#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_017 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(992,14934,49836,59820,23928) ### ### 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],[0,1,4,250,742],[0,1,4,496,497],[0,1,4,496,742], [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],[0,1,237,483,975],[0,1,237,729,730],[0,1,237,729,975], [0,1,247,250,742],[0,1,247,280,484],[0,1,247,483,484],[0,1,247,483,975], [0,1,247,739,742],[0,1,247,739,975],[0,1,493,494,497],[0,1,493,494,527], [0,1,493,496,497],[0,1,493,496,742],[0,1,493,526,527],[0,1,493,526,730], [0,1,493,729,730],[0,1,493,729,975],[0,1,493,739,742],[0,1,493,739,975], [0,2,5,26,272],[2,5,26,272,764],[0,2,5,26,518],[2,5,26,518,764], [0,2,5,251,272],[2,5,251,272,764],[2,5,251,743,764],[0,2,5,497,518], [2,5,497,518,764],[2,5,497,743,764],[0,2,26,29,275],[2,26,29,275,767], [0,2,26,29,521],[2,26,29,521,767],[0,2,26,272,275],[2,26,272,275,767], [2,26,272,764,767],[0,2,26,518,521],[2,26,518,521,767],[2,26,518,764,767], [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],[2,248,251,272,764],[2,248,251,743,764],[0,2,248,272,275], [2,248,272,275,767],[2,248,272,764,767],[0,2,248,275,487],[0,2,248,281,487], [2,248,740,743,764],[2,248,740,764,767],[0,2,494,497,518],[2,494,497,518,764], [2,494,497,743,764],[0,2,494,518,521],[2,494,518,521,767],[2,494,518,764,767], [0,2,494,521,733],[0,2,494,527,733],[2,494,740,743,764],[2,494,740,764,767], [0,3,4,5,497],[0,3,4,250,742],[0,3,4,496,497],[0,3,4,496,742], [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],[0,3,24,270,762], [0,3,24,516,518],[0,3,24,516,762],[0,3,249,250,742],[0,3,249,251,272], [0,3,249,270,272],[0,3,249,270,762],[0,3,249,741,742],[0,3,249,741,762], [0,3,495,496,497],[0,3,495,496,742],[0,3,495,497,518],[0,3,495,516,518], [0,3,495,516,762],[0,3,495,741,742],[0,3,495,741,762],[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],[0,24,27,273,765],[0,24,27,519,521], [0,24,27,519,765],[0,24,270,272,275],[0,24,270,273,275],[0,24,270,273,765], [0,24,270,762,765],[0,24,516,518,521],[0,24,516,519,521],[0,24,516,519,765], [0,24,516,762,765],[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], [0,27,237,483,975],[0,27,237,729,730],[0,27,237,729,975],[0,27,273,275,487], [0,27,273,480,484],[0,27,273,480,487],[0,27,273,483,484],[0,27,273,483,975], [0,27,273,765,975],[0,27,519,521,733],[0,27,519,726,730],[0,27,519,726,733], [0,27,519,729,730],[0,27,519,729,975],[0,27,519,765,975],[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],[246,247,248,251,743],[246,247,248,281,773], [246,247,248,740,743],[246,247,248,740,773],[246,247,250,251,743],[0,246,247,250,742], [246,247,250,742,743],[246,247,280,281,773],[0,246,247,280,484],[246,247,280,484,976], [246,247,280,772,773],[246,247,280,772,976],[0,246,247,483,484],[246,247,483,484,976], [0,246,247,483,975],[246,247,483,975,976],[246,247,739,740,743],[246,247,739,740,773], [0,246,247,739,742],[246,247,739,742,743],[246,247,739,772,773],[246,247,739,772,976], [0,246,247,739,975],[246,247,739,975,976],[0,246,248,251,272],[246,248,251,272,764], [246,248,251,743,764],[0,246,248,272,275],[246,248,272,275,767],[246,248,272,764,767], [0,246,248,275,487],[246,248,275,487,979],[246,248,275,767,979],[0,246,248,281,487], [246,248,281,487,979],[246,248,281,773,979],[246,248,740,743,764],[246,248,740,764,767], [246,248,740,767,979],[246,248,740,773,979],[246,249,250,251,743],[0,246,249,