#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_006 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(464,7014,23436,28140,11256) ### ### 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],[0,1,4,118,346],[0,1,4,232,233],[0,1,4,232,346], [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],[0,1,105,219,447],[0,1,105,333,334],[0,1,105,333,447], [0,1,115,118,346],[0,1,115,148,220],[0,1,115,219,220],[0,1,115,219,447], [0,1,115,343,346],[0,1,115,343,447],[0,1,229,230,233],[0,1,229,230,263], [0,1,229,232,233],[0,1,229,232,346],[0,1,229,262,263],[0,1,229,262,334], [0,1,229,333,334],[0,1,229,333,447],[0,1,229,343,346],[0,1,229,343,447], [0,2,5,26,140],[2,5,26,140,368],[0,2,5,26,254],[2,5,26,254,368], [0,2,5,119,140],[2,5,119,140,368],[2,5,119,347,368],[0,2,5,233,254], [2,5,233,254,368],[2,5,233,347,368],[0,2,26,29,143],[2,26,29,143,371], [0,2,26,29,257],[2,26,29,257,371],[0,2,26,140,143],[2,26,140,143,371], [2,26,140,368,371],[0,2,26,254,257],[2,26,254,257,371],[2,26,254,368,371], [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],[2,116,119,140,368],[2,116,119,347,368],[0,2,116,140,143], [2,116,140,143,371],[2,116,140,368,371],[0,2,116,143,223],[0,2,116,149,223], [2,116,344,347,368],[2,116,344,368,371],[0,2,230,233,254],[2,230,233,254,368], [2,230,233,347,368],[0,2,230,254,257],[2,230,254,257,371],[2,230,254,368,371], [0,2,230,257,337],[0,2,230,263,337],[2,230,344,347,368],[2,230,344,368,371], [0,3,4,5,233],[0,3,4,118,346],[0,3,4,232,233],[0,3,4,232,346], [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],[0,3,24,138,366], [0,3,24,252,254],[0,3,24,252,366],[0,3,117,118,346],[0,3,117,119,140], [0,3,117,138,140],[0,3,117,138,366],[0,3,117,345,346],[0,3,117,345,366], [0,3,231,232,233],[0,3,231,232,346],[0,3,231,233,254],[0,3,231,252,254], [0,3,231,252,366],[0,3,231,345,346],[0,3,231,345,366],[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],[0,24,27,141,369],[0,24,27,255,257], [0,24,27,255,369],[0,24,138,140,143],[0,24,138,141,143],[0,24,138,141,369], [0,24,138,366,369],[0,24,252,254,257],[0,24,252,255,257],[0,24,252,255,369], [0,24,252,366,369],[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], [0,27,105,219,447],[0,27,105,333,334],[0,27,105,333,447],[0,27,141,143,223], [0,27,141,216,220],[0,27,141,216,223],[0,27,141,219,220],[0,27,141,219,447], [0,27,141,369,447],[0,27,255,257,337],[0,27,255,330,334],[0,27,255,330,337], [0,27,255,333,334],[0,27,255,333,447],[0,27,255,369,447],[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],[114,115,116,119,347],[114,115,116,149,377], [114,115,116,344,347],[114,115,116,344,377],[114,115,118,119,347],[0,114,115,118,346], [114,115,118,346,347],[114,115,148,149,377],[0,114,115,148,220],[114,115,148,220,448], [114,115,148,376,377],[114,115,148,376,448],[0,114,115,219,220],[114,115,219,220,448], [0,114,115,219,447],[114,115,219,447,448],[114,115,343,344,347],[114,115,343,344,377], [0,114,115,343,346],[114,115,343,346,347],[114,115,343,376,377],[114,115,343,376,448], [0,114,115,343,447],[114,115,343,447,448],[0,114,116,119,140],[114,116,119,140,368], [114,116,119,347,368],[0,114,116,140,143],[114,116,140,143,371],[114,116,140,368,371], [0,114,116,143,223],[114,116,143,223,451],[114,116,143,371,451],[0,114,116,149,223], [114,116,149,223,451],[114,116,149,377,451],[114,116,344,347,368],[114,116,344,368,371], [114,116,344,371,451],[114,116,344,377,451],[114,117,118,119,347],[0,114,117,118,346], [114,117,118,346,347],[0,114,117,119,140],[114,117,119,140,368],[114,117,119,347,368], [0,114,117,138,140],[114,117,138,140,368],[0,114,117,138,366],[114,117,138,366,368], [0,114,117,345,346],[114,117,345,346,347],[114,117,345,347,368],[0,114,117,345,366], [114,117,345,366,368],[0,114,138,140,143],[114,138,140,143,371],[114,138,140,368,371], [0,114,138,141,143],[114,138,141,143,371],[0,114,138,141,369],[114,138,141,369,371], [114,138,366,368,371],[0,114,138,366,369],[114,138,366,369,371],[0,114,141,143,223], [114,141,143,223,451],[114,141,143,371,451],[0,114,141,216,220],[114,141,216,220,448], [0,114,141,216,223],[114,141,216,223,451],[114,