#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_009 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(612,9462,31748,38160,15264) ### ### 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:=[ [0,1,2,5,155],[0,1,2,5,300],[1,2,5,300,606],[1,2,5,311,606], [0,1,2,35,185],[0,1,2,35,300],[1,2,35,300,606],[1,2,35,341,606], [0,1,2,152,155],[0,1,2,152,185],[1,2,308,311,606],[1,2,308,341,606], [0,1,4,5,155],[0,1,4,5,300],[0,1,4,300,606],[1,4,5,300,606], [1,4,5,311,606],[0,1,4,154,155],[0,1,4,154,460],[0,1,4,310,606], [1,4,310,311,606],[0,1,4,310,460],[0,1,34,35,185],[0,1,34,35,300], [0,1,34,300,606],[1,34,35,300,606],[1,34,35,341,606],[0,1,34,142,292], [0,1,34,142,448],[0,1,34,184,185],[0,1,34,184,292],[0,1,34,340,606], [1,34,340,341,606],[0,1,34,340,448],[0,1,141,142,292],[0,1,141,142,448], [0,1,141,291,292],[0,1,141,291,597],[0,1,141,447,448],[0,1,141,447,597], [0,1,151,152,155],[0,1,151,152,185],[0,1,151,154,155],[0,1,151,154,460], [0,1,151,184,185],[0,1,151,184,292],[0,1,151,291,292],[0,1,151,291,597], [0,1,151,457,460],[0,1,151,457,597],[1,307,308,311,606],[1,307,308,341,606], [0,1,307,310,606],[1,307,310,311,606],[0,1,307,310,460],[0,1,307,340,606], [1,307,340,341,606],[0,1,307,340,448],[0,1,307,447,448],[0,1,307,447,597], [0,1,307,457,460],[0,1,307,457,597],[0,2,5,26,176],[2,5,26,176,482], [0,2,5,26,332],[2,5,26,332,482],[0,2,5,155,176],[2,5,155,176,482], [2,5,155,461,482],[0,2,5,300,301],[0,2,5,301,607],[2,5,300,301,607], [2,5,300,606,607],[0,2,5,311,332],[2,5,311,332,482],[2,5,311,461,482], [0,2,5,311,607],[2,5,311,606,607],[0,2,26,29,179],[2,26,29,179,485], [0,2,26,29,335],[2,26,29,335,485],[0,2,26,176,179],[2,26,176,179,485], [2,26,176,482,485],[0,2,26,332,335],[2,26,332,335,485],[2,26,332,482,485], [0,2,29,145,295],[0,2,29,145,451],[0,2,29,179,295],[0,2,29,335,451], [0,2,35,145,295],[0,2,35,145,451],[0,2,35,185,295],[0,2,35,300,301], [0,2,35,301,607],[2,35,300,301,607],[2,35,300,606,607],[0,2,35,341,451], [0,2,35,341,607],[2,35,341,606,607],[0,2,152,155,176],[2,152,155,176,482], [2,152,155,461,482],[0,2,152,176,179],[2,152,176,179,485],[2,152,176,482,485], [0,2,152,179,295],[0,2,152,185,295],[2,152,458,461,482],[2,152,458,482,485], [0,2,308,311,332],[2,308,311,332,482],[2,308,311,461,482],[0,2,308,311,607], [2,308,311,606,607],[0,2,308,332,335],[2,308,332,335,485],[2,308,332,482,485], [0,2,308,335,451],[0,2,308,341,451],[0,2,308,341,607],[2,308,341,606,607], [2,308,458,461,482],[2,308,458,482,485],[0,3,4,5,155],[0,3,4,5,300], [0,3,4,300,606],[0,3,4,154,155],[0,3,4,154,460],[0,3,4,310,606], [0,3,4,310,460],[0,3,5,26,176],[0,3,5,26,332],[0,3,5,155,176], [0,3,5,300,301],[0,3,5,301,607],[0,3,5,311,332],[0,3,5,311,607], [0,3,24,26,176],[0,3,24,26,332],[0,3,24,174,176],[0,3,24,174,480], [0,3,24,330,332],[0,3,24,330,480],[0,3,153,154,155],[0,3,153,154,460], [0,3,153,155,176],[0,3,153,174,176],[0,3,153,174,480],[0,3,153,459,460], [0,3,153,459,480],[0,3,300,301,302],[0,3,300,302,608],[0,3,301,302,608], [0,3,301,607,608],[0,3,300,606,608],[0,3,309,310,606],[0,3,309,310,460], [0,3,309,311,332],[0,3,309,311,607],[0,3,309,330,332],[0,3,309,330,480], [0,3,309,459,460],[0,3,309,459,480],[0,3,309,606,608],[0,3,309,607,608], [0,24,26,29,179],[0,24,26,29,335],[0,24,26,176,179],[0,24,26,332,335], [0,24,27,29,179],[0,24,27,29,335],[0,24,27,177