#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_004 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(368,5574,18636,22380,8952) ### ### 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:=[ [0,1,2,5,185],[0,1,2,35,215],[0,1,2,182,185],[0,1,2,182,215], [0,1,4,5,185],[0,1,4,94,274],[0,1,4,184,185],[0,1,4,184,274], [0,1,34,35,215],[0,1,34,82,172],[0,1,34,82,262],[0,1,34,124,172], [0,1,34,214,215],[0,1,34,214,262],[0,1,81,82,172],[0,1,81,82,262], [0,1,81,171,172],[0,1,81,171,351],[0,1,81,261,262],[0,1,81,261,351], [0,1,91,94,274],[0,1,91,124,172],[0,1,91,171,172],[0,1,91,171,351], [0,1,91,271,274],[0,1,91,271,351],[0,1,181,182,185],[0,1,181,182,215], [0,1,181,184,185],[0,1,181,184,274],[0,1,181,214,215],[0,1,181,214,262], [0,1,181,261,262],[0,1,181,261,351],[0,1,181,271,274],[0,1,181,271,351], [0,2,5,26,116],[2,5,26,116,296],[0,2,5,26,206],[2,5,26,206,296], [0,2,5,95,116],[2,5,95,116,296],[2,5,95,275,296],[0,2,5,185,206], [2,5,185,206,296],[2,5,185,275,296],[0,2,26,29,119],[2,26,29,119,299], [0,2,26,29,209],[2,26,29,209,299],[0,2,26,116,119],[2,26,116,119,299], [2,26,116,296,299],[0,2,26,206,209],[2,26,206,209,299],[2,26,206,296,299], [0,2,29,85,175],[0,2,29,85,265],[0,2,29,119,175],[0,2,29,209,265], [0,2,35,85,175],[0,2,35,85,265],[0,2,35,125,175],[0,2,35,215,265], [0,2,92,95,116],[2,92,95,116,296],[2,92,95,275,296],[0,2,92,116,119], [2,92,116,119,299],[2,92,116,296,299],[0,2,92,119,175],[0,2,92,125,175], [2,92,272,275,296],[2,92,272,296,299],[0,2,182,185,206],[2,182,185,206,296], [2,182,185,275,296],[0,2,182,206,209],[2,182,206,209,299],[2,182,206,296,299], [0,2,182,209,265],[0,2,182,215,265],[2,182,272,275,296],[2,182,272,296,299], [0,3,4,5,185],[0,3,4,94,274],[0,3,4,184,185],[0,3,4,184,274], [0,3,5,26,116],[0,3,5,26,206],[0,3,5,95,116],[0,3,5,185,206], [0,3,24,26,116],[0,3,24,26,206],[0,3,24,114,116],[0,3,24,114,294], [0,3,24,204,206],[0,3,24,204,294],[0,3,93,94,274],[0,3,93,95,116], [0,3,93,114,116],[0,3,93,114,294],[0,3,93,273,274],[0,3,93,273,294], [0,3,183,184,185],[0,3,183,184,274],[0,3,183,185,206],[0,3,183,204,206], [0,3,183,204,294],[0,3,183,273,274],[0,3,183,273,294],[0,24,26,29,119], [0,24,26,29,209],[0,24,26,116,119],[0,24,26,206,209],[0,24,27,29,119], [0,24,27,29,209],[0,24,27,117,119],[0,24,27,117,297],[0,24,27,207,209], [0,24,27,207,297],[0,24,114,116,119],[0,24,114,117,119],[0,24,114,117,297], [0,24,114,294,297],[0,24,204,206,209],[0,24,204,207,209],[0,24,204,207,297], [0,24,204,294,297],[0,27,29,85,175],[0,27,29,85,265],[0,27,29,119,175], [0,27,29,209,265],[0,27,78,82,172],[0,27,78,82,262],[0,27,78,85,175], [0,27,78,85,265],[0,27,78,168,172],[0,27,78,168,175],[0,27,78,258,262], [0,27,78,258,265],[0,27,81,82,172],[0,27,81,82,262],[0,27,81,171,172], [0,27,81,171,351],[0,27,81,261,262],[0,27,81,261,351],[0,27,117,119,175], [0,27,117,168,172],[0,27,117,168,175],[0,27,117,171,172],[0,27,117,171,351], [0,27,117,297,351],[0,27,207,209,265],[0,27,207,258,262],[0,27,207,258,265], [0,27,207,261,262],[0,27,207,261,351],[0,27,207,297,351],[0,33,34,35,215], [0,33,34,82,172],[0,33,34,82,262],[0,33,34,124,172],[0,33,34,214,215