[0,2,35,263,337], [0,2,116,119,140],[2,116,119,140,254],[2,116,119,233,254],[0,2,116,140,143], [2,116,140,143,257],[2,116,140,254,257],[0,2,116,143,223],[0,2,116,149,223], [0,2,230,233,254],[2,116,230,233,254],[0,2,230,254,257],[2,116,230,254,257], [0,2,230,257,337],[0,2,230,263,337],[0,3,4,5,233],[0,3,4,118,232], [0,3,4,232,233],[0,3,5,26,140],[0,3,5,26,254],[0,3,5,119,140], [0,3,5,233,254],[0,3,24,26,140],[0,3,24,26,254],[0,3,24,138,140], [0,3,24,138,252],[0,3,24,252,254],[0,3,117,118,232],[0,3,117,119,140], [0,3,117,138,140],[0,3,117,138,252],[0,3,117,231,232],[0,3,231,232,233], [0,3,231,233,254],[0,3,117,231,252],[0,3,231,252,254],[0,24,26,29,143], [0,24,26,29,257],[0,24,26,140,143],[0,24,26,254,257],[0,24,27,29,143], [0,24,27,29,257],[0,24,27,141,143],[0,24,27,141,255],[0,24,27,255,257], [0,24,138,140,143],[0,24,138,141,143],[0,24,138,141,255],[0,24,252,254,257], [0,24,138,252,255],[0,24,252,255,257],[0,27,29,109,223],[0,27,29,109,337], [0,27,29,143,223],[0,27,29,257,337],[0,27,102,106,220],[0,27,102,106,334], [0,27,102,109,223],[0,27,102,109,337],[0,27,102,216,220],[0,27,102,216,223], [0,27,102,330,334],[0,27,102,330,337],[0,27,105,106,220],[0,27,105,106,334], [0,27,105,219,220],[0,27,105,219,333],[0,27,105,333,334],[0,27,141,143,223], [0,27,141,216,220],[0,27,141,216,223],[0,27,141,219,220],[0,27,141,219,333], [0,27,255,257,337],[0,27,255,330,334],[0,27,255,330,337],[0,27,141,255,333], [0,27,255,333,334],[0,33,34,35,263],[0,33,34,106,220],[0,33,34,106,334], [0,33,34,148,220],[0,33,34,262,263],[0,33,34,262,334],[0,33,35,109,223], [0,33,35,109,337],[0,33,35,149,223],[0,33,35,263,337],[0,33,102,106,220], [0,33,102,106,334],[0,33,102,109,223],[0,33,102,109,337],[0,33,102,216,220], [0,33,102,216,223],[0,33,102,330,334],[0,33,102,330,337],[0,33,147,148,220], [0,33,147,149,223],[0,33,147,216,220],[0,33,147,216,223],[0,33,261,262,263], [0,33,261,262,334],[0,33,261,263,337],[0,33,261,330,334],[0,33,261,330,337], [114,115,116,119,233],[114,115,116,149,263],[114,115,116,230,233],[114,115,116,230,263], [114,115,118,119,233],[0,114,115,118,232],[114,115,118,232,233],[114,115,148,149,263], [0,114,115,148,220],[114,115,148,220,334],[114,115,148,262,263],[114,115,148,262,334], [0,114,115,219,220],[114,115,219,220,334],[0,114,115,219,333],[114,115,219,333,334], [114,115,229,230,233],[114,115,229,230,263],[0,114,115,229,232],[114,115,229,232,233], [114,115,229,262,263],[114,115,229,262,334],[0,114,115,229,333],[114,115,229,333,334], [0,114,116,119,140],[114,116,119,140,254],[114,116,119,233,254],[0,114,116,140,143], [114,116,140,143,257],[114,116,140,254,257],[0,114,116,143,223],[114,116,143,223,337], [114,116,143,257,337],[0,114,116,149,223],[114,116,149,223,337],[114,116,149,263,337], [114,116,230,233,254],[114,116,230,254,257],[114,116,230,257,337],[114,116,230,263,337], [114,117,118