#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_011 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(704,10614,35436,42540,17016) ### ### 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:=[ [0,1,2,5,353],[0,1,2,35,383],[0,1,2,350,353],[0,1,2,350,383], [0,1,4,5,353],[0,1,4,178,526],[0,1,4,352,353],[0,1,4,352,526], [0,1,34,35,383],[0,1,34,166,340],[0,1,34,166,514],[0,1,34,208,340], [0,1,34,382,383],[0,1,34,382,514],[0,1,165,166,340],[0,1,165,166,514], [0,1,165,339,340],[0,1,165,339,687],[0,1,165,513,514],[0,1,165,513,687], [0,1,175,178,526],[0,1,175,208,340],[0,1,175,339,340],[0,1,175,339,687], [0,1,175,523,526],[0,1,175,523,687],[0,1,349,350,353],[0,1,349,350,383], [0,1,349,352,353],[0,1,349,352,526],[0,1,349,382,383],[0,1,349,382,514], [0,1,349,513,514],[0,1,349,513,687],[0,1,349,523,526],[0,1,349,523,687], [0,2,5,26,200],[2,5,26,200,548],[0,2,5,26,374],[2,5,26,374,548], [0,2,5,179,200],[2,5,179,200,548],[2,5,179,527,548],[0,2,5,353,374], [2,5,353,374,548],[2,5,353,527,548],[0,2,26,29,203],[2,26,29,203,551], [0,2,26,29,377],[2,26,29,377,551],[0,2,26,200,203],[2,26,200,203,551], [2,26,200,548,551],[0,2,26,374,377],[2,26,374,377,551],[2,26,374,548,551], [0,2,29,169,343],[0,2,29,169,517],[0,2,29,203,343],[0,2,29,377,517], [0,2,35,169,343],[0,2,35,169,517],[0,2,35,209,343],[0,2,35,383,517], [0,2,176,179,200],[2,176,179,200,548],[2,176,179,527,548],[0,2,176,200,203], [2,176,200,203,551],[2,176,200,548,551],[0,2,176,203,343],[0,2,176,209,343], [2,176,524,527,548],[2,176,524,548,551],[0,2,350,353,374],[2,350,353,374,548], [2,350,353,527,548],[0,2,350,374,377],[2,350,374,377,551],[2,350,374,548,551], [0,2,350,377,517],[0,2,350,383,517],[2,350,524,527,548],[2,350,524,548,551], [0,3,4,5,353],[0,3,4,178,526],[0,3,4,352,353],[0,3,4,352,526], [0,3,5,26,200],[0,3,5,26,374],[0,3,5,179,200],[0,3,5,353,374], [0,3,24,26,200],[0,3,24,26,374],[0,3,24,198,200],[0,3,24,198,546], [0,3,24,372,374],[0,3,24,372,546],[0,3,177,178,526],[0,3,177,179,200], [0,3,177,198,200],[0,3,177,198,546],[0,3,177,525,526],[0,3,177,525,546], [0,3,351,352,353],[0,3,351,352,526],[0,3,351,353,374],[0,3,351,372,374], [0,3,351,372,546],[0,3,351,525,526],[0,3,351,525,546],[0,24,26,29,203], [0,24,26,29,377],[0,24,26,200,203],[0,24,26,374,377],[0,24,27,29,203], [0,24,27,29,377],[0,24,27,201,203],[0,24,27,201,549],[0,24,27,375,377], [0,24,27,375,549],[0,24,198,200,203],[0,24,198,201,203],[0,24,198,201,549], [0,24,198,546,549],[0,24,372,374,377],[0,24,372,375,377],[0,24,372,375,549], [0,24,372,546,549],[0,27,29,169,343],[0,27,29,169,517],[0,27,29,203,343], [0,27,29,377,517],[0,27,162,166,340],[0,27,162,166,514],[0,27,162,169,343], [0,27,162,169,517],[0,27,162,336,340],[0,27,162,336,343],[0,27,162,510,514], [0,27,162,510,517],[0,27,165,166,340],[0,27,165,166,514],[0,27,165,339,340], [0,27,165,339,687],[0,27,165,513,514],[0,27,165,513,687],[0,27,201,203,343], [0,27,201,336,340],[0,27,201,336,343],[0,27,201,339,340],[0,27,201,339,687], [0,27,201,549,687],[0,27,375,377,517],[0,27,375,510,514],[0,27,375,510,517], [0,27,375,513,514],[0,27,375,513,687],[0,27,375,549,687],[0,33,34,35,383], [0,33,34,166,340],[0,33,34,166,514],[0,33,34,208,340],[0,33,34,382,383], [0,33,34,382,514],[0,33,35,169,343],[0,33,35,169,517],[0,33,35,209,343], [0,33,35,383,517],[0,33,162,166,340],[0,33,162,166,514],[0,33,162