#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_017 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(746,10716,35424,42420,16968) ### ### 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:=[ [0,1,2,5,497],[0,1,2,35,527],[0,1,2,494,497],[0,1,2,494,527], [0,1,4,5,497],[0,1,4,250,496],[0,1,4,496,497],[0,1,34,35,527], [0,1,34,238,484],[0,1,34,238,730],[0,1,34,280,484],[0,1,34,526,527], [0,1,34,526,730],[0,1,237,238,484],[0,1,237,238,730],[0,1,237,483,484], [0,1,237,483,729],[0,1,237,729,730],[0,1,247,250,496],[0,1,247,280,484], [0,1,247,483,484],[0,1,247,483,729],[0,1,493,494,497],[0,1,493,494,527], [0,1,247,493,496],[0,1,493,496,497],[0,1,493,526,527],[0,1,493,526,730], [0,1,247,493,729],[0,1,493,729,730],[0,2,5,26,272],[0,2,5,26,518], [2,5,26,272,518],[0,2,5,251,272],[2,5,251,272,518],[0,2,5,497,518], [2,5,251,497,518],[0,2,26,29,275],[0,2,26,29,521],[2,26,29,275,521], [0,2,26,272,275],[2,26,272,275,521],[0,2,26,518,521],[2,26,272,518,521], [0,2,29,241,487],[0,2,29,241,733],[0,2,29,275,487],[0,2,29,521,733], [0,2,35,241,487],[0,2,35,241,733],[0,2,35,281,487],[0,2,35,527,733], [0,2,248,251,272],[2,248,251,272,518],[2,248,251,497,518],[0,2,248,272,275], [2,248,272,275,521],[2,248,272,518,521],[0,2,248,275,487],[0,2,248,281,487], [0,2,494,497,518],[2,248,494,497,518],[0,2,494,518,521],[2,248,494,518,521], [0,2,494,521,733],[0,2,494,527,733],[0,3,4,5,497],[0,3,4,250,496], [0,3,4,496,497],[0,3,5,26,272],[0,3,5,26,518],[0,3,5,251,272], [0,3,5,497,518],[0,3,24,26,272],[0,3,24,26,518],[0,3,24,270,272], [0,3,24,270,516],[0,3,24,516,518],[0,3,249,250,496],[0,3,249,251,272], [0,3,249,270,272],[0,3,249,270,516],[0,3,249,495,496],[0,3,495,496,497], [0,3,495,497,518],[0,3,249,495,516],[0,3,495,516,518],[0,24,26,29,275], [0,24,26,29,521],[0,24,26,272,275],[0,24,26,518,521],[0,24,27,29,275], [0,24,27,29,521],[0,24,27,273,275],[0,24,27,273,519],[0,24,27,519,521], [0,24,270,272,275],[0,24,270,273,275],[0,24,270,273,519],[0,24,516,518,521], [0,24,270,516,519],[0,24,516,519,521],[0,27,29,241,487],[0,27,29,241,733], [0,27,29,275,487],[0,27,29,521,733],[0,27,234,238,484],[0,27,234,238,730], [0,27,234,241,487],[0,27,234,241,733],[0,27,234,480,484],[0,27,234,480,487], [0,27,234,726,730],[0,27,234,726,733],[0,27,237,238,484],[0,27,237,238,730], [0,27,237,483,484],[0,27,237,483,729],[0,27,237,729,730],[0,27,273,275,487], [0,27,273,480,484],[0,27,273,480,487],[0,27,273,483,484],[0,27,273,483,729], [0,27,519,521,733],[0,27,519,726,730],[0,27,519,726,733],[0,27,273,519,729], [0,27,519,729,730],[0,33,34,35,527],[0,33,34,238,484],[0,33,34,238,730], [0,33,34,280,484],[0,33,34,526,527],[0,33,34,526,730],[0,33,35,241,487], [0,33,35,241,733],[0,33,35,281,487],[0,33,35,527,733],[0,33,234,238,484], [0,33,234,238,730],[0,33,234,241,487],[0,33,234,241,733],[0,33,234,480,484], [0,33,234,480,487],[0,33,234,726,730],[0,33,234,726,733],[0,33,279,280,484], [0,33,279,281,487],[0,33,279,480,484],[0,33,279,480,487],[0,33,525,526,527