141,216,444,448],[114,141,216,444,451], [0,114,141,219,220],[114,141,219,220,448],[0,114,141,219,447],[114,141,219,447,448], [114,141,369,371,451],[114,141,369,444,448],[114,141,369,444,451],[0,114,141,369,447], [114,141,369,447,448],[114,147,148,149,377],[0,114,147,148,220],[114,147,148,220,448], [114,147,148,376,377],[114,147,148,376,448],[0,114,147,149,223],[114,147,149,223,451], [114,147,149,377,451],[0,114,147,216,220],[114,147,216,220,448],[0,114,147,216,223], [114,147,216,223,451],[114,147,216,444,448],[114,147,216,444,451],[114,147,375,376,377], [114,147,375,376,448],[114,147,375,377,451],[114,147,375,444,448],[114,147,375,444,451], [114,342,343,344,347],[114,342,343,344,377],[0,114,342,343,346],[114,342,343,346,347], [114,342,343,376,377],[114,342,343,376,448],[0,114,342,343,447],[114,342,343,447,448], [114,342,344,347,368],[114,342,344,368,371],[114,342,344,371,451],[114,342,344,377,451], [0,114,342,345,346],[114,342,345,346,347],[114,342,345,347,368],[0,114,342,345,366], [114,342,345,366,368],[114,342,366,368,371],[0,114,342,366,369],[114,342,366,369,371], [114,342,369,371,451],[114,342,369,444,448],[114,342,369,444,451],[0,114,342,369,447], [114,342,369,447,448],[114,342,375,376,377],[114,342,375,376,448],[114,342,375,377,451], [114,342,375,444,448],[114,342,375,444,451],[0,228,229,230,233],[228,229,230,233,347], [0,228,229,230,263],[228,229,230,263,377],[228,229,230,344,347],[228,229,230,344,377], [0,228,229,232,233],[228,229,232,233,347],[0,228,229,232,346],[228,229,232,346,347], [0,228,229,262,263],[228,229,262,263,377],[0,228,229,262,334],[228,229,262,334,448], [228,229,262,376,377],[228,229,262,376,448],[0,228,229,333,334],[228,229,333,334,448], [0,228,229,333,447],[228,229,333,447,448],[228,229,343,344,347],[228,229,343,344,377], [0,228,229,343,346],[228,229,343,346,347],[228,229,343,376,377],[228,229,343,376,448], [0,228,229,343,447],[228,229,343,447,448],[0,228,230,233,254],[228,230,233,254,368], [228,230,233,347,368],[0,228,230,254,257],[228,230,254,257,371],[228,230,254,368,371], [0,228,230,257,337],[228,230,257,337,451],[228,230,257,371,451],[0,228,230,263,337], [228,230,263,337,451],[228,230,263,377,451],[228,230,344,347,368],[228,230,344,368,371], [228,230,344,371,451],[228,230,344,377,451],[0,228,231,232,233],[228,231,232,233,347], [0,228,231,232,346],[228,231,232,346,347],[0,228,231,233,254],[228,231,233,254,368], [228,231,233,347,368],[0,228,231,252,254],[228,231,252,254,368],[0,228,231,252,366], [228,231,252,366,368],[0,228,231,345,346],[228,231,345,346,347],[228,231,345,347,368], [0,228,231,345,366],[228,231,345,366,368],[0,228,252,254,257],[228,252,254,257,371], [228,252,254,368,371],[0,228,252,255,257],[228,252,255,257,371],[0,228,252,255,369], [228,252,255,369,371],[228,252,366,368,371],[0,228,252,366,369],[228,252,366,369,371], [0,228,255,257,337],[228,255,257,337,451],[228,255,257,371,451],[0,228,255,330,334], [228,255,330,334,448],[0,228,255,330,337],[228,255,330,337,451],[228,255,330,444,448], [228,255,330,444,451],[0,228,255,333,334],[228,255,333,334,448],[0,228,255,333,447], [228,255,333,447,448],[228,255,369,371,451],[228,255,369,444,448],[228,255,369,444,451], [0,228,255,369,447],[228,255,369,447,448],[0,228,261,262,263],[228,261,262,263,377], [0,228,261,262,334],[228,261,262,334,448],[228,261,262,376,377],[228,261,262,376,448], [0,228,261,263,337],[228,261,263,337,451],[228,261,263,377,451],[0,228,261,330,334], [228,261,330,334,448],[0,228,261,330,337],[228,261,330,337,451],[228,261,330,444,448], [228,261,330,444,451],[228,261,375,376,377],[228,261,375,376,448],[228,261,375,377,451], [228,261,375,444,448],[228,261,375,444,451],[228,342,343,344,347],[228,342,343,344,377], [0,228,342,343,346],[228,342,343,346,347],[228,342,343,376,377],[228,342,343,376,448], [0,228,342,343,447],[228,342,343,447,448],[228,342,344,347,368],[228,342,344,368,371], [228,342,344,371,451],[228,342,344,377,451],[0,228,342,345,346],[228,342,345,346,347], [228,342,345,347,368],[0,228,342,345,366],[228,342,345,366,368],[228,342,366,368,371], [0,228,342,366,369],[228,342,366,369,371