,179],[0,24,27,177,483], [0,24,27,333,335],[0,24,27,333,483],[0,24,174,176,179],[0,24,174,177,179], [0,24,174,177,483],[0,24,174,480,483],[0,24,330,332,335],[0,24,330,333,335], [0,24,330,333,483],[0,24,330,480,483],[0,27,29,145,295],[0,27,29,145,451], [0,27,29,179,295],[0,27,29,335,451],[0,27,138,142,292],[0,27,138,142,448], [0,27,138,145,295],[0,27,138,145,451],[0,27,138,288,292],[0,27,138,288,295], [0,27,138,444,448],[0,27,138,444,451],[0,27,141,142,292],[0,27,141,142,448], [0,27,141,291,292],[0,27,141,291,597],[0,27,141,447,448],[0,27,141,447,597], [0,27,177,179,295],[0,27,177,288,292],[0,27,177,288,295],[0,27,177,291,292], [0,27,177,291,597],[0,27,177,483,597],[0,27,333,335,451],[0,27,333,444,448], [0,27,333,444,451],[0,27,333,447,448],[0,27,333,447,597],[0,27,333,483,597], [0,33,34,35,185],[0,33,34,35,300],[0,33,34,300,606],[0,33,34,142,292], [0,33,34,142,448],[0,33,34,184,185],[0,33,34,184,292],[0,33,34,340,606], [0,33,34,340,448],[0,33,35,145,295],[0,33,35,145,451],[0,33,35,185,295], [0,33,35,300,301],[0,33,35,301,607],[0,33,35,341,451],[0,33,35,341,607], [0,33,138,142,292],[0,33,138,142,448],[0,33,138,145,295],[0,33,138,145,451], [0,33,138,288,292],[0,33,138,288,295],[0,33,138,444,448],[0,33,138,444,451], [0,33,183,184,185],[0,33,183,184,292],[0,33,183,185,295],[0,33,183,288,292], [0,33,183,288,295],[0,33,300,301,302],[0,33,300,302,608],[0,33,301,302,608], [0,33,301,607,608],[0,33,300,606,608],[0,33,339,340,606],[0,33,339,340,448], [0,33,339,341,451],[0,33,339,341,607],[0,33,339,444,448],[0,33,339,444,451], [0,33,339,606,608],[0,33,339,607,608],[0,150,151,152,155],[150,151,152,155,461], [0,150,151,152,185],[150,151,152,185,491],[150,151,152,458,461],[150,151,152,458,491], [0,150,151,154,155],[150,151,154,155,461],[0,150,151,154,460],[150,151,154,460,461], [0,150,151,184,185],[150,151,184,185,491],[0,150,151,184,292],[150,151,184,292,598], [150,151,184,490,491],[150,151,184,490,598],[0,150,151,291,292],[150,151,291,292,598], [0,150,151,291,597],[150,151,291,597,598],[150,151,457,458,461],[150,151,457,458,491], [0,150,151,457,460],[150,151,457,460,461],[150,151,457,490,491],[150,151,457,490,598], [0,150,151,457,597],[150,151,457,597,598],[0,150,152,155,176],[150,152,155,176,482], [150,152,155,461,482],[0,150,152,176,179],[150,152,176,179,485],[150,152,176,482,485], [0,150,152,179,295],[150,152,179,295,601],[150,152,179,485,601],[0,150,152,185,295], [150,152,185,295,601],[150,152,185,491,601],[150,152,458,461,482],[150,152,458,482,485], [150,152,458,485,601],[150,152,458,491,601],[0,150,153,154,155],[150,153,154,155,461], [0,150,153,154,460],[150,153,154,460,461],[0,150,153,155,176],[150,153,155,176,482], [150,153,155,461,482],[0,150,153,174,176],[150,153,174,176,482],[0,150,153,174,480], [150,153,174,480,482],[0,150,153,459,460],[150,153,459,460,461],[150,153,459,461,482], [0,150,153,459,480],[150,153,459,480,482],[0,150,174,176,179],[150,174,176,179,485], [150,174,176,482,485],[0,150,174,177,179],[150,174,177,179,485],[0,150,174,177,483], [150,174,177,483,485],[150,174,480,482,485],[0,150,174,480,483],[150,174,480,483,485], [0,150,177,179,295],[150,177,179,295,601],[150,177,179,485,601],[0,150,177,288,292], [150,177,288,292,598],[0,150,177,288,295],[150,177,288,295,601],[150,177,288,594,598], [150,177,288,594,601],[0,150,177,291