], [0,33,525,526,730],[0,33,525,527,733],[0,33,525,726,730],[0,33,525,726,733], [246,247,248,251,497],[246,247,248,281,527],[246,247,248,494,497],[246,247,248,494,527], [246,247,250,251,497],[0,246,247,250,496],[246,247,250,496,497],[246,247,280,281,527], [0,246,247,280,484],[246,247,280,484,730],[246,247,280,526,527],[246,247,280,526,730], [0,246,247,483,484],[246,247,483,484,730],[0,246,247,483,729],[246,247,483,729,730], [246,247,493,494,497],[246,247,493,494,527],[0,246,247,493,496],[246,247,493,496,497], [246,247,493,526,527],[246,247,493,526,730],[0,246,247,493,729],[246,247,493,729,730], [0,246,248,251,272],[246,248,251,272,518],[246,248,251,497,518],[0,246,248,272,275], [246,248,272,275,521],[246,248,272,518,521],[0,246,248,275,487],[246,248,275,487,733], [246,248,275,521,733],[0,246,248,281,487],[246,248,281,487,733],[246,248,281,527,733], [246,248,494,497,518],[246,248,494,518,521],[246,248,494,521,733],[246,248,494,527,733], [246,249,250,251,497],[0,246,249,250,496],[246,249,250,496,497],[0,246,249,251,272], [246,249,251,272,518],[246,249,251,497,518],[0,246,249,270,272],[246,249,270,272,518], [0,246,249,270,516],[246,249,270,516,518],[0,246,249,495,496],[246,249,495,496,497], [246,249,495,497,518],[0,246,249,495,516],[246,249,495,516,518],[0,246,270,272,275], [246,270,272,275,521],[246,270,272,518,521],[0,246,270,273,275],[246,270,273,275,521], [0,246,270,273,519],[246,270,273,519,521],[246,270,516,518,521],[0,246,270,516,519], [246,270,516,519,521],[0,246,273,275,487],[246,273,275,487,733],[246,273,275,521,733], [0,246,273,480,484],[246,273,480,484,730],[0,246,273,480,487],[246,273,480,487,733], [246,273,480,726,730],[246,273,480,726,733],[0,246,273,483,484],[246,273,483,484,730], [0,246,273,483,729],[246,273,483,729,730],[246,273,519,521,733],[246,273,519,726,730], [246,273,519,726,733],[0,246,273,519,729],[246,273,519,729,730],[246,279,280,281,527], [0,246,279,280,484],[246,279,280,484,730],[246,279,280,526,527],[246,279,280,526,730], [0,246,279,281,487],[246,279,281,487,733],[246,279,281,527,733],[0,246,279,480,484], [246,279,480,484,730],[0,246,279,480,487],[246,279,480,487,733],[246,279,480,726,730], [246,279,480,726,733],[246,279,525,526,527],[246,279,525,526,730],[246,279,525,527,733], [246,279,525,726,730],[246,279,525,726,733],[0,492,493,494,497],[246,492,493,494,497], [0,492,493,494,527],[246,492,493,494,527],[0,246,492,493,496],[0,492,493,496,497], [246,492,493,496,497],[0,492,493,526,527],[246,492,493,526,527],[0,492,493,526,730], [246,492,493,526,730],[0,246,492,493,729],[0,492,493,729,730],[246,492,493,729,730], [0,492,494,497,518],[246,492,494,497,518],[0,492,494,518,521],[246,492,494,518,521], [0,492,494,521,733],[246,492,494,521,733],[0,492,494,527,733],[246,492,494,527,733], [0,246,492,495,496],[0,492,495,496,497],[246,492,495,496,497],[0,492,495,497,518], [246,492,495,497,518],[0,246,492,495,516],[0,492,495,516,518],[246,492,495,516,518], [0,492,516,518,521],[246,492,