], [0,33,34,214,262],[0,33,35,85,175],[0,33,35,85,265],[0,33,35,125,175], [0,33,35,215,265],[0,33,78,82,172],[0,33,78,82,262],[0,33,78,85,175], [0,33,78,85,265],[0,33,78,168,172],[0,33,78,168,175],[0,33,78,258,262], [0,33,78,258,265],[0,33,123,124,172],[0,33,123,125,175],[0,33,123,168,172], [0,33,123,168,175],[0,33,213,214,215],[0,33,213,214,262],[0,33,213,215,265], [0,33,213,258,262],[0,33,213,258,265],[90,91,92,95,275],[90,91,92,125,305], [90,91,92,272,275],[90,91,92,272,305],[90,91,94,95,275],[0,90,91,94,274], [90,91,94,274,275],[90,91,124,125,305],[0,90,91,124,172],[90,91,124,172,352], [90,91,124,304,305],[90,91,124,304,352],[0,90,91,171,172],[90,91,171,172,352], [0,90,91,171,351],[90,91,171,351,352],[90,91,271,272,275],[90,91,271,272,305], [0,90,91,271,274],[90,91,271,274,275],[90,91,271,304,305],[90,91,271,304,352], [0,90,91,271,351],[90,91,271,351,352],[0,90,92,95,116],[90,92,95,116,296], [90,92,95,275,296],[0,90,92,116,119],[90,92,116,119,299],[90,92,116,296,299], [0,90,92,119,175],[90,92,119,175,355],[90,92,119,299,355],[0,90,92,125,175], [90,92,125,175,355],[90,92,125,305,355],[90,92,272,275,296],[90,92,272,296,299], [90,92,272,299,355],[90,92,272,305,355],[90,93,94,95,275],[0,90,93,94,274], [90,93,94,274,275],[0,90,93,95,116],[90,93,95,116,296],[90,93,95,275,296], [0,90,93,114,116],[90,93,114,116,296],[0,90,93,114,294],[90,93,114,294,296], [0,90,93,273,274],[90,93,273,274,275],[90,93,273,275,296],[0,90,93,273,294], [90,93,273,294,296],[0,90,114,116,119],[90,114,116,119,299],[90,114,116,296,299], [0,90,114,117,119],[90,114,117,119,299],[0,90,114,117,297],[90,114,117,297,299], [90,114,294,296,299],[0,90,114,294,297],[90,114,294,297,299],[0,90,117,119,175], [90,117,119,175,355],[90,117,119,299,355],[0,90,117,168,172],[90,117,168,172,352], [0,90,117,168,175],[90,117,168,175,355],[90,117,168,348,352],[90,117,168,348,355], [0,90,117,171,172],[90,117,171,172,352],[0,90,117,171,351],[90,117,171,351,352], [90,117,297,299,355],[90,117,297,348,352],[90,117,297,348,355],[0,90,117,297,351], [90,117,297,351,352],[90,123,124,125,305],[0,90,123,124,172],[90,123,124,172,352], [90,123,124,304,305],[90,123,124,304,352],[0,90,123,125,175],[90,123,125,175,355], [90,123,125,305,355],[0,90,123,168,172],[90,123,168,172,352],[0,90,123,168,175], [90,123,168,175,355],[90,123,168,348,352],[90,123,168,348,355],[90,123,303,304,305], [90,123,303,304,352],[90,123,303,305,355],[90,123,303,348,352],[90,123,303,348,355], [90,270,271,272,275],[90,270,271,272,305],[0,90,270,271,274],[90,270,271,274,275], [90,270,271,304,305],[90,270,271,304,352],[0,90,270,271,351],[90,270,271,351,352], [90,270,272,275,296],[90,270,272,296,299],[90,270,272,299,355],[90,270,272,305,355], [0,90,270,273,274],[90,270,273,274,275],[90,270,273,275,296],[0,90,270,273,294], [90,270,273,294,296],[90,270,294,296,299],[0,90,270,294,297],[90,270,294,297,299], [90,270,297,299,355],[90,270,297,348,352],[90,270,297,348,355],[0,90,270,297,351], [90,270,297,351,352],[90,270,303,304,305],[90,270,303,304,352],[90,270,303,305,355], [90,270,303,348,352],[90,270,303,348,355],[0,180,181,182,185],[180,181,182