#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_009 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(608,9174,30636,36780,14712) ### ### 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:=[ [0,1,2,5,305],[0,1,2,35,335],[0,1,2,302,305],[0,1,2,302,335], [0,1,4,5,305],[0,1,4,154,454],[0,1,4,304,305],[0,1,4,304,454], [0,1,34,35,335],[0,1,34,142,292],[0,1,34,142,442],[0,1,34,184,292], [0,1,34,334,335],[0,1,34,334,442],[0,1,141,142,292],[0,1,141,142,442], [0,1,141,291,292],[0,1,141,291,591],[0,1,141,441,442],[0,1,141,441,591], [0,1,151,154,454],[0,1,151,184,292],[0,1,151,291,292],[0,1,151,291,591], [0,1,151,451,454],[0,1,151,451,591],[0,1,301,302,305],[0,1,301,302,335], [0,1,301,304,305],[0,1,301,304,454],[0,1,301,334,335],[0,1,301,334,442], [0,1,301,441,442],[0,1,301,441,591],[0,1,301,451,454],[0,1,301,451,591], [0,2,5,26,176],[2,5,26,176,476],[0,2,5,26,326],[2,5,26,326,476], [0,2,5,155,176],[2,5,155,176,476],[2,5,155,455,476],[0,2,5,305,326], [2,5,305,326,476],[2,5,305,455,476],[0,2,26,29,179],[2,26,29,179,479], [0,2,26,29,329],[2,26,29,329,479],[0,2,26,176,179],[2,26,176,179,479], [2,26,176,476,479],[0,2,26,326,329],[2,26,326,329,479],[2,26,326,476,479], [0,2,29,145,295],[0,2,29,145,445],[0,2,29,179,295],[0,2,29,329,445], [0,2,35,145,295],[0,2,35,145,445],[0,2,35,185,295],[0,2,35,335,445], [0,2,152,155,176],[2,152,155,176,476],[2,152,155,455,476],[0,2,152,176,179], [2,152,176,179,479],[2,152,176,476,479],[0,2,152,179,295],[0,2,152,185,295], [2,152,452,455,476],[2,152,452,476,479],[0,2,302,305,326],[2,302,305,326,476], [2,302,305,455,476],[0,2,302,326,329],[2,302,326,329,479],[2,302,326,476,479], [0,2,302,329,445],[0,2,302,335,445],[2,302,452,455,476],[2,302,452,476,479], [0,3,4,5,305],[0,3,4,154,454],[0,3,4,304,305],[0,3,4,304,454], [0,3,5,26,176],[0,3,5,26,326],[0,3,5,155,176],[0,3,5,305,326], [0,3,24,26,176],[0,3,24,26,326],[0,3,24,174,176],[0,3,24,174,474], [0,3,24,324,326],[0,3,24,324,474],[0,3,153,154,454],[0,3,153,155,176], [0,3,153,174,176],[0,3,153,174,474],[0,3,153,453,454],[0,3,153,453,474], [0,3,303,304,305],[0,3,303,304,454],[0,3,303,305,326],[0,3,303,324,326], [0,3,303,324,474],[0,3,303,453,454],[0,3,303,453,474],[0,24,26,29,179], [0,24,26,29,329],[0,24,26,176,179],[0,24,26,326,329],[0,24,27,29,179], [0,24,27,29,329],[0,24,27,177,179],[0,24,27,177,477],[0,24,27,327,329], [0,24,27,327,477],[0,24,174,176,179],[0,24,174,177,179],[0,24,174,177,477], [0,24,174,474,477],[0,24,324,326,329],[0,24,324,327,329],[0,24,324,327,477], [0,24,324,474,477],[0,27,29,145,295],[0,27,29,145,445],[0,27,29,179,295], [0,27,29,329,445],[0,27,138,142,292],[0,27,138,142,442],[0,27,138,145,295], [0,27,138,145,445],[0,27,138,288,292],[0,27,138,288,295],[0,27,138,438,442], [0,27,138,438,445],[0,27,141,142,292],[0,27,141,142,442],[0,27,141,291,292], [0,27,141,291,591],[0,27,141,441,442],[0,27,141,441,591],[0,27,177,179,295], [0,27,177,288,292],[0,27,177,288,295],[0,27,177,291,292],[0,27,177,291,591], [0,27,177,477,591],[0,27,327,329,445],[0,27,327,438,442],[0,27,327,438,445], [0,27,327,441,442],[0,27,327,441,591],[0,27,327,477,591],[0,33,34,35,335], [0,33,34,142,292],[0,33,34,142,442],[0,33,34,184,292],[0,33,34,334,335], [0,33,34,334,442],[0,33,35,145,295],[0,33,35,145,445],[0,33,35,185,295], [0,33,35,335,445],[0,33,138,142,292],[0,33,138,142,442],[0,33,138