#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_010 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(656,9894,33036,39660,15864) ### ### 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:=[ [0,1,2,5,329],[0,1,2,35,359],[0,1,2,326,329],[0,1,2,326,359], [0,1,4,5,329],[0,1,4,166,490],[0,1,4,328,329],[0,1,4,328,490], [0,1,34,35,359],[0,1,34,154,316],[0,1,34,154,478],[0,1,34,196,316], [0,1,34,358,359],[0,1,34,358,478],[0,1,153,154,316],[0,1,153,154,478], [0,1,153,315,316],[0,1,153,315,639],[0,1,153,477,478],[0,1,153,477,639], [0,1,163,166,490],[0,1,163,196,316],[0,1,163,315,316],[0,1,163,315,639], [0,1,163,487,490],[0,1,163,487,639],[0,1,325,326,329],[0,1,325,326,359], [0,1,325,328,329],[0,1,325,328,490],[0,1,325,358,359],[0,1,325,358,478], [0,1,325,477,478],[0,1,325,477,639],[0,1,325,487,490],[0,1,325,487,639], [0,2,5,26,188],[2,5,26,188,512],[0,2,5,26,350],[2,5,26,350,512], [0,2,5,167,188],[2,5,167,188,512],[2,5,167,491,512],[0,2,5,329,350], [2,5,329,350,512],[2,5,329,491,512],[0,2,26,29,191],[2,26,29,191,515], [0,2,26,29,353],[2,26,29,353,515],[0,2,26,188,191],[2,26,188,191,515], [2,26,188,512,515],[0,2,26,350,353],[2,26,350,353,515],[2,26,350,512,515], [0,2,29,157,319],[0,2,29,157,481],[0,2,29,191,319],[0,2,29,353,481], [0,2,35,157,319],[0,2,35,157,481],[0,2,35,197,319],[0,2,35,359,481], [0,2,164,167,188],[2,164,167,188,512],[2,164,167,491,512],[0,2,164,188,191], [2,164,188,191,515],[2,164,188,512,515],[0,2,164,191,319],[0,2,164,197,319], [2,164,488,491,512],[2,164,488,512,515],[0,2,326,329,350],[2,326,329,350,512], [2,326,329,491,512],[0,2,326,350,353],[2,326,350,353,515],[2,326,350,512,515], [0,2,326,353,481],[0,2,326,359,481],[2,326,488,491,512],[2,326,488,512,515], [0,3,4,5,329],[0,3,4,166,490],[0,3,4,328,329],[0,3,4,328,490], [0,3,5,26,188],[0,3,5,26,350],[0,3,5,167,188],[0,3,5,329,350], [0,3,24,26,188],[0,3,24,26,350],[0,3,24,186,188],[0,3,24,186,510], [0,3,24,348,350],[0,3,24,348,510],[0,3,165,166,490],[0,3,165,167,188], [0,3,165,186,188],[0,3,165,186,510],[0,3,165,489,490],[0,3,165,489,510], [0,3,327,328,329],[0,3,327,328,490],[0,3,327,329,350],[0,3,327,348,350], [0,3,327,348,510],[0,3,327,489,490],[0,3,327,489,510],[0,24,26,29,191], [0,24,26,29,353],[0,24,26,188,191],[0,24,26,350,353],[0,24,27,29,191], [0,24,27,29,353],[0,24,27,189,191],[0,24,27,189,513],[0,24,27,351,353], [0,24,27,351,513],[0,24,186,188,191],[0,24,186,189,191],[0,24,186,189,513], [0,24,186,510,513],[0,24,348,350,353],[0,24,348,351,353],[0,24,348,351,513], [0,24,348,510,513],[0,27,29,157,319],[0,27,29,157,481],[0,27,29,191,319], [0,27,29,353,481],[0,27,150,154,316],[0,27,150,154,478],[0,27,150,157,319], [0,27,150,157,481],[0,27,150,312,316],[0,27,150,312,319],[0,27,150,474,478], [0,27,150,474,481],[0,27,153,154,316],[0,27,153,154,478],[0,27,153,315,316], [0,27,153,315,639],[0,27,153,477,478],[0,27,153,477,639],[0,27,189,191,319