,169,343], [0,33,162,169,517],[0,33,162,336,340],[0,33,162,336,343],[0,33,162,510,514], [0,33,162,510,517],[0,33,207,208,340],[0,33,207,209,343],[0,33,207,336,340], [0,33,207,336,343],[0,33,381,382,383],[0,33,381,382,514],[0,33,381,383,517], [0,33,381,510,514],[0,33,381,510,517],[174,175,176,179,527],[174,175,176,209,557], [174,175,176,524,527],[174,175,176,524,557],[174,175,178,179,527],[0,174,175,178,526], [174,175,178,526,527],[174,175,208,209,557],[0,174,175,208,340],[174,175,208,340,688], [174,175,208,556,557],[174,175,208,556,688],[0,174,175,339,340],[174,175,339,340,688], [0,174,175,339,687],[174,175,339,687,688],[174,175,523,524,527],[174,175,523,524,557], [0,174,175,523,526],[174,175,523,526,527],[174,175,523,556,557],[174,175,523,556,688], [0,174,175,523,687],[174,175,523,687,688],[0,174,176,179,200],[174,176,179,200,548], [174,176,179,527,548],[0,174,176,200,203],[174,176,200,203,551],[174,176,200,548,551], [0,174,176,203,343],[174,176,203,343,691],[174,176,203,551,691],[0,174,176,209,343], [174,176,209,343,691],[174,176,209,557,691],[174,176,524,527,548],[174,176,524,548,551], [174,176,524,551,691],[174,176,524,557,691],[174,177,178,179,527],[0,174,177,178,526], [174,177,178,526,527],[0,174,177,179,200],[174,177,179,200,548],[174,177,179,527,548], [0,174,177,198,200],[174,177,198,200,548],[0,174,177,198,546],[174,177,198,546,548], [0,174,177,525,526],[174,177,525,526,527],[174,177,525,527,548],[0,174,177,525,546], [174,177,525,546,548],[0,174,198,200,203],[174,198,200,203,551],[174,198,200,548,551], [0,174,198,201,203],[174,198,201,203,551],[0,174,198,201,549],[174,198,201,549,551], [174,198,546,548,551],[0,174,198,546,549],[174,198,546,549,551],[0,174,201,203,343], [174,201,203,343,691],[174,201,203,551,691],[0,174,201,336,340],[174,201,336,340,688], [0,174,201,336,343],[174,201,336,343,691],[174,201,336,684,688],[174,201,336,684,691], [0,174,201,339,340],[174,201,339,340,688],[0,174,201,339,687],[174,201,339,687,688], [174,201,549,551,691],[174,201,549,684,688],[174,201,549,684,691],[0,174,201,549,687], [174,201,549,687,688],[174,207,208,209,557],[0,174,207,208,340],[174,207,208,340,688], [174,207,208,556,557],[174,207,208,556,688],[0,174,207,209,343],[174,207,209,343,691], [174,207,209,557,691],[0,174,207,336,340],[174,207,336,340,688],[0,174,207,336,343], [174,207,336,343,691],[174,207,336,684,688],[174,207,336,684,691],[174,207,555,556,557], [174,207,555,556,688],[174,207,555,557,691],[174,207,555,684,688],[174,207,555,684,691], [174,522,523,524,527],[174,522,523,524,557],[0,174,522,523,526],[174,522,523,526,527], [174,522,523,556,557],[174,522,523,556,688],[0,174,522,523,687],[174,522,523,687,688], [174,522,524,527,548],[174,522,524,548,551],[174,522,524,551,691],[174,522,524,557,691], [0,174,522,525,526],[174,522,525,526,527],[174,522,525,527,548],[0,174,522,525,546], [174,522,525,546,548],[174,522,546,548,551],[0,174,522,546,549],[174,522,546,549,551], [174,522,549,551,691],[174,522,549,684,688],[174,522,549,684,691],[0,174,522,549,687], [174,522,549,687,688],[174,522,555,556,557],[174,522,555,556,688],[174,522,555,557,691], [174,522,555,684,688],[174,522,555,684,691],[0,348,349,350,353],[348,349,350,353,527], [0,348,349,350,383],[348,349,350,383,557],[348,349,350,524,527],[348,349,350,524,557], [0,348,349,352,353],[348,349,352,353