#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_007 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(386,5556,18384,22020,8808) ### ### 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:=[ [0,1,2,5,257],[0,1,2,35,287],[0,1,2,254,257],[0,1,2,254,287], [0,1,4,5,257],[0,1,4,130,256],[0,1,4,256,257],[0,1,34,35,287], [0,1,34,118,244],[0,1,34,118,370],[0,1,34,160,244],[0,1,34,286,287], [0,1,34,286,370],[0,1,117,118,244],[0,1,117,118,370],[0,1,117,243,244], [0,1,117,243,369],[0,1,117,369,370],[0,1,127,130,256],[0,1,127,160,244], [0,1,127,243,244],[0,1,127,243,369],[0,1,253,254,257],[0,1,253,254,287], [0,1,127,253,256],[0,1,253,256,257],[0,1,253,286,287],[0,1,253,286,370], [0,1,127,253,369],[0,1,253,369,370],[0,2,5,26,152],[0,2,5,26,278], [2,5,26,152,278],[0,2,5,131,152],[2,5,131,152,278],[0,2,5,257,278], [2,5,131,257,278],[0,2,26,29,155],[0,2,26,29,281],[2,26,29,155,281], [0,2,26,152,155],[2,26,152,155,281],[0,2,26,278,281],[2,26,152,278,281], [0,2,29,121,247],[0,2,29,121,373],[0,2,29,155,247],[0,2,29,281,373], [0,2,35,121,247],[0,2,35,121,373],[0,2,35,161,247],[0,2,35,287,373], [0,2,128,131,152],[2,128,131,152,278],[2,128,131,257,278],[0,2,128,152,155], [2,128,152,155,281],[2,128,152,278,281],[0,2,128,155,247],[0,2,128,161,247], [0,2,254,257,278],[2,128,254,257,278],[0,2,254,278,281],[2,128,254,278,281], [0,2,254,281,373],[0,2,254,287,373],[0,3,4,5,257],[0,3,4,130,256], [0,3,4,256,257],[0,3,5,26,152],[0,3,5,26,278],[0,3,5,131,152], [0,3,5,257,278],[0,3,24,26,152],[0,3,24,26,278],[0,3,24,150,152], [0,3,24,150,276],[0,3,24,276,278],[0,3,129,130,256],[0,3,129,131,152], [0,3,129,150,152],[0,3,129,150,276],[0,3,129,255,256],[0,3,255,256,257], [0,3,255,257,278],[0,3,129,255,276],[0,3,255,276,278],[0,24,26,29,155], [0,24,26,29,281],[0,24,26,152,155],[0,24,26,278,281],[0,24,27,29,155], [0,24,27,29,281],[0,24,27,153,155],[0,24,27,153,279],[0,24,27,279,281], [0,24,150,152,155],[0,24,150,153,155],[0,24,150,153,279],[0,24,276,278,281], [0,24,150,276,279],[0,24,276,279,281],[0,27,29,121,247],[0,27,29,121,373], [0,27,29,155,247],[0,27,29,281,373],[0,27,114,118,244],[0,27,114,118,370], [0,27,114,121,247],[0,27,114,121,373],[0,27,114,240,244],[0,27,114,240,247], [0,27,114,366,370],[0,27,114,366,373],[0,27,117,118,244],[0,27,117,118,370], [0,27,117,243,244],[0,27,117,243,369],[0,27,117,369,370],[0,27,153,155,247], [0,27,153,240,244],[0,27,153,240,247],[0,27,153,243,244],[0,27,153,243,369], [0,27,279,281,373],[0,27,279,366,370],[0,27,279,366,373],[0,27,153,279,369], [0,27,279,369,370],[0,33,34,35,287],[0,33,34,118,244],[0,33,34,118,370], [0,33,34,160,244],[0,33,34,286,287],[0,33,34,286,370],[0,33,35,121,247], [0,33,35,121,373],[0,33,35,161,247],[0,33,35,287,373],[0,33,114,118,244], [0,33,114,118,370],[0,33,114,121,247],[0,33,114,121,373],[0,33,114,240,244], [0,33,114,240,247],[0,33,114,366,370],[0,33,114,366,373],[0,33,159,160,244], [0,33,159,161,247],[0,33,159,240,244],[0,33,159,240,247],[0,33,285,286,287], [0,33,285,286,370],[0,33,285,287,373],[0,33,285,366,370],[0,33,285,366,373], [126,127,128,131,257],[126,127,128,161,287],[126,127,128,254