], [0,27,189,312,316],[0,27,189,312,319],[0,27,189,315,316],[0,27,189,315,639], [0,27,189,513,639],[0,27,351,353,481],[0,27,351,474,478],[0,27,351,474,481], [0,27,351,477,478],[0,27,351,477,639],[0,27,351,513,639],[0,33,34,35,359], [0,33,34,154,316],[0,33,34,154,478],[0,33,34,196,316],[0,33,34,358,359], [0,33,34,358,478],[0,33,35,157,319],[0,33,35,157,481],[0,33,35,197,319], [0,33,35,359,481],[0,33,150,154,316],[0,33,150,154,478],[0,33,150,157,319], [0,33,150,157,481],[0,33,150,312,316],[0,33,150,312,319],[0,33,150,474,478], [0,33,150,474,481],[0,33,195,196,316],[0,33,195,197,319],[0,33,195,312,316], [0,33,195,312,319],[0,33,357,358,359],[0,33,357,358,478],[0,33,357,359,481], [0,33,357,474,478],[0,33,357,474,481],[162,163,164,167,491],[162,163,164,197,521], 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[0,324,325,326,359],[324,325,326,359,521],[324,325,326,488,491],[324,325,326,488,521], [0,324,325,328,329],[324,325,328,329,491],[0,324,325,328,490],[324,325,328,490,491], [0,324,325,358,359],[324,325,358,359,521],[0,324,325,358,478],[324,325,358,478,640], [324,325,358,520,521],[324,325,358,520,640],[0,324,325,477,478],[324,325,477,478,640], [0,324,325,477,639],[324,325,477,639,640],[324,325,487,488,491],[324,325,487,488,521], [0,324,325,487,490],[324,325,487,490,491],[324,325,487,520,521],[324,325,487,520,640], [0,324,325,487,639],[324,325,487,639,640],[0,324,326,329,350],[324,326,329,350,512], [324,326,329,491,512],[0,324,326,350,353],[324,326,350,353,515],[324,326,350,512,515], [0,324,326,353,481],[324,326,353,481,643],[324,326,353,515,643],[0,324,326,359,481], [324,326,359,481,643],[324,326,359,521,643],[324,326,488,491,512],[324,326,488,512,515], [324,326,488,515,643],[324,326,488,521,643],[0,324,327,328,329],[324,327,328,329,491], [0,324,327,328,490],[324,327,328,490,491],[0,324,327,329,350],[324,327,329,350,512], [324,327,329,491,512],[0,324,327,348,350],[324,327,348,350,512],[0,324,327,348,510], [324,327,348,510,512],[0,324,327,489,490],[324,327,489,490,491],[324,327,489,491,512], [0,324,327,489,510],[324,327,489,510,512],[0,324,348,350,353],[324,348,350,353,515], [324,348,350,512,515],[0,324,348,351,353],[324,348,351,353,515],[0,324,348,351,513], [324,348,351,513,515],[324,348,510,512,515],[0,324,348,510,513],[324,348,510,513,515], [0,324,351,353,481],[324,351,353,481,643],[324,351,353,515,643],[0,324,351,474,478], [324,351,474,478,640],[0,324,351,474,481],[324,351,474,481,643],[324,351,474,636,640], [324,351,474,636,643],[0,324,351,477,478],[324,351,477,478,640],[0,324,351,477,639], [324,351,477,639,640],[324,351,513,515,643],[324,351,513,636,640],[324,351,513,636,643], [0,324,351,513,639],[324,351,513,639,640],[0,324,357,358,359],[324,357,358,359,521], 