#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_019 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(1092,16902,56708,68160,27264) ### ### 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:=[ [0,1,2,5,275],[0,1,2,5,540],[1,2,5,540,1086],[1,2,5,551,1086], [0,1,2,35,305],[0,1,2,35,540],[1,2,35,540,1086],[1,2,35,581,1086], [0,1,2,272,275],[0,1,2,272,305],[1,2,548,551,1086],[1,2,548,581,1086], [0,1,4,5,275],[0,1,4,5,540],[0,1,4,540,1086],[1,4,5,540,1086], [1,4,5,551,1086],[0,1,4,274,275],[0,1,4,274,820],[0,1,4,550,1086], [1,4,550,551,1086],[0,1,4,550,820],[0,1,34,35,305],[0,1,34,35,540], [0,1,34,540,1086],[1,34,35,540,1086],[1,34,35,581,1086],[0,1,34,262,532], [0,1,34,262,808],[0,1,34,304,305],[0,1,34,304,532],[0,1,34,580,1086], [1,34,580,581,1086],[0,1,34,580,808],[0,1,261,262,532],[0,1,261,262,808], [0,1,261,531,532],[0,1,261,531,1077],[0,1,261,807,808],[0,1,261,807,1077], [0,1,271,272,275],[0,1,271,272,305],[0,1,271,274,275],[0,1,271,274,820], [0,1,271,304,305],[0,1,271,304,532],[0,1,271,531,532],[0,1,271,531,1077], [0,1,271,817,820],[0,1,271,817,1077],[1,547,548,551,1086],[1,547,548,581,1086], [0,1,547,550,1086],[1,547,550,551,1086],[0,1,547,550,820],[0,1,547,580,1086], [1,547,580,581,1086],[0,1,547,580,808],[0,1,547,807,808],[0,1,547,807,1077], [0,1,547,817,820],[0,1,547,817,1077],[0,2,5,26,296],[2,5,26,296,842], [0,2,5,26,572],[2,5,26,572,842],[0,2,5,275,296],[2,5,275,296,842], [2,5,275,821,842],[0,2,5,540,541],[0,2,5,541,1087],[2,5,540,541,1087], [2,5,540,1086,1087],[0,2,5,551,572],[2,5,551,572,842],[2,5,551,821,842], [0,2,5,551,1087],[2,5,551,1086,1087],[0,2,26,29,299],[2,26,29,299,845], [0,2,26,29,575],[2,26,29,575,845],[0,2,26,296,299],[2,26,296,299,845], [2,26,296,842,845],[0,2,26,572,575],[2,26,572,575,845],[2,26,572,842,845], [0,2,29,265,535],[0,2,29,265,811],[0,2,29,299,535],[0,2,29,575,811], [0,2,35,265,535],[0,2,35,265,811],[0,2,35,305,535],[0,2,35,540,541], [0,2,35,541,1087],[2,35,540,541,1087],[2,35,540,1086,1087],[0,2,35,581,811], [0,2,35,581,1087],[2,35,581,1086,1087],[0,2,272,275,296],[2,272,275,296,842], [2,272,275,821,842],[0,2,272,296,299],[2,272,296,299,845],[2,272,296,842,845], [0,2,272,299,535],[0,2,272,305,535],[2,272,818,821,842],[2,272,818,842,845], [0,2,548,551,572],[2,548,551,572,842],[2,548,551,821,842],[0,2,548,551,1087], [2,548,551,1086,1087],[0,2,548,572,575],[2,548,572,575,845],[2,548,572,842,845], [0,2,548,575,811],[0,2,548,581,811],[0,2,548,581,1087],[2,548,581,1086,1087], [2,548,818,821,842],[2,548,818,842,845],[0,3,4,5,275],[0,3,4,5,540], [0,3,4,540,1086],[0,3,4,274,275],[0,3,4,274,820],[0,3,4,550,1086], [0,3,4,550,820],[0,3,5,26,296],[0,3,5,26,572],[0,3,5,275,296], [0,3,5,540,541],[0,3,5,541,1087],[0,3,5,551,572],[0,3,5,551,1087], [0,3,24,26,296],[0,3,24,26,572],[0,3,24,294,296],[0,3,24,294,840], [0,3,24,570,572],[0,3,24,570,840],[0,3,273,274,275],[0,3,273,274,820], [0,3,273,275,296],[0,3,273,294,296],[0,3,273,294,840],[0,3,273,819,820], [0,3,273,819,840],[0,3,540,541,542],[0,3,540,542,1088],[0,3,541,542,1088], [0,3,541,1087,1088],[0,3,540,1086,1088],[0,3,549,550,1086],[0,3,549,550,820], [0,3,549,551,572],[0,3,549,551,1087],[0,3,549,570,572],[0,3,549,570,840], [0,3,549,819,820],[0,3,549,819,840],[0,3,549,1086,1088],[0,3,549,1087,1088], [0,24,26,29,299],[0,24,26,29,575],[0,24,26,296,299],[0,24,26,572,575], [0,24,27,29,299],[0,24,27,29,575],[0,24,27,297,299],[0,24,27,297,843], [0,24,27,573,575],[0,24,27,573,843],[0,24,294,296,299],[0,24,294,297,299], [0,24,294,297,843],[0,24,294,840,843],[0,24,570,572,575],[0,24,570,573,575], [0,24,570,573,843],[0,24,570,840,843],[0,27,29,265,535],[0,27,29,265,811], [0,27,29,299,535],[0,27,29,575,811],[0,27,258,262,532],[0,27,258,262,808], [0,27,258,265,535],[0,27,258,265,811],[0,27,258,528,532],[0,27,258,528,535], [0,27,258,804,808],[0,27,258,804,811],[0,27,261,262,532],[0,27,261,262,808], [0,27,261,531,532],[0,27,261,531,1077],[0,27,261,807,808],[0,27,261,807,1077], [0,27,297,299,535],[0,27,297,528,532],[0,27,297,528,535],[0,27,297,531,532], [0,27,297,531,1077],[0,27,297,843,1077],[0,27,573,575,811],[0,27,573,804,808], [0,27,573,804,811],[0,27,573,807,808],[0,27,573,807,1077],[0,27,573,843,1077], [0,33,34,35,305],[0,33,34,35,540],[0,33,34,540,1086],[0,33,34,262,532], [0,33,34,262,808],[0,33,34,304,305],[0,33,34,304,532],[0,33,34,580,1086], [0,33,34,580,808],[0,33,35,265,535],[0,33,35,265,811],[0,33,35,305,535], [0,33,35,540,541],[0,33,35,541,1087],[0,33,35,581,811],[0,33,35,581,1087], [0,33,258,262,532],[0,33,258,262,808],[0,33,258,265,535],[0,33,258,265,811], [0,33,258,528,532],[0,33,258,528,535],[0,33,258,804,808],[0,33,258,804,811], [0,33,303,304,305],[0,33,303,304,532],[0,33,303,305,535],[0,33,303,528,532], [0,33,303,528,535],[0,33,540,541,542],[0,33,540,542,1088],[0,33,541,542,1088], [0,33,541,1087,1088],[0,33,540,1086,1088],[0,33,579,580,1086],[0,33,579,580,808], [0,33,579,581,811],[0,33,579,581,1087],[0,33,579,804,808],[0,33,579,804,811], [0,33,579,1086,1088],[0,33,579,1087,1088],[0,270,271,272,275],[270,271,272,275,821], [0,270,271,272,305],[270,271,272,305,851],[270,271,272,818,821],[270,271,272,818,851], [0,270,271,274,275],[270,271,274,275,821],[0,270,271,274,820],[270,271,274,820,821], [0,270,271,304,305],[270,271,304,305,851],[0,270,271,304,532],[270,271,304,532,1078], [270,271,304,850,851],[270,271,304,850,1078],[0,270,271,531,532],[270,271,531,532,1078], [0,270,271,531,1077],[270,271,531,1077,1078],[270,271,817,818,821],[270,271,817,818,851], [0,270,271,817,820],[270,271,817,820,821],[270,271,817,850,851],[270,271,817,850,1078], [0,270,271,817,1077],[270,271,817,1077,1078],[0,270,272,275,296],[270,272,275,296,842], [270,272,275,821,842],[0,270,272,296,299],[270,272,296,299,845],[270,272,296,842,845], [0,270,272,299,535],[270,272,299,535,1081],[270,272,299,845,1081],[0,270,272,305,535], [270,272,305,535,1081],[270,272,305,851,1081],[270,272,818,821,842],[270,272,818,842,845], [270,272,818,845,1081],[270,272,818,851,1081],[0,270,273,274,275],[270,273,274,275,821], [0,270,273,274,820],[270,273,274,820,821],[0,270,273,275,296],[270,273,275,296,842], [270,273,275,821,842],[0,270,273,294,296],[270,273,294,296,842],[0,270,273,294,840], [270,273,294,840,842],[0,270,273,819,820],[270