,119,233],[0,114,117,118,232],[114,117,118,232,233],[0,114,117,119,140], [114,117,119,140,254],[114,117,119,233,254],[0,114,117,138,140],[114,117,138,140,254], [0,114,117,138,252],[114,117,138,252,254],[0,114,117,231,232],[114,117,231,232,233], [114,117,231,233,254],[0,114,117,231,252],[114,117,231,252,254],[0,114,138,140,143], [114,138,140,143,257],[114,138,140,254,257],[0,114,138,141,143],[114,138,141,143,257], [0,114,138,141,255],[114,138,141,255,257],[114,138,252,254,257],[0,114,138,252,255], [114,138,252,255,257],[0,114,141,143,223],[114,141,143,223,337],[114,141,143,257,337], [0,114,141,216,220],[114,141,216,220,334],[0,114,141,216,223],[114,141,216,223,337], [114,141,216,330,334],[114,141,216,330,337],[0,114,141,219,220],[114,141,219,220,334], [0,114,141,219,333],[114,141,219,333,334],[114,141,255,257,337],[114,141,255,330,334], [114,141,255,330,337],[0,114,141,255,333],[114,141,255,333,334],[114,147,148,149,263], [0,114,147,148,220],[114,147,148,220,334],[114,147,148,262,263],[114,147,148,262,334], [0,114,147,149,223],[114,147,149,223,337],[114,147,149,263,337],[0,114,147,216,220], [114,147,216,220,334],[0,114,147,216,223],[114,147,216,223,337],[114,147,216,330,334], [114,147,216,330,337],[114,147,261,262,263],[114,147,261,262,334],[114,147,261,263,337], [114,147,261,330,334],[114,147,261,330,337],[0,228,229,230,233],[114,228,229,230,233], [0,228,229,230,263],[114,228,229,230,263],[0,114,228,229,232],[0,228,229,232,233], [114,228,229,232,233],[0,228,229,262,263],[114,228,229,262,263],[0,228,229,262,334], [114,228,229,262,334],[0,114,228,229,333],[0,228,229,333,334],[114,228,229,333,334], [0,228,230,233,254],[114,228,230,233,254],[0,228,230,254,257],[114,228,230,254,257], [0,228,230,257,337],[114,228,230,257,337],[0,228,230,263,337],[114,228,230,263,337], [0,114,228,231,232],[0,228,231,232,233],[114,228,231,232,233],[0,228,231,233,254], [114,228,231,233,254],[0,114,228,231,252],[0,228,231,252,254],[114,228,231,252,254], [0,228,252,254,257],[114,228,252,254,257],[0,114,228,252,255],[0,228,252,255,257], [114,228,252,255,257],[0,228,255,257,337],[114,228,255,257,337],[0,228,255,330,334], [114,228,255,330,334],[0,228,255,330,337],[114,228,255,330,337],[0,114,228,255,333], [0,228,255,333,334],[114,228,255,333,334],[0,228,261,262,263],[114,228,261,262,263], [0,228,261,262,334],[114,228,261,262,334],[0,228,261,263,337],[114,228,261,263,337], [0,228,261,330,334],[114,228,261,330,334],[0,228,261,330,337],[114,228,261,330,337], [1,2,5,41,155],[1,2,5,41,269],[2,5,41,155,269],[1,2,5,119,155], [2,5,119,155,269],[1,2,5,233,269],[2,5,119,233,269],[1,2,35,109,223], [1,2,35,109,337],[1,2,35,149,223],[1,2,35,263,337],[1,2,38,41,155], [1,2,38,41,269],[2,38,41,155,269],[1,2,38,112,226],[1,2,38,112,340], [1,2,38,152,155],[2,38,152,155,269],[1,2,38,152,226],[1,2,38,266,269], [2,38,152,266,269