#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_010 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(660,10206,34244,41160,16464) ### ### 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:=[ [0,1,2,5,167],[0,1,2,5,324],[1,2,5,324,654],[1,2,5,335,654], [0,1,2,35,197],[0,1,2,35,324],[1,2,35,324,654],[1,2,35,365,654], [0,1,2,164,167],[0,1,2,164,197],[1,2,332,335,654],[1,2,332,365,654], [0,1,4,5,167],[0,1,4,5,324],[0,1,4,324,654],[1,4,5,324,654], [1,4,5,335,654],[0,1,4,166,167],[0,1,4,166,496],[0,1,4,334,654], [1,4,334,335,654],[0,1,4,334,496],[0,1,34,35,197],[0,1,34,35,324], [0,1,34,324,654],[1,34,35,324,654],[1,34,35,365,654],[0,1,34,154,316], [0,1,34,154,484],[0,1,34,196,197],[0,1,34,196,316],[0,1,34,364,654], [1,34,364,365,654],[0,1,34,364,484],[0,1,153,154,316],[0,1,153,154,484], [0,1,153,315,316],[0,1,153,315,645],[0,1,153,483,484],[0,1,153,483,645], [0,1,163,164,167],[0,1,163,164,197],[0,1,163,166,167],[0,1,163,166,496], [0,1,163,196,197],[0,1,163,196,316],[0,1,163,315,316],[0,1,163,315,645], [0,1,163,493,496],[0,1,163,493,645],[1,331,332,335,654],[1,331,332,365,654], [0,1,331,334,654],[1,331,334,335,654],[0,1,331,334,496],[0,1,331,364,654], [1,331,364,365,654],[0,1,331,364,484],[0,1,331,483,484],[0,1,331,483,645], [0,1,331,493,496],[0,1,331,493,645],[0,2,5,26,188],[2,5,26,188,518], [0,2,5,26,356],[2,5,26,356,518],[0,2,5,167,188],[2,5,167,188,518], [2,5,167,497,518],[0,2,5,324,325],[0,2,5,325,655],[2,5,324,325,655], [2,5,324,654,655],[0,2,5,335,356],[2,5,335,356,518],[2,5,335,497,518], [0,2,5,335,655],[2,5,335,654,655],[0,2,26,29,191],[2,26,29,191,521], [0,2,26,29,359],[2,26,29,359,521],[0,2,26,188,191],[2,26,188,191,521], [2,26,188,518,521],[0,2,26,356,359],[2,26,356,359,521],[2,26,356,518,521], [0,2,29,157,319],[0,2,29,157,487],[0,2,29,191,319],[0,2,29,359,487], [0,2,35,157,319],[0,2,35,157,487],[0,2,35,197,319],[0,2,35,324,325], [0,2,35,325,655],[2,35,324,325,655],[2,35,324,654,655],[0,2,35,365,487], [0,2,35,365,655],[2,35,365,654,655],[0,2,164,167,188],[2,164,167,188,518], [2,164,167,497,518],[0,2,164,188,191],[2,164,188,191,521],[2,164,188,518,521], [0,2,164,191,319],[0,2,164,197,319],[2,164,494,497,518],[2,164,494,518,521], [0,2,332,335,356],[2,332,335,356,518],[2,332,335,497,518],[0,2,332,335,655], [2,332,335,654,655],[0,2,332,356,359],[2,332,356,359,521],[2,332,356,518,521], [0,2,332,359,487],[0,2,332,365,487],[0,2,332,365,655],[2,332,365,654,655], [2,332,494,497,518],[2,332,494,518,521],[0,3,4,5,167],[0,3,4,5,324], [0,3,4,324,654],[0,3,4,166,167],[0,3,4,166,496],[0,3,4,334,654], [0,3,4,334,496],[0,3,5,26,188],[0,3,5,26,356],[0,3,5,167,188], [0,3,5,324,325],[0,3,5,325,655],[0,3,5,335,356],[0,3,5,335,655], [0,3,24,26,188],[0,3,24,26,356],[0,3,24,186,188],[0,3,24,186,516], [0,3,24,354,356],[0,3,24,354,516],[0,3,165,166,167],[0,3,165,166,496], [0,3,165,167,188],[0,3,165,186,188],[0,3,165,186,516],[0,3,165,495,496], [0,3,165,495,516],[0,3,324,325,326],[0,3,324,326,656],[0,3,325,326,656], [0,3,325,655,656],[0,3,324,654,656],[0,3,333,334,654],[0,3,333,334,496], [0,3,333,335,356],[0,3,333,335,655],[0,3,333,354,356],[0,3,333,354,516], [0,3,333,495,496],[0,3,333,495,516],[0,3,333,654,656],[0,3,333,655,656], [0,24,26,29,191],[0,24,26,29,359],[0,24,26,188,191],[0,24,26,356,359], [0,24,27,29,191],[0,24,27,29,359],[0,24,27,