,273,819,820,821],[270,273,819,821,842], [0,270,273,819,840],[270,273,819,840,842],[0,270,294,296,299],[270,294,296,299,845], [270,294,296,842,845],[0,270,294,297,299],[270,294,297,299,845],[0,270,294,297,843], [270,294,297,843,845],[270,294,840,842,845],[0,270,294,840,843],[270,294,840,843,845], [0,270,297,299,535],[270,297,299,535,1081],[270,297,299,845,1081],[0,270,297,528,532], [270,297,528,532,1078],[0,270,297,528,535],[270,297,528,535,1081],[270,297,528,1074,1078], [270,297,528,1074,1081],[0,270,297,531,532],[270,297,531,532,1078],[0,270,297,531,1077], [270,297,531,1077,1078],[270,297,843,845,1081],[270,297,843,1074,1078],[270,297,843,1074,1081], [0,270,297,843,1077],[270,297,843,1077,1078],[0,270,303,304,305],[270,303,304,305,851], [0,270,303,304,532],[270,303,304,532,1078],[270,303,304,850,851],[270,303,304,850,1078], [0,270,303,305,535],[270,303,305,535,1081],[270,303,305,851,1081],[0,270,303,528,532], [270,303,528,532,1078],[0,270,303,528,535],[270,303,528,535,1081],[270,303,528,1074,1078], [270,303,528,1074,1081],[270,303,849,850,851],[270,303,849,850,1078],[270,303,849,851,1081], [270,303,849,1074,1078],[270,303,849,1074,1081],[270,816,817,818,821],[270,816,817,818,851], [0,270,816,817,820],[270,816,817,820,821],[270,816,817,850,851],[270,816,817,850,1078], [0,270,816,817,1077],[270,816,817,1077,1078],[270,816,818,821,842],[270,816,818,842,845], [270,816,818,845,1081],[270,816,818,851,1081],[0,270,816,819,820],[270,816,819,820,821], [270,816,819,821,842],[0,270,816,819,840],[270,816,819,840,842],[270,816,840,842,845], [0,270,816,840,843],[270,816,840,843,845],[270,816,843,845,1081],[270,816,843,1074,1078], [270,816,843,1074,1081],[0,270,816,843,1077],[270,816,843,1077,1078],[270,816,849,850,851], [270,816,849,850,1078],[270,816,849,851,1081],[270,816,849,1074,1078],[270,816,849,1074,1081], [546,547,548,551,821],[546,547,548,551,1086],[546,547,548,581,851],[546,547,548,581,1086], [546,547,548,818,821],[546,547,548,818,851],[546,547,550,551,821],[0,546,547,550,1086], [546,547,550,551,1086],[0,546,547,550,820],[546,547,550,820,821],[546,547,580,581,851], [0,546,547,580,1086],[546,547,580,581,1086],[0,546,547,580,808],[546,547,580,808,1078], [546,547,580,850,851],[546,547,580,850,1078],[0,546,547,807,808],[546,547,807,808,1078], [0,546,547,807,1077],[546,547,807,1077,1078],[546,547,817,818,821],[546,547,817,818,851], [0,546,547,817,820],[546,547,817,820,821],[546,547,817,850,851],[546,547,817,850,1078], [0,546,547,817,1077],[546,547,817,1077,1078],[0,546,548,551,572],[546,548,551,572,842], [546,548,551,821,842],[0,546,548,551,1087],[546,548,551,1086,1087],[0,546,548,572,575], [546,548,572,575,845],[546,548,572,842,845],[0,546,548,575,811],[546,548,575,811,1081], [546,548,575,845,1081],[0,546,548,581,811],[546,548,581,811,1081],[546,548,581,851,1081], [0,546,548,581,1087],[546,548,581,1086,1087],[546,548,818,821,842],[546,548,818,842,845], [546,548,818,845,1081],[546,548,818,851,1081],[546,549,550,551,821],[0,546,549,550,1086], [546,549,550,551,1086],[0,546,549,550,820],[546,549,550,820,821],[0,546,549,551,572], [546,549,551,572,842