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[324,486,519,520,640],[324,486,519,521,643],[324,486,519,636,640],[324,486,519,636,643], [1,2,5,41,203],[2,5,41,203,527],[1,2,5,41,365],[2,5,41,365,527], [1,2,5,167,203],[2,5,167,203,527],[2,5,167,491,527],[1,2,5,329,365], [2,5,329,365,527],[2,5,329,491,527],[1,2,35,157,319],[1,2,35,157,481], [1,2,35,197,319],[1,2,35,359,481],[1,2,38,41,203],[2,38,41,203,527], [1,2,38,41,365],[2,38,41,365,527],[1,2,38,160,322],[1,2,38,160,484], [1,2,38,200,203],[2,38,200,203,527],[1,2,38,200,322],[2,38,200,524,527], [1,2,38,362,365],[2,38,362,365,527],[1,2,38,362,484],[2,38,362,524,527], [1,2,156,157,319],[1,2,156,157,481],[1,2,156,160,322],[1,2,156,160,484], [1,2,156,318,319],[1,2,156,318,322],[1,2,156,480,481],[1,2,156,480,484], [1,2,164,167,203],[2,164,167,203,527],[2,164,167,491,527],[1,2,164,197,319], [1,2,164,200,203],[2,164,200,203,527],[1,2,164,200,322],[2,164,200,524,527], [1,2,164,318,319],[1,2,164,318,322],[2,164,488,491,527],[2,164,488,524,527], [1,2,326,329,365],[2,326,329,365,527],[2,326,329,491,527],[1,2,326,359,481], [1,2,326,362,365],[2,326,362,365,527],[1,2,326,362,484],[2,326,362,524,527], [1,2,326,480,481],[1,2,326,480,484],[2,326,488,491,527],[2,326,488,524,527], [1,4,5,41,203],[1,4,5,41,365],[1,4,5,167,203],[1,4,5,329,365], [1,4,39,41,203],[1,4,39,41,365],[1,4,39,201,203],[1,4,39,201,525], [1,4,39,363,365],[1,4,39,363,525],[1,4,166,167,203],[1,4,166,201,203], [1,4,166,201,525],[1,4,166,490,525],[1,4,328,329,365],[1,4,328,363,365], [1,4,328,363,525],[1,4,328,490,525],[1,34,35,157,319],[1,34,35,157,481], [1,34,35,197,319],[1,34,35,359,481],[1,34,151,154,316],[1,34,151,154,478], [1,34,151,157,319],[1,34,151,157,481],[1,34,151,313,316],[1,34,151,313,319], [1,34,151,475,478],[1,34,151,475,481],[1,34,196,197,319],[1,34,196,313,316], [1,34,196,313,319],[1,34,358,359,481],[1,34,358,475,478],[1,34,358,475,481], [1,36,38,41,203],[1,36,38,41,365],[1,36,38,160,322],[1,36,38,160,484], 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[58,382,383,386,392],[382,383,386,392,554],[382,383,386,548,554],[58,382,383,389,392], [382,383,389,392,554],[382,383,389,551,554],[382,383,545,548,554],[382,383,545,551,554], [58,382,385,386,392],[382,385,386,392,554],[382,385,386,548,554],[58,382,385,390,392], [382,385,390,392,554],[58,382,385,390,552],[382,385,390,552,554],[382,385,547,548,554], [58,382,385,547,552],[382,385,547,552,554],[58,382,387,389,392],[382,387,389,392,554], [382,387,389,551,554],[58,382,387,390,392],[382,387,390,392,554],[58,382,387,390,552], [382,387,390,552,554],[382,387,549,551,554],[58,382,387,549,552],[382,387,549,552,554], [382,544,545,548,554],[382,544,545,551,554],[382,544,547,548,554],[58,382,544,547,552], [382,544,547,552,554],[382,544,549,551,554],[58,382,544,549,552],[382,544,549,552,554], [59,62,68,160,322],[59,62,68,160,484],[59,62,68,230,322],[59,62,68,392,484], [59,62,224,230,322],[59,62,386,392,484],[59,65,68,160,322],[59,65,68,160,484], 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