516,518,521],[0,246,492,516,519],[0,492,516,519,521], [246,492,516,519,521],[0,492,519,521,733],[246,492,519,521,733],[0,492,519,726,730], [246,492,519,726,730],[0,492,519,726,733],[246,492,519,726,733],[0,246,492,519,729], [0,492,519,729,730],[246,492,519,729,730],[0,492,525,526,527],[246,492,525,526,527], [0,492,525,526,730],[246,492,525,526,730],[0,492,525,527,733],[246,492,525,527,733], [0,492,525,726,730],[246,492,525,726,730],[0,492,525,726,733],[246,492,525,726,733], [1,2,5,41,287],[1,2,5,41,533],[2,5,41,287,533],[1,2,5,251,287], [2,5,251,287,533],[1,2,5,497,533],[2,5,251,497,533],[1,2,35,241,487], [1,2,35,241,733],[1,2,35,281,487],[1,2,35,527,733],[1,2,38,41,287], [1,2,38,41,533],[2,38,41,287,533],[1,2,38,244,490],[1,2,38,244,736], [1,2,38,284,287],[2,38,284,287,533],[1,2,38,284,490],[1,2,38,530,533], [2,38,284,530,533],[1,2,38,530,736],[1,2,240,241,487],[1,2,240,241,733], [1,2,240,244,490],[1,2,240,244,736],[1,2,240,486,487],[1,2,240,486,490], [1,2,240,732,733],[1,2,240,732,736],[1,2,248,251,287],[2,248,251,287,533], [2,248,251,497,533],[1,2,248,281,487],[1,2,248,284,287],[2,248,284,287,533], [1,2,248,284,490],[2,248,284,530,533],[1,2,248,486,487],[1,2,248,486,490], [1,2,494,497,533],[2,248,494,497,533],[1,2,494,527,733],[1,2,494,530,533], [2,248,494,530,533],[1,2,494,530,736],[1,2,494,732,733],[1,2,494,732,736], [1,4,5,41,287],[1,4,5,41,533],[1,4,5,251,287],[1,4,5,497,533], [1,4,39,41,287],[1,4,39,41,533],[1,4,39,285,287],[1,4,39,285,531], [1,4,39,531,533],[1,4,250,251,287],[1,4,250,285,287],[1,4,250,285,531], [1,4,496,497,533],[1,4,250,496,531],[1,4,496,531,533],[1,34,35,241,487], [1,34,35,241,733],[1,34,35,281,487],[1,34,35,527,733],[1,34,235,238,484], [1,34,235,238,730],[1,34,235,241,487],[1,34,235,241,733],[1,34,235,481,484], [1,34,235,481,487],[1,34,235,727,730],[1,34,235,727,733],[1,34,280,281,487], [1,34,280,481,484],[1,34,280,481,487],[1,34,526,527,733],[1,34,526,727,730], [1,34,526,727,733],[1,36,38,41,287],[1,36,38,41,533],[1,36,38,244,490], [1,36,38,244,736],[1,36,38,284,287],[1,36,38,284,490],[1,36,38,530,533], [1,36,38,530,736],[1,36,39,41,287],[1,36,39,41,533],[1,36,39,285,287], [1,36,39,285,531],[1,36,39,531,533],[1,36,235,238,484],[1,36,235,238,730], [1,36,235,241,487],[1,36,235,241,733],[1,36,235,481,484],[1,36,235,481,487], [1,36,235,727,730],[1,36,235,727,733],[1,36,237,238,484],[1,36,237,238,730], [1,36,237,483,484],[1,36,237,483,729],[1,36,237,729,730],[1,36,240,241,487], [1,36,240,241,733],[1,36,240,244,490],[1,36,240,244,736],[1,36,240,486,487], [1,36,240,486,490],[1,36,240,732,733],[1,36,240,732,736],[1,36,282,284,287], [1,36,282,284,490],[1,36,282,285,287],[1,36,282,285,531],[1,36,282,481,484], [1,36,282,481,487],[1,36,282,483,484],[1,36,282,483,729],[1,36,282,486,487], [1,36,282,486,490],[1,36,528,530,533],[1,36,528,530,736],[1,36,282,528,531], [1,36,528,531,533],[1,36,528,727,730],[1,36,528,727,733],[1,36,282,528,729], [1,36,528,729,730],[1,36,528,732,733],[1,36,528