,527],[0,348,349,352,526],[348,349,352,526,527], [0,348,349,382,383],[348,349,382,383,557],[0,348,349,382,514],[348,349,382,514,688], [348,349,382,556,557],[348,349,382,556,688],[0,348,349,513,514],[348,349,513,514,688], [0,348,349,513,687],[348,349,513,687,688],[348,349,523,524,527],[348,349,523,524,557], [0,348,349,523,526],[348,349,523,526,527],[348,349,523,556,557],[348,349,523,556,688], [0,348,349,523,687],[348,349,523,687,688],[0,348,350,353,374],[348,350,353,374,548], [348,350,353,527,548],[0,348,350,374,377],[348,350,374,377,551],[348,350,374,548,551], [0,348,350,377,517],[348,350,377,517,691],[348,350,377,551,691],[0,348,350,383,517], [348,350,383,517,691],[348,350,383,557,691],[348,350,524,527,548],[348,350,524,548,551], [348,350,524,551,691],[348,350,524,557,691],[0,348,351,352,353],[348,351,352,353,527], [0,348,351,352,526],[348,351,352,526,527],[0,348,351,353,374],[348,351,353,374,548], [348,351,353,527,548],[0,348,351,372,374],[348,351,372,374,548],[0,348,351,372,546], [348,351,372,546,548],[0,348,351,525,526],[348,351,525,526,527],[348,351,525,527,548], [0,348,351,525,546],[348,351,525,546,548],[0,348,372,374,377],[348,372,374,377,551], [348,372,374,548,551],[0,348,372,375,377],[348,372,375,377,551],[0,348,372,375,549], [348,372,375,549,551],[348,372,546,548,551],[0,348,372,546,549],[348,372,546,549,551], [0,348,375,377,517],[348,375,377,517,691],[348,375,377,551,691],[0,348,375,510,514], [348,375,510,514,688],[0,348,375,510,517],[348,375,510,517,691],[348,375,510,684,688], [348,375,510,684,691],[0,348,375,513,514],[348,375,513,514,688],[0,348,375,513,687], [348,375,513,687,688],[348,375,549,551,691],[348,375,549,684,688],[348,375,549,684,691], [0,348,375,549,687],[348,375,549,687,688],[0,348,381,382,383],[348,381,382,383,557], [0,348,381,382,514],[348,381,382,514,688],[348,381,382,556,557],[348,381,382,556,688], [0,348,381,383,517],[348,381,383,517,691],[348,381,383,557,691],[0,348,381,510,514], [348,381,510,514,688],[0,348,381,510,517],[348,381,510,517,691],[348,381,510,684,688], [348,381,510,684,691],[348,381,555,556,557],[348,381,555,556,688],[348,381,555,557,691], [348,381,555,684,688],[348,381,555,684,691],[348,522,523,524,527],[348,522,523,524,557], [0,348,522,523,526],[348,522,523,526,527],[348,522,523,556,557],[348,522,523,556,688], [0,348,522,523,687],[348,522,523,687,688],[348,522,524,527,548],[348,522,524,548,551], [348,522,524,551,691],[348,522,524,557,691],[0,348,522,525,526],[348,522,525,526,527], [348,522,525,527,548],[0,348,522,525,546],[348,522,525,546,548],[348,522,546,548,551], [0,348,522,546,549],[348,522,546,549,551],[348,522,549,551,691],[348,522,549,684,688], [348,522,549,684,691],[0,348,522,549,687],[348,522,549,687,688],[348,522,555,556,557], [348,522,555,556,688],[348,522,555,557,691],[348,522,555,684,688],[348,522,555,684,691], [1,2,5,41,215],[2,5,41,215,563],[1,2,5,41,389],[2,5,41,389,563], [1,2,5,179,215],[2,5,179,215,563],[2,5,179,527,563],[1,2,5,353,389], [2,5,353,389,563],[2,5,353,527,563],[1,2,35,169,343],[1,2,35,169,517], [1,2,35,209,343],[1,2,35,383,517],[1,2,38,41,215],[2,38,41,215,563], [1,2,38,41,389],[2,38,41,389,563],[1,2,38,172,346],[1,2,38,172,520], [1,2,38,212,215],[2,38,212,215,563],[1,2,38,212,346],[2,38,212,560,563], [1,2,38,386,389],[2,38,386,389,563],[1,2,38,386,520],[2,38,386,560,563], [1,