,257],[126,127,128,254,287], [126,127,130,131,257],[0,126,127,130,256],[126,127,130,256,257],[126,127,160,161,287], [0,126,127,160,244],[126,127,160,244,370],[126,127,160,286,287],[126,127,160,286,370], [0,126,127,243,244],[126,127,243,244,370],[0,126,127,243,369],[126,127,243,369,370], [126,127,253,254,257],[126,127,253,254,287],[0,126,127,253,256],[126,127,253,256,257], [126,127,253,286,287],[126,127,253,286,370],[0,126,127,253,369],[126,127,253,369,370], [0,126,128,131,152],[126,128,131,152,278],[126,128,131,257,278],[0,126,128,152,155], [126,128,152,155,281],[126,128,152,278,281],[0,126,128,155,247],[126,128,155,247,373], [126,128,155,281,373],[0,126,128,161,247],[126,128,161,247,373],[126,128,161,287,373], [126,128,254,257,278],[126,128,254,278,281],[126,128,254,281,373],[126,128,254,287,373], [126,129,130,131,257],[0,126,129,130,256],[126,129,130,256,257],[0,126,129,131,152], [126,129,131,152,278],[126,129,131,257,278],[0,126,129,150,152],[126,129,150,152,278], [0,126,129,150,276],[126,129,150,276,278],[0,126,129,255,256],[126,129,255,256,257], [126,129,255,257,278],[0,126,129,255,276],[126,129,255,276,278],[0,126,150,152,155], [126,150,152,155,281],[126,150,152,278,281],[0,126,150,153,155],[126,150,153,155,281], [0,126,150,153,279],[126,150,153,279,281],[126,150,276,278,281],[0,126,150,276,279], [126,150,276,279,281],[0,126,153,155,247],[126,153,155,247,373],[126,153,155,281,373], [0,126,153,240,244],[126,153,240,244,370],[0,126,153,240,247],[126,153,240,247,373], [126,153,240,366,370],[126,153,240,366,373],[0,126,153,243,244],[126,153,243,244,370], [0,126,153,243,369],[126,153,243,369,370],[126,153,279,281,373],[126,153,279,366,370], [126,153,279,366,373],[0,126,153,279,369],[126,153,279,369,370],[126,159,160,161,287], [0,126,159,160,244],[126,159,160,244,370],[126,159,160,286,287],[126,159,160,286,370], [0,126,159,161,247],[126,159,161,247,373],[126,159,161,287,373],[0,126,159,240,244], [126,159,240,244,370],[0,126,159,240,247],[126,159,240,247,373],[126,159,240,366,370], [126,159,240,366,373],[126,159,285,286,287],[126,159,285,286,370],[126,159,285,287,373], [126,159,285,366,370],[126,159,285,366,373],[0,252,253,254,257],[126,252,253,254,257], [0,252,253,254,287],[126,252,253,254,287],[0,126,252,253,256],[0,252,253,256,257], [126,252,253,256,257],[0,252,253,286,287],[126,252,253,286,287],[0,252,253,286,370], [126,252,253,286,370],[0,126,252,253,369],[0,252,253,369,370],[126,252,253,369,370], [0,252,254,257,278],[126,252,254,257,278],[0,252,254,278,281],[126,252,254,278,281], [0,252,254,281,373],[126,252,254,281,373],[0,252,254,287,373],[126,252,254,287,373], [0,126,252,255,256],[0,252,255,256,257],[126,252,255,256,257],[0,252,255,257,278], [126,252,255,257,278],[0,126,252,255,276],[0,252,255,276,278],[126,252,255,276,278], [0,252,276,278,281],[126,252,276,278,281],[0,126,252,276,279],[0,252,276,279,281], [126,252,276,279,281],[0,252,279,281,373],[126,252,279,281,373],[0,252,279,366,370], [126,252,279,366,370],[0,252,279,366,373],[126,252,279,366,373],[0,126,252,279,369], [0,252,279,369,370],[126,252,279,369,370],[0,252,285,