,732,736],[1,247,248,251,287], [247,248,251,287,533],[247,248,251,497,533],[1,247,248,281,487],[247,248,281,487,733], [247,248,281,527,733],[1,247,248,284,287],[247,248,284,287,533],[1,247,248,284,490], [247,248,284,490,736],[247,248,284,530,533],[247,248,284,530,736],[1,247,248,486,487], [247,248,486,487,733],[1,247,248,486,490],[247,248,486,490,736],[247,248,486,732,733], [247,248,486,732,736],[247,248,494,497,533],[247,248,494,527,733],[247,248,494,530,533], [247,248,494,530,736],[247,248,494,732,733],[247,248,494,732,736],[1,247,250,251,287], [247,250,251,287,533],[247,250,251,497,533],[1,247,250,285,287],[247,250,285,287,533], [1,247,250,285,531],[247,250,285,531,533],[247,250,496,497,533],[1,247,250,496,531], [247,250,496,531,533],[1,247,280,281,487],[247,280,281,487,733],[247,280,281,527,733], [1,247,280,481,484],[247,280,481,484,730],[1,247,280,481,487],[247,280,481,487,733], [247,280,481,727,730],[247,280,481,727,733],[247,280,526,527,733],[247,280,526,727,730], [247,280,526,727,733],[1,247,282,284,287],[247,282,284,287,533],[1,247,282,284,490], [247,282,284,490,736],[247,282,284,530,533],[247,282,284,530,736],[1,247,282,285,287], [247,282,285,287,533],[1,247,282,285,531],[247,282,285,531,533],[1,247,282,481,484], [247,282,481,484,730],[1,247,282,481,487],[247,282,481,487,733],[247,282,481,727,730], [247,282,481,727,733],[1,247,282,483,484],[247,282,483,484,730],[1,247,282,483,729], [247,282,483,729,730],[1,247,282,486,487],[247,282,486,487,733],[1,247,282,486,490], [247,282,486,490,736],[247,282,486,732,733],[247,282,486,732,736],[247,282,528,530,533], [247,282,528,530,736],[1,247,282,528,531],[247,282,528,531,533],[247,282,528,727,730], [247,282,528,727,733],[1,247,282,528,729],[247,282,528,729,730],[247,282,528,732,733], [247,282,528,732,736],[1,493,494,497,533],[247,493,494,497,533],[1,493,494,527,733], [247,493,494,527,733],[1,493,494,530,533],[247,493,494,530,533],[1,493,494,530,736], [247,493,494,530,736],[1,493,494,732,733],[247,493,494,732,733],[1,493,494,732,736], [247,493,494,732,736],[1,493,496,497,533],[247,493,496,497,533],[1,247,493,496,531], [1,493,496,531,533],[247,493,496,531,533],[1,493,526,527,733],[247,493,526,527,733], [1,493,526,727,730],[247,493,526,727,730],[1,493,526,727,733],[247,493,526,727,733], [1,493,528,530,533],[247,493,528,530,533],[1,493,528,530,736],[247,493,528,530,736], [1,247,493,528,531],[1,493,528,531,533],[247,493,528,531,533],[1,493,528,727,730], [247,493,528,727,730],[1,493,528,727,733],[247,493,528,727,733],[1,247,493,528,729], [1,493,528,729,730],[247,493,528,729,730],[1,493,528,732,733],[247,493,528,732,733], [1,493,528,732,736],[247,493,528,732,736],[2,29,240,241,487],[2,29,240,241,733], [2,29,240,244,490],[2,29,240,244,736],[2,29,240,486,487],[2,29,240,486,490], [2,29,240,732,733],[2,29,240,732,736],[2,29,242,244,490],[2,29,242,244,736], [2,29,242,488,490],[2,29,242,488,734],[2,29,242,734,736],[2,29,275,486,487], [2,29,275,486,490],[2,29,275