],[546,549,551,821,842],[0,546,549,551,1087],[546,549,551,1086,1087], [0,546,549,570,572],[546,549,570,572,842],[0,546,549,570,840],[546,549,570,840,842], [0,546,549,819,820],[546,549,819,820,821],[546,549,819,821,842],[0,546,549,819,840], [546,549,819,840,842],[0,546,549,1086,1088],[0,546,549,1087,1088],[546,549,1086,1087,1088], [0,546,570,572,575],[546,570,572,575,845],[546,570,572,842,845],[0,546,570,573,575], [546,570,573,575,845],[0,546,570,573,843],[546,570,573,843,845],[546,570,840,842,845], [0,546,570,840,843],[546,570,840,843,845],[0,546,573,575,811],[546,573,575,811,1081], [546,573,575,845,1081],[0,546,573,804,808],[546,573,804,808,1078],[0,546,573,804,811], [546,573,804,811,1081],[546,573,804,1074,1078],[546,573,804,1074,1081],[0,546,573,807,808], [546,573,807,808,1078],[0,546,573,807,1077],[546,573,807,1077,1078],[546,573,843,845,1081], [546,573,843,1074,1078],[546,573,843,1074,1081],[0,546,573,843,1077],[546,573,843,1077,1078], [546,579,580,581,851],[0,546,579,580,1086],[546,579,580,581,1086],[0,546,579,580,808], [546,579,580,808,1078],[546,579,580,850,851],[546,579,580,850,1078],[0,546,579,581,811], [546,579,581,811,1081],[546,579,581,851,1081],[0,546,579,581,1087],[546,579,581,1086,1087], [0,546,579,804,808],[546,579,804,808,1078],[0,546,579,804,811],[546,579,804,811,1081], [546,579,804,1074,1078],[546,579,804,1074,1081],[546,579,849,850,851],[546,579,849,850,1078], [546,579,849,851,1081],[546,579,849,1074,1078],[546,579,849,1074,1081],[0,546,579,1086,1088], [0,546,579,1087,1088],[546,579,1086,1087,1088],[546,816,817,818,821],[546,816,817,818,851], [0,546,816,817,820],[546,816,817,820,821],[546,816,817,850,851],[546,816,817,850,1078], [0,546,816,817,1077],[546,816,817,1077,1078],[546,816,818,821,842],[546,816,818,842,845], [546,816,818,845,1081],[546,816,818,851,1081],[0,546,816,819,820],[546,816,819,820,821], [546,816,819,821,842],[0,546,816,819,840],[546,816,819,840,842],[546,816,840,842,845], [0,546,816,840,843],[546,816,840,843,845],[546,816,843,845,1081],[546,816,843,1074,1078], [546,816,843,1074,1081],[0,546,816,843,1077],[546,816,843,1077,1078],[546,816,849,850,851], [546,816,849,850,1078],[546,816,849,851,1081],[546,816,849,1074,1078],[546,816,849,1074,1081], [1,2,5,41,311],[2,5,41,311,857],[1,2,5,41,587],[2,5,41,587,857], [1,2,5,275,311],[2,5,275,311,857],[2,5,275,821,857],[1,2,5,551,587], [2,5,551,587,857],[2,5,551,821,857],[1,2,35,265,535],[1,2,35,265,811], [1,2,35,305,535],[1,2,35,581,811],[1,2,38,41,311],[2,38,41,311,857], [1,2,38,41,587],[2,38,41,587,857],[1,2,38,268,538],[1,2,38,268,814], [1,2,38,308,311],[2,38,308,311,857],[1,2,38,308,538],[2,38,308,854,857], [1,2,38,584,587],[2,38,584,587,857],[1,2,38,584,814],[2,38,584,854,857], [1,2,264,265,535],[1,2,264,265,811],[1,2,264,268,538],[1,2,264,268,814], [1,2,264,534,535],[1,2,264,534,538],[1,2,264,810,811],[1,2,264,810,814], [1,2,272,275,311],[2,272,275,311,857],[2,272,275,821,857],[1,2,272,305,535], [1,2,272,308,311],[2,272,308,311,857],[1,2,272,308,538],[2,272,308,854,857], [1,2,272,534,535],[1,2,272,534,538],[2,272,818,821,857],[2,272,818,854,857], 