],[1,2,38,266,340],[1,2,108,109,223],[1,2,108,109,337], [1,2,108,112,226],[1,2,108,112,340],[1,2,108,222,223],[1,2,108,222,226], [1,2,108,336,337],[1,2,108,336,340],[1,2,116,119,155],[2,116,119,155,269], [2,116,119,233,269],[1,2,116,149,223],[1,2,116,152,155],[2,116,152,155,269], [1,2,116,152,226],[2,116,152,266,269],[1,2,116,222,223],[1,2,116,222,226], [1,2,230,233,269],[2,116,230,233,269],[1,2,230,263,337],[1,2,230,266,269], [2,116,230,266,269],[1,2,230,266,340],[1,2,230,336,337],[1,2,230,336,340], [1,4,5,41,155],[1,4,5,41,269],[1,4,5,119,155],[1,4,5,233,269], [1,4,39,41,155],[1,4,39,41,269],[1,4,39,153,155],[1,4,39,153,267], [1,4,39,267,269],[1,4,118,119,155],[1,4,118,153,155],[1,4,118,153,267], [1,4,232,233,269],[1,4,118,232,267],[1,4,232,267,269],[1,34,35,109,223], [1,34,35,109,337],[1,34,35,149,223],[1,34,35,263,337],[1,34,103,106,220], [1,34,103,106,334],[1,34,103,109,223],[1,34,103,109,337],[1,34,103,217,220], [1,34,103,217,223],[1,34,103,331,334],[1,34,103,331,337],[1,34,148,149,223], [1,34,148,217,220],[1,34,148,217,223],[1,34,262,263,337],[1,34,262,331,334], [1,34,262,331,337],[1,36,38,41,155],[1,36,38,41,269],[1,36,38,112,226], [1,36,38,112,340],[1,36,38,152,155],[1,36,38,152,226],[1,36,38,266,269], [1,36,38,266,340],[1,36,39,41,155],[1,36,39,41,269],[1,36,39,153,155], [1,36,39,153,267],[1,36,39,267,269],[1,36,103,106,220],[1,36,103,106,334], [1,36,103,109,223],[1,36,103,109,337],[1,36,103,217,220],[1,36,103,217,223], [1,36,103,331,334],[1,36,103,331,337],[1,36,105,106,220],[1,36,105,106,334], [1,36,105,219,220],[1,36,105,219,333],[1,36,105,333,334],[1,36,108,109,223], [1,36,108,109,337],[1,36,108,112,226],[1,36,108,112,340],[1,36,108,222,223], [1,36,108,222,226],[1,36,108,336,337],[1,36,108,336,340],[1,36,150,152,155], [1,36,150,152,226],[1,36,150,153,155],[1,36,150,153,267],[1,36,150,217,220], [1,36,150,217,223],[1,36,150,219,220],[1,36,150,219,333],[1,36,150,222,223], [1,36,150,222,226],[1,36,264,266,269],[1,36,264,266,340],[1,36,150,264,267], [1,36,264,267,269],[1,36,264,331,334],[1,36,264,331,337],[1,36,150,264,333], [1,36,264,333,334],[1,36,264,336,337],[1,36,264,336,340],[1,115,116,119,155], [115,116,119,155,269],[115,116,119,233,269],[1,115,116,149,223],[115,116,149,223,337], [115,116,149,263,337],[1,115,116,152,155],[115,116,152,155,269],[1,115,116,152,226], [115,116,152,226,340],[115,116,152,266,269],[115,116,152,266,340],[1,115,116,222,223], [115,116,222,223,337],[1,115,116,222,226],[115,116,222,226,340],[115,116,222,336,337], [115,116,222,336,340],[115,116,230,233,269],[115,116,230,263,337],[115,116,230,266,269], [115,116,230,266,340],[115,116,230,336,337],[115,116,230,336,340],[1,115,118,119,155], [115,118,119,155,269],[115,118,119,233,269],[1,115,118,153,155],[115,118,153,155,269], [1,115,118,153,267],[115,118,153,267,269],[115,118,232,233,269],[1