,185,275], [0,180,181,182,215],[180,181,182,215,305],[180,181,182,272,275],[180,181,182,272,305], [0,180,181,184,185],[180,181,184,185,275],[0,180,181,184,274],[180,181,184,274,275], [0,180,181,214,215],[180,181,214,215,305],[0,180,181,214,262],[180,181,214,262,352], [180,181,214,304,305],[180,181,214,304,352],[0,180,181,261,262],[180,181,261,262,352], [0,180,181,261,351],[180,181,261,351,352],[180,181,271,272,275],[180,181,271,272,305], [0,180,181,271,274],[180,181,271,274,275],[180,181,271,304,305],[180,181,271,304,352], [0,180,181,271,351],[180,181,271,351,352],[0,180,182,185,206],[180,182,185,206,296], [180,182,185,275,296],[0,180,182,206,209],[180,182,206,209,299],[180,182,206,296,299], [0,180,182,209,265],[180,182,209,265,355],[180,182,209,299,355],[0,180,182,215,265], [180,182,215,265,355],[180,182,215,305,355],[180,182,272,275,296],[180,182,272,296,299], [180,182,272,299,355],[180,182,272,305,355],[0,180,183,184,185],[180,183,184,185,275], [0,180,183,184,274],[180,183,184,274,275],[0,180,183,185,206],[180,183,185,206,296], [180,183,185,275,296],[0,180,183,204,206],[180,183,204,206,296],[0,180,183,204,294], [180,183,204,294,296],[0,180,183,273,274],[180,183,273,274,275],[180,183,273,275,296], [0,180,183,273,294],[180,183,273,294,296],[0,180,204,206,209],[180,204,206,209,299], [180,204,206,296,299],[0,180,204,207,209],[180,204,207,209,299],[0,180,204,207,297], [180,204,207,297,299],[180,204,294,296,299],[0,180,204,294,297],[180,204,294,297,299], [0,180,207,209,265],[180,207,209,265,355],[180,207,209,299,355],[0,180,207,258,262], [180,207,258,262,352],[0,180,207,258,265],[180,207,258,265,355],[180,207,258,348,352], [180,207,258,348,355],[0,180,207,261,262],[180,207,261,262,352],[0,180,207,261,351], [180,207,261,351,352],[180,207,297,299,355],[180,207,297,348,352],[180,207,297,348,355], [0,180,207,297,351],[180,207,297,351,352],[0,180,213,214,215],[180,213,214,215,305], [0,180,213,214,262],[180,213,214,262,352],[180,213,214,304,305],[180,213,214,304,352], [0,180,213,215,265],[180,213,215,265,355],[180,213,215,305,355],[0,180,213,258,262], [180,213,258,262,352],[0,180,213,258,265],[180,213,258,265,355],[180,213,258,348,352], [180,213,258,348,355],[180,213,303,304,305],[180,213,303,304,352],[180,213,303,305,355], [180,213,303,348,352],[180,213,303,348,355],[180,270,271,272,275],[180,270,271,272,305], [0,180,270,271,274],[180,270,271,274,275],[180,270,271,304,305],[180,270,271,304,352], [0,180,270,271,351],[180,270,271,351,352],[180,270,272,275,296],[180,270,272,296,299], [180,270,272,299,355],[180,270,272,305,355],[0,180,270,273,274],[180,270,273,274,275], [180,270,273,275,296],[0,180,270,273,294],[180,270,273,294,296],[180,270,294,296,299], [0,180,270,294,297],[180,270,294,297,299],[180,270,297,299,355],[180,270,297,348,352], [180,270,297,348,355],[0,180,270,297,351],[180,270,297,351,352],[180,270,303,304,305], [180,270,303,304,352],[180,270,303,305,355],[180,270,303,348,352],[180,270,303,348,355], [1,2,5,41,131],[2,5,41,131,311],[1,2,5,41,221],[2,5,41,221,311], [1,2,5,95,131],[2,5,95,131,311],[2,5,95,275,311],[1,2,5,185,221], [2,5,185,221,