,145,295], [0,33,138,145,445],[0,33,138,288,292],[0,33,138,288,295],[0,33,138,438,442], [0,33,138,438,445],[0,33,183,184,292],[0,33,183,185,295],[0,33,183,288,292], [0,33,183,288,295],[0,33,333,334,335],[0,33,333,334,442],[0,33,333,335,445], [0,33,333,438,442],[0,33,333,438,445],[150,151,152,155,455],[150,151,152,185,485], [150,151,152,452,455],[150,151,152,452,485],[150,151,154,155,455],[0,150,151,154,454], [150,151,154,454,455],[150,151,184,185,485],[0,150,151,184,292],[150,151,184,292,592], [150,151,184,484,485],[150,151,184,484,592],[0,150,151,291,292],[150,151,291,292,592], [0,150,151,291,591],[150,151,291,591,592],[150,151,451,452,455],[150,151,451,452,485], [0,150,151,451,454],[150,151,451,454,455],[150,151,451,484,485],[150,151,451,484,592], [0,150,151,451,591],[150,151,451,591,592],[0,150,152,155,176],[150,152,155,176,476], [150,152,155,455,476],[0,150,152,176,179],[150,152,176,179,479],[150,152,176,476,479], [0,150,152,179,295],[150,152,179,295,595],[150,152,179,479,595],[0,150,152,185,295], [150,152,185,295,595],[150,152,185,485,595],[150,152,452,455,476],[150,152,452,476,479], [150,152,452,479,595],[150,152,452,485,595],[150,153,154,155,455],[0,150,153,154,454], [150,153,154,454,455],[0,150,153,155,176],[150,153,155,176,476],[150,153,155,455,476], [0,150,153,174,176],[150,153,174,176,476],[0,150,153,174,474],[150,153,174,474,476], [0,150,153,453,454],[150,153,453,454,455],[150,153,453,455,476],[0,150,153,453,474], [150,153,453,474,476],[0,150,174,176,179],[150,174,176,179,479],[150,174,176,476,479], [0,150,174,177,179],[150,174,177,179,479],[0,150,174,177,477],[150,174,177,477,479], [150,174,474,476,479],[0,150,174,474,477],[150,174,474,477,479],[0,150,177,179,295], [150,177,179,295,595],[150,177,179,479,595],[0,150,177,288,292],[150,177,288,292,592], [0,150,177,288,295],[150,177,288,295,595],[150,177,288,588,592],[150,177,288,588,595], [0,150,177,291,292],[150,177,291,292,592],[0,150,177,291,591],[150,177,291,591,592], [150,177,477,479,595],[150,177,477,588,592],[150,177,477,588,595],[0,150,177,477,591], [150,177,477,591,592],[150,183,184,185,485],[0,150,183,184,292],[150,183,184,292,592], [150,183,184,484,485],[150,183,184,484,592],[0,150,183,185,295],[150,183,185,295,595], [150,183,185,485,595],[0,150,183,288,292],[150,183,288,292,592],[0,150,183,288,295], [150,183,288,295,595],[150,183,288,588,592],[150,183,288,588,595],[150,183,483,484,485], [150,183,483,484,592],[150,183,483,485,595],[150,183,483,588,592],[150,183,483,588,595], [150,450,451,452,455],[150,450,451,452,485],[0,150,450,451,454],[150,450,451,454,455], [150,450,451,484,485],[150,450,451,484,592],[0,150,450,451,591],[150,450,451,591,592], [150,450,452,455,476],[150,450,452,476,479],[150,450,452,479,595],[150,450,452,485,595], [0,150,450,453,454],[150,450,453,454,455],[150,450,453,455,476],[0,150,450,453,474], [150,450,453,474,476],[150,450,474,476,479],[0,150,450,474,477],[150,450,474,477,479], [150,450,477,479,595],[150,450,477,588,592],[150,450,477,588,595],[0,150,450,477,591], [150,450,477,591,592],[150,450,483,484,485],[150,450,483,484,592],[150,450,483,485,595], [150,450,483,588,592],[150,450,483,588,595],[0,300,301,302,305],[300,301,302,305,455], [0,300,301,302,335],[300,301,302,335,485],[300,301,302,452,455],[300,301,302,452,485], [0,300,301,304,305],[300,301,304,305,