],[228,342,369,371,451],[228,342,369,444,448], [228,342,369,444,451],[0,228,342,369,447],[228,342,369,447,448],[228,342,375,376,377], [228,342,375,376,448],[228,342,375,377,451],[228,342,375,444,448],[228,342,375,444,451], [1,2,5,41,155],[2,5,41,155,383],[1,2,5,41,269],[2,5,41,269,383], [1,2,5,119,155],[2,5,119,155,383],[2,5,119,347,383],[1,2,5,233,269], [2,5,233,269,383],[2,5,233,347,383],[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],[2,38,41,155,383], [1,2,38,41,269],[2,38,41,269,383],[1,2,38,112,226],[1,2,38,112,340], [1,2,38,152,155],[2,38,152,155,383],[1,2,38,152,226],[2,38,152,380,383], [1,2,38,266,269],[2,38,266,269,383],[1,2,38,266,340],[2,38,266,380,383], [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],[2,116,119,155,383],[2,116,119,347,383],[1,2,116,149,223], [1,2,116,152,155],[2,116,152,155,383],[1,2,116,152,226],[2,116,152,380,383], [1,2,116,222,223],[1,2,116,222,226],[2,116,344,347,383],[2,116,344,380,383], [1,2,230,233,269],[2,230,233,269,383],[2,230,233,347,383],[1,2,230,263,337], [1,2,230,266,269],[2,230,266,269,383],[1,2,230,266,340],[2,230,266,380,383], [1,2,230,336,337],[1,2,230,336,340],[2,230,344,347,383],[2,230,344,380,383], [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],[1,4,39,153,381], [1,4,39,267,269],[1,4,39,267,381],[1,4,118,119,155],[1,4,118,153,155], [1,4,118,153,381],[1,4,118,346,381],[1,4,232,233,269],[1,4,232,267,269], [1,4,232,267,381],[1,4,232,346,381],[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],[1,36,39,153,381], [1,36,39,267,269],[1,36,39,267,381],[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],[1,36,105,219,447],[1,36,105,333,334],[1,36,105,333,447], [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],[1,36,150,153,381], [1,36,150,217,220],[1,36,150,217,223],[1,36,150,219,220],[1,36,150,219,447], [1,36,150,222,223],[1,36,150,222,226],[1,36,150,378,381],[1,36,150,378,447], [1,36,264,266,269],[1,36,264,266,340],[1,36,264,267,269],[1,36,264,267,381], [1,36,264,331,334],[1,36,264,331,337],[1,36,264,333,334],[1,36,264,333,447], [1,36,264,336,337],[1,36,264,336,340],[1,36,264,378,381],[1,36,264,378,447], [1,115,116,119,155],[115,116,119,155,383],[115,116,119,347,383],[1,115,116,149,223], [115,116,149,223,451],[115,116,149,377,451],[1,115,116,152,155],[115,116,152,155,383], [1,115,116,152,226],[115,116,152,226,454],[115,116,152,380,383],[115,116,152,380,454], [1,115,116,222,223],[115,116,222,223,451],[1,115,116,222,226],[115,116,222,226,454], [115,116,222,450,451],[115,116,222,450,454],[115,116,344,347,383],[115,116,344,377,451], [115,116,344,380,383],[115,116,344,380,454],[115,116,344,450,451],[115,116,344,450,454], [1,115,118,119,155],[115,118,119,155,383],[115,118,119,347,383],[1,115,118,153,155], [115,118,153,155,383],[1,115,118,153,381],[115,118,153,381,383],[115,118,346,347,383], [1,115,118,346,381],[115,118,346,381,383],[1,115,148,149,223],[115,148,149,223,451], [115,148,149,377,451],[1,115,148,217,220],[115,148,217,220,448],[1,115,148,217,223], 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[90,93,95,101,215],[90,93,95,101,329],[90,93,95,209,215],[90,93,95,323,329], [90,93,100,101,215],[90,93,100,101,329],[90,93,100,214,215],[90,93,100,214,442], [90,93,100,328,329],[90,93,100,328,442],[90,93,207,208,436],[90,93,207,209,215], [90,93,207,214,215],[90,93,207,214,442],[90,93,207,435,436],[90,93,207,435,442], [90,93,321,322,323],[90,93,321,322,436],[90,93,321,323,329],[90,93,321,328,329], [90,93,321,328,442],[90,93,321,435,436],[90,93,321,435,442],[90,97,98,101,215], [90,97,98,101,329],[90,97,98,212,215],[90,97,98,326,329],[90,97,100,101,215], [90,97,100,101,329],[90,97,100,214,215],[90,97,100,214,442],[90,97,100,328,329], [90,97,100,328,442],[90,97,211,212,215],[90,97,211,214,215],[90,97,211,214,442], [90,97,211,439,442],[90,97,325,326,329],[90,97,325,328,329],[90,97,325,328,442], [90,97,325,439,442],[204,205,206,209,437],[204,205,206,434,437],[204,205,208,209,437], [90,204,205,208,436],[204,205,208,436,437],[204,205,433,434,437],[90,204,205,433,436], 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