,115,118,232,267], [115,118,232,267,269],[1,115,148,149,223],[115,148,149,223,337],[115,148,149,263,337], [1,115,148,217,220],[115,148,217,220,334],[1,115,148,217,223],[115,148,217,223,337], [115,148,217,331,334],[115,148,217,331,337],[115,148,262,263,337],[115,148,262,331,334], [115,148,262,331,337],[1,115,150,152,155],[115,150,152,155,269],[1,115,150,152,226], [115,150,152,226,340],[115,150,152,266,269],[115,150,152,266,340],[1,115,150,153,155], [115,150,153,155,269],[1,115,150,153,267],[115,150,153,267,269],[1,115,150,217,220], [115,150,217,220,334],[1,115,150,217,223],[115,150,217,223,337],[115,150,217,331,334], [115,150,217,331,337],[1,115,150,219,220],[115,150,219,220,334],[1,115,150,219,333], [115,150,219,333,334],[1,115,150,222,223],[115,150,222,223,337],[1,115,150,222,226], [115,150,222,226,340],[115,150,222,336,337],[115,150,222,336,340],[115,150,264,266,269], [115,150,264,266,340],[1,115,150,264,267],[115,150,264,267,269],[115,150,264,331,334], [115,150,264,331,337],[1,115,150,264,333],[115,150,264,333,334],[115,150,264,336,337], [115,150,264,336,340],[1,229,230,233,269],[115,229,230,233,269],[1,229,230,263,337], [115,229,230,263,337],[1,229,230,266,269],[115,229,230,266,269],[1,229,230,266,340], [115,229,230,266,340],[1,229,230,336,337],[115,229,230,336,337],[1,229,230,336,340], [115,229,230,336,340],[1,229,232,233,269],[115,229,232,233,269],[1,115,229,232,267], [1,229,232,267,269],[115,229,232,267,269],[1,229,262,263,337],[115,229,262,263,337], [1,229,262,331,334],[115,229,262,331,334],[1,229,262,331,337],[115,229,262,331,337], [1,229,264,266,269],[115,229,264,266,269],[1,229,264,266,340],[115,229,264,266,340], [1,115,229,264,267],[1,229,264,267,269],[115,229,264,267,269],[1,229,264,331,334], [115,229,264,331,334],[1,229,264,331,337],[115,229,264,331,337],[1,115,229,264,333], [1,229,264,333,334],[115,229,264,333,334],[1,229,264,336,337],[115,229,264,336,337], [1,229,264,336,340],[115,229,264,336,340],[2,29,108,109,223],[2,29,108,109,337], [2,29,108,112,226],[2,29,108,112,340],[2,29,108,222,223],[2,29,108,222,226], [2,29,108,336,337],[2,29,108,336,340],[2,29,110,112,226],[2,29,110,112,340], [2,29,110,224,226],[2,29,110,224,338],[2,29,110,338,340],[2,29,143,222,223], [2,29,143,222,226],[2,29,143,224,226],[2,29,143,224,338],[2,29,257,336,337], [2,29,257,336,340],[2,29,143,257,338],[2,29,257,338,340],[2,38,110,112,226], [2,38,110,112,340],[2,38,110,224,226],[2,38,110,224,338],[2,38,110,338,340], [2,38,152,224,226],[2,38,152,224,338],[2,38,152,266,338],[2,38,266,338,340], [2,116,143,222,223],[116,143,222,223,337],[2,116,143,222,226],[116,143,222,226,340], [116,143,222,336,337],[116,143,222,336,340],[2,116,143,224,226],[116,143,224,226,340], [2,116,143,224,338],[116,143,224,338,340],[116,143,257,336,337],[116,143,257,336,340], [2,116,143,257,338],[116,143,257,338,340],