,488,490],[2,29,275,488,734],[2,29,521,732,733], [2,29,521,732,736],[2,29,275,521,734],[2,29,521,734,736],[2,38,242,244,490], [2,38,242,244,736],[2,38,242,488,490],[2,38,242,488,734],[2,38,242,734,736], [2,38,284,488,490],[2,38,284,488,734],[2,38,284,530,734],[2,38,530,734,736], [2,248,275,486,487],[248,275,486,487,733],[2,248,275,486,490],[248,275,486,490,736], [248,275,486,732,733],[248,275,486,732,736],[2,248,275,488,490],[248,275,488,490,736], [2,248,275,488,734],[248,275,488,734,736],[248,275,521,732,733],[248,275,521,732,736], [2,248,275,521,734],[248,275,521,734,736],[2,248,284,488,490],[248,284,488,490,736], [2,248,284,488,734],[248,284,488,734,736],[2,248,284,530,734],[248,284,530,734,736], [2,494,521,732,733],[248,494,521,732,733],[2,494,521,732,736],[248,494,521,732,736], [2,248,494,521,734],[2,494,521,734,736],[248,494,521,734,736],[2,248,494,530,734], [2,494,530,734,736],[248,494,530,734,736],[3,4,5,8,500],[3,4,5,497,500], [3,4,7,8,500],[3,4,7,238,484],[3,4,7,238,730],[3,4,7,253,484], [3,4,7,499,500],[3,4,7,499,730],[3,4,237,238,484],[3,4,237,238,730], [3,4,237,483,484],[3,4,237,483,729],[3,4,237,729,730],[3,4,250,253,484], [3,4,250,483,484],[3,4,250,483,729],[3,4,496,497,500],[3,4,496,499,500], [3,4,496,499,730],[3,4,250,496,729],[3,4,496,729,730],[3,5,8,23,269], [3,5,8,23,515],[5,8,23,269,515],[3,5,8,254,269],[5,8,254,269,515], [3,5,8,500,515],[5,8,254,500,515],[3,5,23,26,272],[3,5,23,26,518], [5,23,26,272,518],[3,5,23,269,272],[5,23,269,272,518],[3,5,23,515,518], [5,23,269,515,518],[3,5,251,254,269],[5,251,254,269,515],[5,251,254,500,515], [3,5,251,269,272],[5,251,269,272,518],[5,251,269,515,518],[3,5,497,500,515], [5,251,497,500,515],[3,5,497,515,518],[5,251,497,515,518],[3,6,7,8,500], [3,6,7,238,484],[3,6,7,238,730],[3,6,7,253,484],[3,6,7,499,500], [3,6,7,499,730],[3,6,8,23,269],[3,6,8,23,515],[3,6,8,254,269], [3,6,8,500,515],[3,6,21,23,269],[3,6,21,23,515],[3,6,21,238,484], [3,6,21,238,730],[3,6,21,267,269],[3,6,21,267,484],[3,6,21,513,515], [3,6,21,513,730],[3,6,252,253,484],[3,6,252,254,269],[3,6,252,267,269], [3,6,252,267,484],[3,6,498,499,500],[3,6,498,499,730],[3,6,498,500,515], [3,6,498,513,515],[3,6,498,513,730],[3,21,23,26,272],[3,21,23,26,518], [3,21,23,269,272],[3,21,23,515,518],[3,21,24,26,272],[3,21,24,26,518], [3,21,24,238,484],[3,21,24,238,730],[3,21,24,270,272],[3,21,24,270,484], [3,21,24,516,518],[3,21,24,516,730],[3,21,267,269,272],[3,21,267,270,272], 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[75,78,742,743,745],[75,78,742,744,745],[75,78,743,744,745],[78,81,742,743,745], [78,81,742,744,745],[78,81,743,744,745],[81,84,742,743,745],[81,84,742,744,745], [81,84,743,744,745],[84,87,742,743,745],[84,87,742,744,745],[84,87,743,744,745], [87,90,742,743,745],[87,90,742,744,745],[87,90,743,744,745],[90,93,742,743,745], [90,93,742,744,745],[90,93,743,744,745],[93,96,742,743,745],[93,96,742,744,745], [93,96,743,744,745],[96,99,742,743,745],[96,99,742,744,745],[96