189,191],[0,24,27,189,519], [0,24,27,357,359],[0,24,27,357,519],[0,24,186,188,191],[0,24,186,189,191], [0,24,186,189,519],[0,24,186,516,519],[0,24,354,356,359],[0,24,354,357,359], [0,24,354,357,519],[0,24,354,516,519],[0,27,29,157,319],[0,27,29,157,487], [0,27,29,191,319],[0,27,29,359,487],[0,27,150,154,316],[0,27,150,154,484], [0,27,150,157,319],[0,27,150,157,487],[0,27,150,312,316],[0,27,150,312,319], [0,27,150,480,484],[0,27,150,480,487],[0,27,153,154,316],[0,27,153,154,484], [0,27,153,315,316],[0,27,153,315,645],[0,27,153,483,484],[0,27,153,483,645], [0,27,189,191,319],[0,27,189,312,316],[0,27,189,312,319],[0,27,189,315,316], [0,27,189,315,645],[0,27,189,519,645],[0,27,357,359,487],[0,27,357,480,484], [0,27,357,480,487],[0,27,357,483,484],[0,27,357,483,645],[0,27,357,519,645], [0,33,34,35,197],[0,33,34,35,324],[0,33,34,324,654],[0,33,34,154,316], [0,33,34,154,484],[0,33,34,196,197],[0,33,34,196,316],[0,33,34,364,654], [0,33,34,364,484],[0,33,35,157,319],[0,33,35,157,487],[0,33,35,197,319], [0,33,35,324,325],[0,33,35,325,655],[0,33,35,365,487],[0,33,35,365,655], [0,33,150,154,316],[0,33,150,154,484],[0,33,150,157,319],[0,33,150,157,487], [0,33,150,312,316],[0,33,150,312,319],[0,33,150,480,484],[0,33,150,480,487], [0,33,195,196,197],[0,33,195,196,316],[0,33,195,197,319],[0,33,195,312,316], [0,33,195,312,319],[0,33,324,325,326],[0,33,324,326,656],[0,33,325,326,656], [0,33,325,655,656],[0,33,324,654,656],[0,33,363,364,654],[0,33,363,364,484], [0,33,363,365,487],[0,33,363,365,655],[0,33,363,480,484],[0,33,363,480,487], [0,33,363,654,656],[0,33,363,655,656],[0,162,163,164,167],[162,163,164,167,497], [0,162,163,164,197],[162,163,164,197,527],[162,163,164,494,497],[162,163,164,494,527], [0,162,163,166,167],[162,163,166,167,497],[0,162,163,166,496],[162,163,166,496,497], [0,162,163,196,197],[162,163,196,197,527],[0,162,163,196,316],[162,163,196,316,646], [162,163,196,526,527],[162,163,196,526,646],[0,162,163,315,316],[162,163,315,316,646], [0,162,163,315,645],[162,163,315,645,646],[162,163,493,494,497],[162,163,493,494,527], [0,162,163,493,496],[162,163,493,496,497],[162,163,493,526,527],[162,163,493,526,646], [0,162,163,493,645],[162,163,493,645,646],[0,162,164,167,188],[162,164,167,188,518], [162,164,167,497,518],[0,162,164,188,191],[162,164,188,191,521],[162,164,188,518,521], [0,162,164,191,319],[162,164,191,319,649],[162,164,191,521,649],[0,162,164,197,319], [162,164,197,319,649],[162,164,197,527,649],[162,164,494,497,518],[162,164,494,518,521], [162,164,494,521,649],[162,164,494,527,649],[0,162,165,166,167],[162,165,166,167,497], [0,162,165,166,496],[162,165,166,496,497],[0,162,165,167,188],[162,165,167,188,518], [162,165,167,497,518],[0,162,165,186,188],[162,165,186,188,518],[0,162,165,186,516], [162,165,186,516,518],[0,162,165,495,496],[162,165,495,496,497],[162,165,495,497,518], [0,162,165,495,516],[162,165,495,516,518],[0,162,186,188,191],[162,186,188,191,521], [162,186,188,518,521],[0,162,186,189,191],[162,186,189,191,521],[0,162,186,189,519], [162,186,189,519,521],[162,186,516,518,521],[0,162,186,516,519],[162,186,516,519,521], [0,162,189,191,319],[162,189,191,319,649],[162,189,191,521,649],[0,162,189,312,316], [162,189,312,316,646],[0,162,189,312,319],[162,189,312,319,649],[162,189,312,642,646], [162,189,312,642,649],[0,162,189,315