[2,116,152,224,226],[116,152,224,226,340], [2,116,152,224,338],[116,152,224,338,340],[2,116,152,266,338],[116,152,266,338,340], [2,230,257,336,337],[116,230,257,336,337],[2,230,257,336,340],[116,230,257,336,340], [2,116,230,257,338],[2,230,257,338,340],[116,230,257,338,340],[2,116,230,266,338], [2,230,266,338,340],[116,230,266,338,340],[3,4,5,8,236],[3,4,5,233,236], [3,4,7,8,236],[3,4,7,106,220],[3,4,7,106,334],[3,4,7,121,220], [3,4,7,235,236],[3,4,7,235,334],[3,4,105,106,220],[3,4,105,106,334], [3,4,105,219,220],[3,4,105,219,333],[3,4,105,333,334],[3,4,118,121,220], [3,4,118,219,220],[3,4,118,219,333],[3,4,232,233,236],[3,4,232,235,236], [3,4,232,235,334],[3,4,118,232,333],[3,4,232,333,334],[3,5,8,23,137], [3,5,8,23,251],[5,8,23,137,251],[3,5,8,122,137],[5,8,122,137,251], [3,5,8,236,251],[5,8,122,236,251],[3,5,23,26,140],[3,5,23,26,254], [5,23,26,140,254],[3,5,23,137,140],[5,23,137,140,254],[3,5,23,251,254], [5,23,137,251,254],[3,5,119,122,137],[5,119,122,137,251],[5,119,122,236,251], [3,5,119,137,140],[5,119,137,140,254],[5,119,137,251,254],[3,5,233,236,251], [5,119,233,236,251],[3,5,233,251,254],[5,119,233,251,254],[3,6,7,8,236], [3,6,7,106,220],[3,6,7,106,334],[3,6,7,121,220],[3,6,7,235,236], [3,6,7,235,334],[3,6,8,23,137],[3,6,8,23,251],[3,6,8,122,137], [3,6,8,236,251],[3,6,21,23,137],[3,6,21,23,251],[3,6,21,106,220], [3,6,21,106,334],[3,6,21,135,137],[3,6,21,135,220],[3,6,21,249,251], [3,6,21,249,334],[3,6,120,121,220],[3,6,120,122,137],[3,6,120,135,137], [3,6,120,135,220],[3,6,234,235,236],[3,6,234,235,334],[3,6,234,236,251], [3,6,234,249,251],[3,6,234,249,334],[3,21,23,26,140],[3,21,23,26,254], [3,21,23,137,140],[3,21,23,251,254],[3,21,24,26,140],[3,21,24,26,254], [3,21,24,106,220],[3,21,24,106,334],[3,21,24,138,140],[3,21,24,138,220], [3,21,24,252,254],[3,21,24,252,334],[3,21,135,137,140],[3,21,135,138,140], [3,21,135,138,220],[3,21,249,251,254],[3,21,249,252,254],[3,21,249,252,334], [3,24,105,106,220],[3,24,105,106,334],[3,24,105,219,220],[3,24,105,219,333], [3,24,105,333,334],[3,24,138,219,220],[3,24,138,219,333],[3,24,138,252,333], [3,24,252,333,334],[117,118,119,122,236],[117,118,119,233,236],[117,118,121,122,236], [3,117,118,121,220],[117,118,121,220,334],[117,118,121,235,236],[117,118,121,235,334], [3,117,118,219,220],[117,118,219,220,334],[3,117,118,219,333],[117,118,219,333,334], [117,118,232,233,236],[117,118,232,235,236],[117,118,232,235,334],[3,117,118,232,333], [117,118,232,333,334],[3,117,119,122,137],[117,119,122,137,251],[117,119,122,236,251], [3,117,119,137,140],[117,119,137,140,254],[117,119,137,251,254],[117,119,233,236,251], [117,119,233,251,254],[117,120,121,122,236],[3,117,120,121,220],[117,120,121,220,334], [117,120,121,235,236],[117,120,121,235,334],[3,117,120,122,137],[117,120,122,137,251], 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