,292],[150,177,291,292,598],[0,150,177,291,597], [150,177,291,597,598],[150,177,483,485,601],[150,177,483,594,598],[150,177,483,594,601], [0,150,177,483,597],[150,177,483,597,598],[0,150,183,184,185],[150,183,184,185,491], [0,150,183,184,292],[150,183,184,292,598],[150,183,184,490,491],[150,183,184,490,598], [0,150,183,185,295],[150,183,185,295,601],[150,183,185,491,601],[0,150,183,288,292], [150,183,288,292,598],[0,150,183,288,295],[150,183,288,295,601],[150,183,288,594,598], [150,183,288,594,601],[150,183,489,490,491],[150,183,489,490,598],[150,183,489,491,601], [150,183,489,594,598],[150,183,489,594,601],[150,456,457,458,461],[150,456,457,458,491], [0,150,456,457,460],[150,456,457,460,461],[150,456,457,490,491],[150,456,457,490,598], [0,150,456,457,597],[150,456,457,597,598],[150,456,458,461,482],[150,456,458,482,485], [150,456,458,485,601],[150,456,458,491,601],[0,150,456,459,460],[150,456,459,460,461], [150,456,459,461,482],[0,150,456,459,480],[150,456,459,480,482],[150,456,480,482,485], [0,150,456,480,483],[150,456,480,483,485],[150,456,483,485,601],[150,456,483,594,598], [150,456,483,594,601],[0,150,456,483,597],[150,456,483,597,598],[150,456,489,490,491], [150,456,489,490,598],[150,456,489,491,601],[150,456,489,594,598],[150,456,489,594,601], [306,307,308,311,461],[306,307,308,311,606],[306,307,308,341,491],[306,307,308,341,606], [306,307,308,458,461],[306,307,308,458,491],[306,307,310,311,461],[0,306,307,310,606], [306,307,310,311,606],[0,306,307,310,460],[306,307,310,460,461],[306,307,340,341,491], [0,306,307,340,606],[306,307,340,341,606],[0,306,307,340,448],[306,307,340,448,598], [306,307,340,490,491],[306,307,340,490,598],[0,306,307,447,448],[306,307,447,448,598], [0,306,307,447,597],[306,307,447,597,598],[306,307,457,458,461],[306,307,457,458,491], [0,306,307,457,460],[306,307,457,460,461],[306,307,457,490,491],[306,307,457,490,598], [0,306,307,457,597],[306,307,457,597,598],[0,306,308,311,332],[306,308,311,332,482], [306,308,311,461,482],[0,306,308,311,607],[306,308,311,606,607],[0,306,308,332,335], [306,308,332,335,485],[306,308,332,482,485],[0,306,308,335,451],[306,308,335,451,601], [306,308,335,485,601],[0,306,308,341,451],[306,308,341,451,601],[306,308,341,491,601], [0,306,308,341,607],[306,308,341,606,607],[306,308,458,461,482],[306,308,458,482,485], [306,308,458,485,601],[306,308,458,491,601],[306,309,310,311,461],[0,306,309,310,606], [306,309,310,311,606],[0,306,309,310,460],[306,309,310,460,461],[0,306,309,311,332], [306,309,311,332,482],[306,309,311,461,482],[0,306,309,311,607],[306,309,311,606,607], [0,306,309,330,332],[306,309,330,332,482],[0,306,309,330,480],[306,309,330,480,482], [0,306,309,459,460],[306,309,459,460,461],[306,309,459,461,482],[0,306,309,459,480], [306,309,459,480,482],[0,306,309,606,608],[0,306,309,607,608],[306,309,606,607,608], [0,306,330,332,335],[306,330,332,335,485],[306,330,332,482,485],[0,306,330,333,335], [306,330,333,335,485],[0,306,330,333,483],[306,330,333,483,485],[306,330,480,482,485], [0,306,330,480,483],[306,330,480,483,485],[0,306,333,335,451],[306,333,335,451,601], [306,333,335,485,601],[0,306,333,444,448],[306,333,444,448,598],[0,306,333,444,451], [306,333,444,451,601],[306,333,444,594,598],[306,333,444,594,601],[0,306,333,447,448], [306,333,447,448,598],[0,306,333,447,597],