286,287],[126,252,285,286,287], [0,252,285,286,370],[126,252,285,286,370],[0,252,285,287,373],[126,252,285,287,373], [0,252,285,366,370],[126,252,285,366,370],[0,252,285,366,373],[126,252,285,366,373], [1,2,5,41,167],[1,2,5,41,293],[2,5,41,167,293],[1,2,5,131,167], [2,5,131,167,293],[1,2,5,257,293],[2,5,131,257,293],[1,2,35,121,247], [1,2,35,121,373],[1,2,35,161,247],[1,2,35,287,373],[1,2,38,41,167], [1,2,38,41,293],[2,38,41,167,293],[1,2,38,124,250],[1,2,38,124,376], [1,2,38,164,167],[2,38,164,167,293],[1,2,38,164,250],[1,2,38,290,293], [2,38,164,290,293],[1,2,38,290,376],[1,2,120,121,247],[1,2,120,121,373], [1,2,120,124,250],[1,2,120,124,376],[1,2,120,246,247],[1,2,120,246,250], [1,2,120,372,373],[1,2,120,372,376],[1,2,128,131,167],[2,128,131,167,293], [2,128,131,257,293],[1,2,128,161,247],[1,2,128,164,167],[2,128,164,167,293], [1,2,128,164,250],[2,128,164,290,293],[1,2,128,246,247],[1,2,128,246,250], [1,2,254,257,293],[2,128,254,257,293],[1,2,254,287,373],[1,2,254,290,293], [2,128,254,290,293],[1,2,254,290,376],[1,2,254,372,373],[1,2,254,372,376], [1,4,5,41,167],[1,4,5,41,293],[1,4,5,131,167],[1,4,5,257,293], [1,4,39,41,167],[1,4,39,41,293],[1,4,39,165,167],[1,4,39,165,291], [1,4,39,291,293],[1,4,130,131,167],[1,4,130,165,167],[1,4,130,165,291], [1,4,256,257,293],[1,4,130,256,291],[1,4,256,291,293],[1,34,35,121,247], [1,34,35,121,373],[1,34,35,161,247],[1,34,35,287,373],[1,34,115,118,244], [1,34,115,118,370],[1,34,115,121,247],[1,34,115,121,373],[1,34,115,241,244], [1,34,115,241,247],[1,34,115,367,370],[1,34,115,367,373],[1,34,160,161,247], [1,34,160,241,244],[1,34,160,241,247],[1,34,286,287,373],[1,34,286,367,370], [1,34,286,367,373],[1,36,38,41,167],[1,36,38,41,293],[1,36,38,124,250], [1,36,38,124,376],[1,36,38,164,167],[1,36,38,164,250],[1,36,38,290,293], [1,36,38,290,376],[1,36,39,41,167],[1,36,39,41,293],[1,36,39,165,167], [1,36,39,165,291],[1,36,39,291,293],[1,36,115,118,244],[1,36,115,118,370], [1,36,115,121,247],[1,36,115,121,373],[1,36,115,241,244],[1,36,115,241,247], [1,36,115,367,370],[1,36,115,367,373],[1,36,117,118,244],[1,36,117,118,370], [1,36,117,243,244],[1,36,117,243,369],[1,36,117,369,370],[1,36,120,121,247], [1,36,120,121,373],[1,36,120,124,250],[1,36,120,124,376],[1,36,120,246,247], [1,36,120,246,250],[1,36,120,372,373],[1,36,120,372,376],[1,36,162,164,167], [1,36,162,164,250],[1,36,162,165,167],[1,36,162,165,291],[1,36,162,241,244], [1,36,162,241,247],[1,36,162,243,244],[1,36,162,243,369],[1,36,162,246,247], [1,36,162,246,250],[1,36,288,290,293],[1,36,288,290,376],[1,36,162,288,291], [1,36,288,291,293],[1,36,288,367,370],[1,36,288,367,373],[1,36,162,288,369], [1,36,288,369,370],[1,36,288,372,373],[1,36,288,372,376],[1,127,128,131,167], [127,128,131,167,293],[127,128,131,257,293],[1,127,128,161,247],[127,128,161,247,373], [127,128,161,287,373],[1,127,128,164,167],[127,128,164,167,293],[1,127,128,164,250], [127,128,164,250,376],[127,128,164,290,293],[127,128,164,290,376],[1,127,128,246,247], [127,128,246,247,373],[1,127,128,246,250],[127,128,246,250,376],[127,128,246,372,373], [127,128,246,372,376],[127,128,254