455],[0,300,301,304,454],[300,301,304,454,455], [0,300,301,334,335],[300,301,334,335,485],[0,300,301,334,442],[300,301,334,442,592], [300,301,334,484,485],[300,301,334,484,592],[0,300,301,441,442],[300,301,441,442,592], [0,300,301,441,591],[300,301,441,591,592],[300,301,451,452,455],[300,301,451,452,485], [0,300,301,451,454],[300,301,451,454,455],[300,301,451,484,485],[300,301,451,484,592], [0,300,301,451,591],[300,301,451,591,592],[0,300,302,305,326],[300,302,305,326,476], [300,302,305,455,476],[0,300,302,326,329],[300,302,326,329,479],[300,302,326,476,479], [0,300,302,329,445],[300,302,329,445,595],[300,302,329,479,595],[0,300,302,335,445], [300,302,335,445,595],[300,302,335,485,595],[300,302,452,455,476],[300,302,452,476,479], [300,302,452,479,595],[300,302,452,485,595],[0,300,303,304,305],[300,303,304,305,455], [0,300,303,304,454],[300,303,304,454,455],[0,300,303,305,326],[300,303,305,326,476], [300,303,305,455,476],[0,300,303,324,326],[300,303,324,326,476],[0,300,303,324,474], [300,303,324,474,476],[0,300,303,453,454],[300,303,453,454,455],[300,303,453,455,476], [0,300,303,453,474],[300,303,453,474,476],[0,300,324,326,329],[300,324,326,329,479], [300,324,326,476,479],[0,300,324,327,329],[300,324,327,329,479],[0,300,324,327,477], [300,324,327,477,479],[300,324,474,476,479],[0,300,324,474,477],[300,324,474,477,479], [0,300,327,329,445],[300,327,329,445,595],[300,327,329,479,595],[0,300,327,438,442], [300,327,438,442,592],[0,300,327,438,445],[300,327,438,445,595],[300,327,438,588,592], [300,327,438,588,595],[0,300,327,441,442],[300,327,441,442,592],[0,300,327,441,591], [300,327,441,591,592],[300,327,477,479,595],[300,327,477,588,592],[300,327,477,588,595], [0,300,327,477,591],[300,327,477,591,592],[0,300,333,334,335],[300,333,334,335,485], [0,300,333,334,442],[300,333,334,442,592],[300,333,334,484,485],[300,333,334,484,592], [0,300,333,335,445],[300,333,335,445,595],[300,333,335,485,595],[0,300,333,438,442], [300,333,438,442,592],[0,300,333,438,445],[300,333,438,445,595],[300,333,438,588,592], [300,333,438,588,595],[300,333,483,484,485],[300,333,483,484,592],[300,333,483,485,595], [300,333,483,588,592],[300,333,483,588,595],[300,450,451,452,455],[300,450,451,452,485], [0,300,450,451,454],[300,450,451,454,455],[300,450,451,484,485],[300,450,451,484,592], [0,300,450,451,591],[300,450,451,591,592],[300,450,452,455,476],[300,450,452,476,479], [300,450,452,479,595],[300,450,452,485,595],[0,300,450,453,454],[300,450,453,454,455], [300,450,453,455,476],[0,300,450,453,474],[300,450,453,474,476],[300,450,474,476,479], [0,300,450,474,477],[300,450,474,477,479],[300,450,477,479,595],[300,450,477,588,592], [300,450,477,588,595],[0,300,450,477,591],[300,450,477,591,592],[300,450,483,484,485], [300,450,483,484,592],[300,450,483,485,595],[300,450,483,588,592],[300,450,483,588,595], [1,2,5,41,191],[2,5,41,191,491],[1,2,5,41,341],[2,5,41,341,491], [1,2,5,155,191],[2,5,155,191,491],[2,5,155,455,491],[1,2,5,305,341], [2,5,305,341,491],[2,5,305,455,491],[1,2,35,145,295],[1,2,35,145,445], [1,2,35,185,295],[1,2,35,335,445],[1,2,38,41,191],[2,38,41,191,491], [1,2,38,41,341],[2,38,41,341,491],[1,2,38,148,298],[1,2,38,148,448], [1,2,38,188,191],[2,38,188,191,491],[1,2,38,188,298],[2,38,188,488,491], [1,2,38,338,341],[2,38,338,341,491],[1,2,38,338,448],[2,38,338,488,491], [1,