,99,743,744,745], [99,102,742,743,745],[99,102,742,744,745],[99,102,743,744,745],[102,105,742,743,745], [102,105,742,744,745],[102,105,743,744,745],[105,108,742,743,745],[105,108,742,744,745], [105,108,743,744,745],[108,111,742,743,745],[108,111,742,744,745],[108,111,743,744,745], [111,114,742,743,745],[111,114,742,744,745],[111,114,743,744,745],[114,117,742,743,745], [114,117,742,744,745],[114,117,743,744,745],[117,120,742,743,745],[117,120,742,744,745], [117,120,743,744,745],[120,123,742,743,745],[120,123,742,744,745],[120,123,743,744,745], [123,126,742,743,745],[123,126,742,744,745],[123,126,743,744,745],[126,129,742,743,745], [126,129,742,744,745],[126,129,743,744,745],[129,132,742,743,745],[129,132,742,744,745], [129,132,743,744,745],[132,135,742,743,745],[132,135,742,744,745],[132,135,743,744,745], [135,138,742,743,745],[135,138,742,744,745],[135,138,743,744,745],[138,141,742,743,745], [138,141,742,744,745],[138,141,743,744,745],[141,144,742,743,745],[141,144,742,744,745], [141,144,743,744,745],[144,147,742,743,745],[144,147,742,744,745],[144,147,743,744,745], [147,150,742,743,745],[147,150,742,744,745],[147,150,743,744,745],[150,153,742,743,745], [150,153,742,744,745],[150,153,743,744,745],[153,156,742,743,745],[153,156,742,744,745], [153,156,743,744,745],[156,159,742,743,745],[156,159,742,744,745],[156,159,743,744,745], [159,162,742,743,745],[159,162,742,744,745],[159,162,743,744,745],[162,165,742,743,745], [162,165,742,744,745],[162,165,743,744,745],[165,168,742,743,745],[165,168,742,744,745], [165,168,743,744,745],[168,171,742,743,745],[168,171,742,744,745],[168,171,743,744,745], [171,174,742,743,745],[171,174,742,744,745],[171,174,743,744,745],[174,177,742,743,745], [174,177,742,744,745],[174,177,743,744,745],[177,180,742,743,745],[177,180,742,744,745], [177,180,743,744,745],[180,183,742,743,745],[180,183,742,744,745],[180,183,743,744,745], [183,186,742,743,745],[183,186,742,744,745],[183,186,743,744,745],[186,189,742,743,745], [186,189,742,744,745],[186,189,743,744,745],[189,192,742,743,745],[189,192,742,744,745], [189,192,743,744,745],[192,195,742,743,745],[192,195,742,744,745],[192,195,743,744,745], [195,198,742,743,745],[195,198,742,744,745],[195,198,743,744,745],[198,201,742,743,745], [198,201,742,744,745],[198,201,743,744,745],[201,204,742,743,745],[201,204,742,744,745], [201,204,743,744,745],[204,207,742,743,745],[204,207,742,744,745],[204,207,743,744,745], [207,210,742,743,745],[207,210,742,744,745],[207,210,743,744,745],[210,213,742,743,745], [210,213,742,744,745],[210,213,743,744,745],[213,216,742,743,745],[213,216,742,744,745], [213,216,743,744,745],[216,219,742,743,745],[216,219,742,744,745],[216,219,743,744,745], [219,222,742,743,745],[219,222,742,744,745],[219,222,743,744,745],[222,225,742,743,745], [222,225,742,744,745],[222,225,743,744,745],[225,228,742,743,745],[225,228,742,744,745], [225,228,743,744,745],[228,231,742,743,745],[228,231,742,744,745],[228,231,743,744,745] ];