,316],[162,189,315,316,646],[0,162,189,315,645], [162,189,315,645,646],[162,189,519,521,649],[162,189,519,642,646],[162,189,519,642,649], [0,162,189,519,645],[162,189,519,645,646],[0,162,195,196,197],[162,195,196,197,527], [0,162,195,196,316],[162,195,196,316,646],[162,195,196,526,527],[162,195,196,526,646], [0,162,195,197,319],[162,195,197,319,649],[162,195,197,527,649],[0,162,195,312,316], [162,195,312,316,646],[0,162,195,312,319],[162,195,312,319,649],[162,195,312,642,646], [162,195,312,642,649],[162,195,525,526,527],[162,195,525,526,646],[162,195,525,527,649], [162,195,525,642,646],[162,195,525,642,649],[162,492,493,494,497],[162,492,493,494,527], [0,162,492,493,496],[162,492,493,496,497],[162,492,493,526,527],[162,492,493,526,646], [0,162,492,493,645],[162,492,493,645,646],[162,492,494,497,518],[162,492,494,518,521], [162,492,494,521,649],[162,492,494,527,649],[0,162,492,495,496],[162,492,495,496,497], [162,492,495,497,518],[0,162,492,495,516],[162,492,495,516,518],[162,492,516,518,521], [0,162,492,516,519],[162,492,516,519,521],[162,492,519,521,649],[162,492,519,642,646], [162,492,519,642,649],[0,162,492,519,645],[162,492,519,645,646],[162,492,525,526,527], [162,492,525,526,646],[162,492,525,527,649],[162,492,525,642,646],[162,492,525,642,649], [330,331,332,335,497],[330,331,332,335,654],[330,331,332,365,527],[330,331,332,365,654], [330,331,332,494,497],[330,331,332,494,527],[330,331,334,335,497],[0,330,331,334,654], [330,331,334,335,654],[0,330,331,334,496],[330,331,334,496,497],[330,331,364,365,527], [0,330,331,364,654],[330,331,364,365,654],[0,330,331,364,484],[330,331,364,484,646], [330,331,364,526,527],[330,331,364,526,646],[0,330,331,483,484],[330,331,483,484,646], [0,330,331,483,645],[330,331,483,645,646],[330,331,493,494,497],[330,331,493,494,527], [0,330,331,493,496],[330,331,493,496,497],[330,331,493,526,527],[330,331,493,526,646], [0,330,331,493,645],[330,331,493,645,646],[0,330,332,335,356],[330,332,335,356,518], [330,332,335,497,518],[0,330,332,335,655],[330,332,335,654,655],[0,330,332,356,359], [330,332,356,359,521],[330,332,356,518,521],[0,330,332,359,487],[330,332,359,487,649], [330,332,359,521,649],[0,330,332,365,487],[330,332,365,487,649],[330,332,365,527,649], [0,330,332,365,655],[330,332,365,654,655],[330,332,494,497,518],[330,332,494,518,521], [330,332,494,521,649],[330,332,494,527,649],[330,333,334,335,497],[0,330,333,334,654], [330,333,334,335,654],[0,330,333,334,496],[330,333,334,496,497],[0,330,333,335,356], [330,333,335,356,518],[330,333,335,497,518],[0,330,333,335,655],[330,333,335,654,655], [0,330,333,354,356],[330,333,354,356,518],[0,330,333,354,516],[330,333,354,516,518], [0,330,333,495,496],[330,333,495,496,497],[330,333,495,497,518],[0,330,333,495,516], [330,333,495,516,518],[0,330,333,654,656],[0,330,333,655,656],[330,333,654,655,656], [0,330,354,356,359],[330,354,356,359,521],[330,354,356,518,521],[0,330,354,357,359], [330,354,357,359,521],[0,330,354,357,519],[330,354,357,519,521],[330,354,516,518,521], [0,330,354,516,519],[330,354,516,519,521],[0,330,357,359,487],[330,357,359,487,649], [330,357,359,521,649],[0,330,357,480,484],[330,357,480,484,646],[0,330,357,480,487], [330,357,480,487,649],[330,357,480,642,646],[330,357,480,642,649],[0,330,357,483,484], [330,357,483,484,646],[0,330,357,483,645],