[306,333,447,597,598],[306,333,483,485,601], [306,333,483,594,598],[306,333,483,594,601],[0,306,333,483,597],[306,333,483,597,598], [306,339,340,341,491],[0,306,339,340,606],[306,339,340,341,606],[0,306,339,340,448], [306,339,340,448,598],[306,339,340,490,491],[306,339,340,490,598],[0,306,339,341,451], [306,339,341,451,601],[306,339,341,491,601],[0,306,339,341,607],[306,339,341,606,607], [0,306,339,444,448],[306,339,444,448,598],[0,306,339,444,451],[306,339,444,451,601], [306,339,444,594,598],[306,339,444,594,601],[306,339,489,490,491],[306,339,489,490,598], [306,339,489,491,601],[306,339,489,594,598],[306,339,489,594,601],[0,306,339,606,608], [0,306,339,607,608],[306,339,606,607,608],[306,456,457,458,461],[306,456,457,458,491], [0,306,456,457,460],[306,456,457,460,461],[306,456,457,490,491],[306,456,457,490,598], [0,306,456,457,597],[306,456,457,597,598],[306,456,458,461,482],[306,456,458,482,485], [306,456,458,485,601],[306,456,458,491,601],[0,306,456,459,460],[306,456,459,460,461], [306,456,459,461,482],[0,306,456,459,480],[306,456,459,480,482],[306,456,480,482,485], [0,306,456,480,483],[306,456,480,483,485],[306,456,483,485,601],[306,456,483,594,598], [306,456,483,594,601],[0,306,456,483,597],[306,456,483,597,598],[306,456,489,490,491], [306,456,489,490,598],[306,456,489,491,601],[306,456,489,594,598],[306,456,489,594,601], [1,2,5,41,191],[2,5,41,191,497],[1,2,5,41,347],[2,5,41,347,497], [1,2,5,155,191],[2,5,155,191,497],[2,5,155,461,497],[1,2,5,311,347], [2,5,311,347,497],[2,5,311,461,497],[1,2,35,145,295],[1,2,35,145,451], [1,2,35,185,295],[1,2,35,341,451],[1,2,38,41,191],[2,38,41,191,497], [1,2,38,41,347],[2,38,41,347,497],[1,2,38,148,298],[1,2,38,148,454], [1,2,38,188,191],[2,38,188,191,497],[1,2,38,188,298],[2,38,188,494,497], [1,2,38,344,347],[2,38,344,347,497],[1,2,38,344,454],[2,38,344,494,497], [1,2,144,145,295],[1,2,144,145,451],[1,2,144,148,298],[1,2,144,148,454], [1,2,144,294,295],[1,2,144,294,298],[1,2,144,450,451],[1,2,144,450,454], [1,2,152,155,191],[2,152,155,191,497],[2,152,155,461,497],[1,2,152,185,295], [1,2,152,188,191],[2,152,188,191,497],[1,2,152,188,298],[2,152,188,494,497], [1,2,152,294,295],[1,2,152,294,298],[2,152,458,461,497],[2,152,458,494,497], [1,2,308,311,347],[2,308,311,347,497],[2,308,311,461,497],[1,2,308,341,451], [1,2,308,344,347],[2,308,344,347,497],[1,2,308,344,454],[2,308,344,494,497], [1,2,308,450,451],[1,2,308,450,454],[2,308,458,461,497],[2,308,458,494,497], [1,4,5,41,191],[1,4,5,41,347],[1,4,5,155,191],[1,4,5,311,347], [1,4,39,41,191],[1,4,39,41,347],[1,4,39,189,191],[1,4,39,189,495], [1,4,39,345,347],[1,4,39,345,495],[1,4,154,155,191],[1,4,154,189,191], [1,4,154,189,495],[1,4,154,460,495],[1,4,310,311,347],[1,4,310,345,347], [1,4,310,345,495],[1,4,310,460,495],[1,34,35,145,295],[1,34,35,145,451], [1,34,35,185,295],[1,34,35,341,451],[1,34,139,142,292],[1,34,139,142,448], [1,34,139,145,295],[1,34,139,145,451],[1,34,139,289,292],[1,34,139,289,295], [1,34,139,445,448],[1,34,139,445,451],[1,34,184,185,295],[1,34,184,289,292], [1,34,184,289,295],[1,34,340,341,451],[1,34,340,445,448],[1,34,340,445,451], [1,36,38,41,191],[1,36,38,41,347],[1,36,38,148,298],[1,36,38,148,454], [1,36,38,188,191],[1,36,38,188,298],[1,36,38,344,347],[1,36,38,344,454], 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