250,742], [246,249,250,742,743],[0,246,249,251,272],[246,249,251,272,764],[246,249,251,743,764], [0,246,249,270,272],[246,249,270,272,764],[0,246,249,270,762],[246,249,270,762,764], [0,246,249,741,742],[246,249,741,742,743],[246,249,741,743,764],[0,246,249,741,762], [246,249,741,762,764],[0,246,270,272,275],[246,270,272,275,767],[246,270,272,764,767], [0,246,270,273,275],[246,270,273,275,767],[0,246,270,273,765],[246,270,273,765,767], [246,270,762,764,767],[0,246,270,762,765],[246,270,762,765,767],[0,246,273,275,487], [246,273,275,487,979],[246,273,275,767,979],[0,246,273,480,484],[246,273,480,484,976], [0,246,273,480,487],[246,273,480,487,979],[246,273,480,972,976],[246,273,480,972,979], [0,246,273,483,484],[246,273,483,484,976],[0,246,273,483,975],[246,273,483,975,976], [246,273,765,767,979],[246,273,765,972,976],[246,273,765,972,979],[0,246,273,765,975], [246,273,765,975,976],[246,279,280,281,773],[0,246,279,280,484],[246,279,280,484,976], [246,279,280,772,773],[246,279,280,772,976],[0,246,279,281,487],[246,279,281,487,979], [246,279,281,773,979],[0,246,279,480,484],[246,279,480,484,976],[0,246,279,480,487], [246,279,480,487,979],[246,279,480,972,976],[246,279,480,972,979],[246,279,771,772,773], [246,279,771,772,976],[246,279,771,773,979],[246,279,771,972,976],[246,279,771,972,979], [246,738,739,740,743],[246,738,739,740,773],[0,246,738,739,742],[246,738,739,742,743], [246,738,739,772,773],[246,738,739,772,976],[0,246,738,739,975],[246,738,739,975,976], [246,738,740,743,764],[246,738,740,764,767],[246,738,740,767,979],[246,738,740,773,979], [0,246,738,741,742],[246,738,741,742,743],[246,738,741,743,764],[0,246,738,741,762], [246,738,741,762,764],[246,738,762,764,767],[0,246,738,762,765],[246,738,762,765,767], [246,738,765,767,979],[246,738,765,972,976],[246,738,765,972,979],[0,246,738,765,975], [246,738,765,975,976],[246,738,771,772,773],[246,738,771,772,976],[246,738,771,773,979], [246,738,771,972,976],[246,738,771,972,979],[0,492,493,494,497],[492,493,494,497,743], [0,492,493,494,527],[492,493,494,527,773],[492,493,494,740,743],[492,493,494,740,773], [0,492,493,496,497],[492,493,496,497,743],[0,492,493,496,742],[492,493,496,742,743], [0,492,493,526,527],[492,493,526,527,773],[0,492,493,526,730],[492,493,526,730,976], [492,493,526,772,773],[492,493,526,772,976],[0,492,493,729,730],[492,493,729,730,976], [0,492,493,729,975],[492,493,729,975,976],[492,493,739,740,743],[492,493,739,740,773], [0,492,493,739,742],[492,493,739,742,743],[492,493,739,772,773],[492,493,739,772,976], [0,492,493,739,975],[492,493,739,975,976],[0,492,494,497,518],[492,494,497,518,764], [492,494,497,743,764],[0,492,494,518,521],[492,494,518,521,767],[492,494,518,764,767], [0,492,494,521,733],[492,494,521,733,979],[492,494,521,767,979],[0,492,494,527,733], [492,494,527,733,979],[492,494,527,773,979],[492,494,740,743,764],[492,494,740,764,767], [492,494,740,767,979],[492,494,740,773,979],[0,492,495,496,497],[492,495,496,497,743], [0,492,495,496,742],[492,495,496,742,743],[0,492,495,497,518],[492,495,497,518,764], [492,495,497,743,764],[0,492,495,516,518],[492,495,516,518,764],[0,492,495,516,762], [492,495,516,762,764],[0,492,495,741,742],[492,495,741,742,743],[492,495,741,743,764], [0,492,495,741,762],[492,495,741,762,764],[0,492,516,518,521],[492,516,518,521,767], [492,516,518,764,767],[0,492,516,519,521],[492,516,519,521,767],[0,492,516,519,765], [492,516,519,765,767],[492,516