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[222,492,499,502,1048],[492,499,502,1048,1049],[492,499,1045,1046,1049],[222,492,499,1045,1048], [492,499,1045,1048,1049],[492,1038,1039,1040,1043],[222,492,1038,1039,1042],[492,1038,1039,1042,1043], [492,1038,1040,1043,1049],[492,1038,1040,1046,1049],[222,492,1038,1041,1042],[492,1038,1041,1042,1043], [492,1038,1041,1043,1049],[222,492,1038,1041,1048],[492,1038,1041,1048,1049],[492,1038,1045,1046,1049], [222,492,1038,1045,1048],[492,1038,1045,1048,1049],[768,769,770,773,1043],[768,769,770,773,1089], [768,769,770,1040,1043],[768,769,772,773,1043],[222,768,769,772,1089],[768,769,772,773,1089], [222,768,769,772,1042],[768,769,772,1042,1043],[768,769,1039,1040,1043],[222,768,769,1039,1042], [768,769,1039,1042,1043],[222,768,770,773,779],[768,770,773,779,1049],[768,770,773,1043,1049], [222,768,770,773,1090],[768,770,773,1089,1090],[222,768,770,776,779],[768,770,776,779,1049], [768,770,776,1046,1049],[768,770,1040,1043,1049],[768,770,1040,1046,1049],[768,771,772,773,1043], 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[224,494,500,1046,1083],[494,500,1046,1083,1084],[494,1040,1046,1080,1081],[494,1040,1046,1080,1084], [224,494,1040,1046,1083],[494,1040,1046,1083,1084],[224,770,776,810,811],[770,776,810,811,1081], [224,770,776,810,814],[770,776,810,814,1084],[770,776,810,1080,1081],[770,776,810,1080,1084], [224,770,776,813,814],[770,776,813,814,1084],[224,770,776,813,1083],[770,776,813,1083,1084], [770,776,1046,1080,1081],[770,776,1046,1080,1084],[224,770,776,1046,1083],[770,776,1046,1083,1084], [770,1040,1046,1080,1081],[770,1040,1046,1080,1084],[224,770,1040,1046,1083],[770,1040,1046,1083,1084], [225,226,227,230,500],[225,226,227,230,543],[226,227,230,543,1089],[226,227,230,776,1089], [225,226,227,497,500],[226,227,773,776,1089],[225,226,229,230,500],[225,226,229,230,543], [225,226,229,543,1089],[226,229,230,543,1089],[226,229,230,776,1089],[225,226,229,499,500], [225,226,229,499,1045],[225,226,229,775,1089],[226,229,775,776,1089],[225,226,229,775,1045], 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[227,773,779,782,811],[773,779,782,811,1081],[773,779,782,1052,1081],[227,773,779,809,811], [773,779,809,811,1081],[227,773,779,809,814],[773,779,809,814,1084],[773,779,809,1079,1081], [773,779,809,1079,1084],[227,773,779,813,814],[773,779,813,814,1084],[227,773,779,813,1083], [773,779,813,1083,1084],[773,779,1049,1052,1081],[773,779,1049,1079,1081],[773,779,1049,1079,1084], [227,773,779,1049,1083],[773,779,1049,1083,1084],[773,1043,1046,1052,1081],[773,1043,1049,1052,1081], [773,1043,1049,1079,1081],[773,1043,1049,1079,1084],[227,773,1043,1049,1083],[773,1043,1049,1083,1084], [228,229,230,233,503],[228,229,230,233,543],[229,230,233,543,1089],[229,230,233,779,1089], [228,229,230,500,503],[229,230,776,779,1089],[228,229,232,233,503],[228,229,232,233,543], [228,229,232,543,1089],[229,232,233,543,1089],[229,232,233,779,1089],[228,229,232,502,503], [228,229,232,502,1048],[228,229,232,778,1089],[229,232,778,779,1089],[228,229,232,778,1048], 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