311],[2,5,185,275,311],[1,2,35,85,175],[1,2,35,85,265], [1,2,35,125,175],[1,2,35,215,265],[1,2,38,41,131],[2,38,41,131,311], [1,2,38,41,221],[2,38,41,221,311],[1,2,38,88,178],[1,2,38,88,268], [1,2,38,128,131],[2,38,128,131,311],[1,2,38,128,178],[2,38,128,308,311], [1,2,38,218,221],[2,38,218,221,311],[1,2,38,218,268],[2,38,218,308,311], [1,2,84,85,175],[1,2,84,85,265],[1,2,84,88,178],[1,2,84,88,268], [1,2,84,174,175],[1,2,84,174,178],[1,2,84,264,265],[1,2,84,264,268], [1,2,92,95,131],[2,92,95,131,311],[2,92,95,275,311],[1,2,92,125,175], [1,2,92,128,131],[2,92,128,131,311],[1,2,92,128,178],[2,92,128,308,311], [1,2,92,174,175],[1,2,92,174,178],[2,92,272,275,311],[2,92,272,308,311], [1,2,182,185,221],[2,182,185,221,311],[2,182,185,275,311],[1,2,182,215,265], [1,2,182,218,221],[2,182,218,221,311],[1,2,182,218,268],[2,182,218,308,311], [1,2,182,264,265],[1,2,182,264,268],[2,182,272,275,311],[2,182,272,308,311], [1,4,5,41,131],[1,4,5,41,221],[1,4,5,95,131],[1,4,5,185,221], [1,4,39,41,131],[1,4,39,41,221],[1,4,39,129,131],[1,4,39,129,309], [1,4,39,219,221],[1,4,39,219,309],[1,4,94,95,131],[1,4,94,129,131], [1,4,94,129,309],[1,4,94,274,309],[1,4,184,185,221],[1,4,184,219,221], [1,4,184,219,309],[1,4,184,274,309],[1,34,35,85,175],[1,34,35,85,265], [1,34,35,125,175],[1,34,35,215,265],[1,34,79,82,172],[1,34,79,82,262], [1,34,79,85,175],[1,34,79,85,265],[1,34,79,169,172],[1,34,79,169,175], [1,34,79,259,262],[1,34,79,259,265],[1,34,124,125,175],[1,34,124,169,172], [1,34,124,169,175],[1,34,214,215,265],[1,34,214,259,262],[1,34,214,259,265], [1,36,38,41,131],[1,36,38,41,221],[1,36,38,88,178],[1,36,38,88,268], [1,36,38,128,131],[1,36,38,128,178],[1,36,38,218,221],[1,36,38,218,268], [1,36,39,41,131],[1,36,39,41,221],[1,36,39,129,131],[1,36,39,129,309], [1,36,39,219,221],[1,36,39,219,309],[1,36,79,82,172],[1,36,79,82,262], [1,36,79,85,175],[1,36,79,85,265],[1,36,79,169,172],[1,36,79,169,175], [1,36,79,259,262],[1,36,79,259,265],[1,36,81,82,172],[1,36,81,82,262], [1,36,81,171,172],[1,36,81,171,351],[1,36,81,261,262],[1,36,81,261,351], [1,36,84,85,175],[1,36,84,85,265],[1,36,84,88,178],[1,36,84,88,268], [1,36,84,174,175],[1,36,84,174,178],[1,36,84,264,265],[1,36,84,264,268], [1,36,126,128,131],[1,36,126,128,178],[1,36,126,129,131],[1,36,126,129,309], [1,36,126,169,172],[1,36,126,169,175],[1,36,126,171,172],[1,36,126,171,351], [1,36,126,174,175],[1,36,126,174,178],[1,36,126,306,309],[1,36,126,306,351], [1,36,216,218,221],[1,36,216,218,268],[1,36,216,219,221],[1,36,216,219,309], [1,36,216,259,262],[1,36,216,259,265],[1,36,216,261,262],[1,36,216,261,351], [1,36,216,264,265],[1,36,216,264,268],[1,36,216,306,309],[1,36,216,306,351], [1,91,92,95,131],[91,92,95,131,311],[91,92,95,275,311],[1,91,92,125,175], [91,92,125,175,355],[91,92,125,305,355],[1,91,92,128,131],[91,92,128,131,311], [1,91,92,128,178],[91,92,128,178,358],[91,92,128,308,311],[91,92,128,308,358], [1,91,92,174,175],[91,92,174,175,355],[1,91,92,174,178],[91,92,174,178,358], [91,92,174,354,355],[91,92,174,354,358],[91,92,272,275,311],[91,92,272,305,355], 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