2,144,145,295],[1,2,144,145,445],[1,2,144,148,298],[1,2,144,148,448], [1,2,144,294,295],[1,2,144,294,298],[1,2,144,444,445],[1,2,144,444,448], [1,2,152,155,191],[2,152,155,191,491],[2,152,155,455,491],[1,2,152,185,295], [1,2,152,188,191],[2,152,188,191,491],[1,2,152,188,298],[2,152,188,488,491], [1,2,152,294,295],[1,2,152,294,298],[2,152,452,455,491],[2,152,452,488,491], [1,2,302,305,341],[2,302,305,341,491],[2,302,305,455,491],[1,2,302,335,445], [1,2,302,338,341],[2,302,338,341,491],[1,2,302,338,448],[2,302,338,488,491], [1,2,302,444,445],[1,2,302,444,448],[2,302,452,455,491],[2,302,452,488,491], [1,4,5,41,191],[1,4,5,41,341],[1,4,5,155,191],[1,4,5,305,341], [1,4,39,41,191],[1,4,39,41,341],[1,4,39,189,191],[1,4,39,189,489], [1,4,39,339,341],[1,4,39,339,489],[1,4,154,155,191],[1,4,154,189,191], [1,4,154,189,489],[1,4,154,454,489],[1,4,304,305,341],[1,4,304,339,341], [1,4,304,339,489],[1,4,304,454,489],[1,34,35,145,295],[1,34,35,145,445], [1,34,35,185,295],[1,34,35,335,445],[1,34,139,142,292],[1,34,139,142,442], [1,34,139,145,295],[1,34,139,145,445],[1,34,139,289,292],[1,34,139,289,295], [1,34,139,439,442],[1,34,139,439,445],[1,34,184,185,295],[1,34,184,289,292], [1,34,184,289,295],[1,34,334,335,445],[1,34,334,439,442],[1,34,334,439,445], [1,36,38,41,191],[1,36,38,41,341],[1,36,38,148,298],[1,36,38,148,448], [1,36,38,188,191],[1,36,38,188,298],[1,36,38,338,341],[1,36,38,338,448], [1,36,39,41,191],[1,36,39,41,341],[1,36,39,189,191],[1,36,39,189,489], [1,36,39,339,341],[1,36,39,339,489],[1,36,139,142,292],[1,36,139,142,442], [1,36,139,145,295],[1,36,139,145,445],[1,36,139,289,292],[1,36,139,289,295], [1,36,139,439,442],[1,36,139,439,445],[1,36,141,142,292],[1,36,141,142,442], [1,36,141,291,292],[1,36,141,291,591],[1,36,141,441,442],[1,36,141,441,591], [1,36,144,145,295],[1,36,144,145,445],[1,36,144,148,298],[1,36,144,148,448], [1,36,144,294,295],[1,36,144,294,298],[1,36,144,444,445],[1,36,144,444,448], [1,36,186,188,191],[1,36,186,188,298],[1,36,186,189,191],[1,36,186,189,489], [1,36,186,289,292],[1,36,186,289,295],[1,36,186,291,292],[1,36,186,291,591], [1,36,186,294,295],[1,36,186,294,298],[1,36,186,486,489],[1,36,186,486,591], [1,36,336,338,341],[1,36,336,338,448],[1,36,336,339,341],[1,36,336,339,489], [1,36,336,439,442],[1,36,336,439,445],[1,36,336,441,442],[1,36,336,441,591], [1,36,336,444,445],[1,36,336,444,448],[1,36,336,486,489],[1,36,336,486,591], [1,151,152,155,191],[151,152,155,191,491],[151,152,155,455,491],[1,151,152,185,295], [151,152,185,295,595],[151,152,185,485,595],[1,151,152,188,191],[151,152,188,191,491], [1,151,152,188,298],[151,152,188,298,598],[151,152,188,488,491],[151,152,188,488,598], [1,151,152,294,295],[151,152,294,295,595],[1,151,152,294,298],[151,152,294,298,598], [151,152,294,594,595],[151,152,294,594,598],[151,152,452,455,491],[151,152,452,485,595], [151,152,452,488,491],[151,152,452,488,598],[151,152,452,594,595],[151,152,452,594,598], [1,151,154,155,191],[151,154,155,191,491],[151,154,155,455,491],[1,151,154,189,191], [151,154,189,191,491],[1,151,154,189,489],[151,154,189,489,491],[151,154,454,455,491], [1,151,154,454,489],[151,154,454,489,491],[1,151,184,185,295],[151,184,185,295,595], [151,184,185,485,595],[1,151,184,289,292],[151,184,289,292,592],[1,151,184,289,295], 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