,762,764,767],[0,492,516,762,765],[492,516,762,765,767], [0,492,519,521,733],[492,519,521,733,979],[492,519,521,767,979],[0,492,519,726,730], [492,519,726,730,976],[0,492,519,726,733],[492,519,726,733,979],[492,519,726,972,976], [492,519,726,972,979],[0,492,519,729,730],[492,519,729,730,976],[0,492,519,729,975], [492,519,729,975,976],[492,519,765,767,979],[492,519,765,972,976],[492,519,765,972,979], [0,492,519,765,975],[492,519,765,975,976],[0,492,525,526,527],[492,525,526,527,773], [0,492,525,526,730],[492,525,526,730,976],[492,525,526,772,773],[492,525,526,772,976], [0,492,525,527,733],[492,525,527,733,979],[492,525,527,773,979],[0,492,525,726,730], [492,525,726,730,976],[0,492,525,726,733],[492,525,726,733,979],[492,525,726,972,976], [492,525,726,972,979],[492,525,771,772,773],[492,525,771,772,976],[492,525,771,773,979], [492,525,771,972,976],[492,525,771,972,979],[492,738,739,740,743],[492,738,739,740,773], [0,492,738,739,742],[492,738,739,742,743],[492,738,739,772,773],[492,738,739,772,976], [0,492,738,739,975],[492,738,739,975,976],[492,738,740,743,764],[492,738,740,764,767], [492,738,740,767,979],[492,738,740,773,979],[0,492,738,741,742],[492,738,741,742,743], [492,738,741,743,764],[0,492,738,741,762],[492,738,741,762,764],[492,738,762,764,767], [0,492,738,762,765],[492,738,762,765,767],[492,738,765,767,979],[492,738,765,972,976], [492,738,765,972,979],[0,492,738,765,975],[492,738,765,975,976],[492,738,771,772,773], [492,738,771,772,976],[492,738,771,773,979],[492,738,771,972,976],[492,738,771,972,979], [1,2,5,41,287],[2,5,41,287,779],[1,2,5,41,533],[2,5,41,533,779], [1,2,5,251,287],[2,5,251,287,779],[2,5,251,743,779],[1,2,5,497,533], [2,5,497,533,779],[2,5,497,743,779],[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],[2,38,41,287,779], [1,2,38,41,533],[2,38,41,533,779],[1,2,38,244,490],[1,2,38,244,736], [1,2,38,284,287],[2,38,284,287,779],[1,2,38,284,490],[2,38,284,776,779], [1,2,38,530,533],[2,38,530,533,779],[1,2,38,530,736],[2,38,530,776,779], [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],[2,248,251,287,779],[2,248,251,743,779],[1,2,248,281,487], [1,2,248,284,287],[2,248,284,287,779],[1,2,248,284,490],[2,248,284,776,779], [1,2,248,486,487],[1,2,248,486,490],[2,248,740,743,779],[2,248,740,776,779], [1,2,494,497,533],[2,494,497,533,779],[2,494,497,743,779],[1,2,494,527,733], [1,2,494,530,533],[2,494,530,533,779],[1,2,494,530,736],[2,494,530,776,779], [1,2,494,732,733],[1,2,494,732,736],[2,494,740,743,779],[2,494,740,776,779], [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],[1,4,39,285,777], [1,4,39,531,533],[1,4,39,531,777],[1,4,250,251,287],[1,4,250,285,287], [1,4,250,285,777],[1,4,250,742,777],[1,4,496,497,533],[1,4,496,531,533], [1,4,496,531,777],[1,4,496,742,777],[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],[1,36,39,285,777], [1,36,39,531,533],[1,36,39,531,777],[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],[1,36,237,483,975],[1,36,237,729,730],[1,36,237,729,975], [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],[1,36,282,285,777], [1,36,282,481,484],[1,36,282,481,487],[1,36,282,483,484],[1,36,282,483,975], [1,36,282,486,487],[1,36,282,486,490],[1,36,282,774,777],[1,36,282,774,975], [1,36,528,530,533],[1,36,528,530,736],[1,36,528,531,533],[1,36,528,531,777], [1,36,528,727,730],[1,36,528,727,733],[1,36,528,729,730],[1,36,528,729,975], 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