2,168,169,343],[1,2,168,169,517],[1,2,168,172,346],[1,2,168,172,520], [1,2,168,342,343],[1,2,168,342,346],[1,2,168,516,517],[1,2,168,516,520], [1,2,176,179,215],[2,176,179,215,563],[2,176,179,527,563],[1,2,176,209,343], [1,2,176,212,215],[2,176,212,215,563],[1,2,176,212,346],[2,176,212,560,563], [1,2,176,342,343],[1,2,176,342,346],[2,176,524,527,563],[2,176,524,560,563], [1,2,350,353,389],[2,350,353,389,563],[2,350,353,527,563],[1,2,350,383,517], [1,2,350,386,389],[2,350,386,389,563],[1,2,350,386,520],[2,350,386,560,563], [1,2,350,516,517],[1,2,350,516,520],[2,350,524,527,563],[2,350,524,560,563], [1,4,5,41,215],[1,4,5,41,389],[1,4,5,179,215],[1,4,5,353,389], [1,4,39,41,215],[1,4,39,41,389],[1,4,39,213,215],[1,4,39,213,561], [1,4,39,387,389],[1,4,39,387,561],[1,4,178,179,215],[1,4,178,213,215], [1,4,178,213,561],[1,4,178,526,561],[1,4,352,353,389],[1,4,352,387,389], [1,4,352,387,561],[1,4,352,526,561],[1,34,35,169,343],[1,34,35,169,517], [1,34,35,209,343],[1,34,35,383,517],[1,34,163,166,340],[1,34,163,166,514], [1,34,163,169,343],[1,34,163,169,517],[1,34,163,337,340],[1,34,163,337,343], [1,34,163,511,514],[1,34,163,511,517],[1,34,208,209,343],[1,34,208,337,340], [1,34,208,337,343],[1,34,382,383,517],[1,34,382,511,514],[1,34,382,511,517], [1,36,38,41,215],[1,36,38,41,389],[1,36,38,172,346],[1,36,38,172,520], [1,36,38,212,215],[1,36,38,212,346],[1,36,38,386,389],[1,36,38,386,520], [1,36,39,41,215],[1,36,39,41,389],[1,36,39,213,215],[1,36,39,213,561], [1,36,39,387,389],[1,36,39,387,561],[1,36,163,166,340],[1,36,163,166,514], [1,36,163,169,343],[1,36,163,169,517],[1,36,163,337,340],[1,36,163,337,343], [1,36,163,511,514],[1,36,163,511,517],[1,36,165,166,340],[1,36,165,166,514], [1,36,165,339,340],[1,36,165,339,687],[1,36,165,513,514],[1,36,165,513,687], [1,36,168,169,343],[1,36,168,169,517],[1,36,168,172,346],[1,36,168,172,520], [1,36,168,342,343],[1,36,168,342,346],[1,36,168,516,517],[1,36,168,516,520], [1,36,210,212,215],[1,36,210,212,346],[1,36,210,213,215],[1,36,210,213,561], [1,36,210,337,340],[1,36,210,337,343],[1,36,210,339,340],[1,36,210,339,687], [1,36,210,342,343],[1,36,210,342,346],[1,36,210,558,561],[1,36,210,558,687], [1,36,384,386,389],[1,36,384,386,520],[1,36,384,387,389],[1,36,384,387,561], [1,36,384,511,514],[1,36,384,511,517],[1,36,384,513,514],[1,36,384,513,687], [1,36,384,516,517],[1,36,384,516,520],[1,36,384,558,561],[1,36,384,558,687], [1,175,176,179,215],[175,176,179,215,563],[175,176,179,527,563],[1,175,176,209,343], [175,176,209,343,691],[175,176,209,557,691],[1,175,176,212,215],[175,176,212,215,563], [1,175,176,212,346],[175,176,212,346,694],[175,176,212,560,563],[175,176,212,560,694], [1,175,176,342,343],[175,176,342,343,691],[1,175,176,342,346],[175,176,342,346,694], [175,176,342,690,691],[175,176,342,690,694],[175,176,524,527,563],[175,176,524,557,691], [175,176,524,560,563],[175,176,524,560,694],[175,176,524,690,691],[175,176,524,690,694], [1,175,178,179,215],[175,178,179,215,563],[175,178,179,527,563],[1,175,178,213,215], [175,178,213,215,563],[1,175,178,213,561],[175,178,213,561,563],[175,178,526,527,563], [1,175,178,526,561],[175,178,526,561,563],[1,175,208,209,343],[175,208,209,343,691], [175,208,209,557,691],[1,175,208,337,340],[175,208,337,340,688],[1,175,208,337,343], 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