[330,357,483,645,646],[330,357,519,521,649], [330,357,519,642,646],[330,357,519,642,649],[0,330,357,519,645],[330,357,519,645,646], [330,363,364,365,527],[0,330,363,364,654],[330,363,364,365,654],[0,330,363,364,484], [330,363,364,484,646],[330,363,364,526,527],[330,363,364,526,646],[0,330,363,365,487], [330,363,365,487,649],[330,363,365,527,649],[0,330,363,365,655],[330,363,365,654,655], [0,330,363,480,484],[330,363,480,484,646],[0,330,363,480,487],[330,363,480,487,649], [330,363,480,642,646],[330,363,480,642,649],[330,363,525,526,527],[330,363,525,526,646], [330,363,525,527,649],[330,363,525,642,646],[330,363,525,642,649],[0,330,363,654,656], [0,330,363,655,656],[330,363,654,655,656],[330,492,493,494,497],[330,492,493,494,527], [0,330,492,493,496],[330,492,493,496,497],[330,492,493,526,527],[330,492,493,526,646], [0,330,492,493,645],[330,492,493,645,646],[330,492,494,497,518],[330,492,494,518,521], [330,492,494,521,649],[330,492,494,527,649],[0,330,492,495,496],[330,492,495,496,497], [330,492,495,497,518],[0,330,492,495,516],[330,492,495,516,518],[330,492,516,518,521], [0,330,492,516,519],[330,492,516,519,521],[330,492,519,521,649],[330,492,519,642,646], [330,492,519,642,649],[0,330,492,519,645],[330,492,519,645,646],[330,492,525,526,527], [330,492,525,526,646],[330,492,525,527,649],[330,492,525,642,646],[330,492,525,642,649], [1,2,5,41,203],[2,5,41,203,533],[1,2,5,41,371],[2,5,41,371,533], [1,2,5,167,203],[2,5,167,203,533],[2,5,167,497,533],[1,2,5,335,371], [2,5,335,371,533],[2,5,335,497,533],[1,2,35,157,319],[1,2,35,157,487], [1,2,35,197,319],[1,2,35,365,487],[1,2,38,41,203],[2,38,41,203,533], [1,2,38,41,371],[2,38,41,371,533],[1,2,38,160,322],[1,2,38,160,490], [1,2,38,200,203],[2,38,200,203,533],[1,2,38,200,322],[2,38,200,530,533], [1,2,38,368,371],[2,38,368,371,533],[1,2,38,368,490],[2,38,368,530,533], [1,2,156,157,319],[1,2,156,157,487],[1,2,156,160,322],[1,2,156,160,490], [1,2,156,318,319],[1,2,156,318,322],[1,2,156,486,487],[1,2,156,486,490], [1,2,164,167,203],[2,164,167,203,533],[2,164,167,497,533],[1,2,164,197,319], [1,2,164,200,203],[2,164,200,203,533],[1,2,164,200,322],[2,164,200,530,533], [1,2,164,318,319],[1,2,164,318,322],[2,164,494,497,533],[2,164,494,530,533], [1,2,332,335,371],[2,332,335,371,533],[2,332,335,497,533],[1,2,332,365,487], [1,2,332,368,371],[2,332,368,371,533],[1,2,332,368,490],[2,332,368,530,533], [1,2,332,486,487],[1,2,332,486,490],[2,332,494,497,533],[2,332,494,530,533], [1,4,5,41,203],[1,4,5,41,371],[1,4,5,167,203],[1,4,5,335,371], [1,4,39,41,203],[1,4,39,41,371],[1,4,39,201,203],[1,4,39,201,531], [1,4,39,369,371],[1,4,39,369,531],[1,4,166,167,203],[1,4,166,201,203], [1,4,166,201,531],[1,4,166,496,531],[1,4,334,335,371],[1,4,334,369,371], [1,4,334,369,531],[1,4,334,496,531],[1,34,35,157,319],[1,34,35,157,487], [1,34,35,197,319],[1,34,35,365,487],[1,34,151,154,316],[1,34,151,154,484], [1,34,151,157,319],[1,34,151,157,487],[1,34,151,313,316],[1,34,151,313,319], [1,34,151,481,484],[1,34,151,481,487],[1,34,196,197,319],[1,34,196,313,316], [1,34,196,313,319],[1,34,364,365,487],[1,34,364,481,484],[1,34,364,481,487], [1,36,38,41,203],[1,36,38,41,371],[1,36,38,160,322],[1,36,38,160,490], [1,36,38,200,203],[1,36,38,200,322],[1,36,38,368,371],[1,36,38,368,490], 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