,257,293],[127,128,254,287,373],[127,128,254,290,293], [127,128,254,290,376],[127,128,254,372,373],[127,128,254,372,376],[1,127,130,131,167], [127,130,131,167,293],[127,130,131,257,293],[1,127,130,165,167],[127,130,165,167,293], [1,127,130,165,291],[127,130,165,291,293],[127,130,256,257,293],[1,127,130,256,291], [127,130,256,291,293],[1,127,160,161,247],[127,160,161,247,373],[127,160,161,287,373], [1,127,160,241,244],[127,160,241,244,370],[1,127,160,241,247],[127,160,241,247,373], [127,160,241,367,370],[127,160,241,367,373],[127,160,286,287,373],[127,160,286,367,370], [127,160,286,367,373],[1,127,162,164,167],[127,162,164,167,293],[1,127,162,164,250], [127,162,164,250,376],[127,162,164,290,293],[127,162,164,290,376],[1,127,162,165,167], [127,162,165,167,293],[1,127,162,165,291],[127,162,165,291,293],[1,127,162,241,244], [127,162,241,244,370],[1,127,162,241,247],[127,162,241,247,373],[127,162,241,367,370], [127,162,241,367,373],[1,127,162,243,244],[127,162,243,244,370],[1,127,162,243,369], [127,162,243,369,370],[1,127,162,246,247],[127,162,246,247,373],[1,127,162,246,250], [127,162,246,250,376],[127,162,246,372,373],[127,162,246,372,376],[127,162,288,290,293], [127,162,288,290,376],[1,127,162,288,291],[127,162,288,291,293],[127,162,288,367,370], [127,162,288,367,373],[1,127,162,288,369],[127,162,288,369,370],[127,162,288,372,373], [127,162,288,372,376],[1,253,254,257,293],[127,253,254,257,293],[1,253,254,287,373], [127,253,254,287,373],[1,253,254,290,293],[127,253,254,290,293],[1,253,254,290,376], [127,253,254,290,376],[1,253,254,372,373],[127,253,254,372,373],[1,253,254,372,376], [127,253,254,372,376],[1,253,256,257,293],[127,253,256,257,293],[1,127,253,256,291], [1,253,256,291,293],[127,253,256,291,293],[1,253,286,287,373],[127,253,286,287,373], [1,253,286,367,370],[127,253,286,367,370],[1,253,286,367,373],[127,253,286,367,373], [1,253,288,290,293],[127,253,288,290,293],[1,253,288,290,376],[127,253,288,290,376], [1,127,253,288,291],[1,253,288,291,293],[127,253,288,291,293],[1,253,288,367,370], [127,253,288,367,370],[1,253,288,367,373],[127,253,288,367,373],[1,127,253,288,369], [1,253,288,369,370],[127,253,288,369,370],[1,253,288,372,373],[127,253,288,372,373], [1,253,288,372,376],[127,253,288,372,376],[2,29,120,121,247],[2,29,120,121,373], [2,29,120,124,250],[2,29,120,124,376],[2,29,120,246,247],[2,29,120,246,250], [2,29,120,372,373],[2,29,120,372,376],[2,29,122,124,250],[2,29,122,124,376], [2,29,122,248,250],[2,29,122,248,374],[2,29,122,374,376],[2,29,155,246,247], [2,29,155,246,250],[2,29,155,248,250],[2,29,155,248,374],[2,29,281,372,373], [2,29,281,372,376],[2,29,155,281,374],[2,29,281,374,376],[2,38,122,124,250], [2,38,122,124,376],[2,38,122,248,250],[2,38,122,248,374],[2,38,122,374,376], [2,38,164,248,250],[2,38,164,248,374],[2,38,164,290,374],[2,38,290,374,376], [2,128,155,246,247],[128,155,246,247,373],[2,128,155,246,250],[128,155,246,250,376], [128,155,246,372,373],[128,155,246,372,376],[2,128,155,248,250],[128,155,248,250,376], [2,128,155,248,374],[128,155,248,374,376],[128,155,281,372,373],[128,155,281,372,376], [2,128,155,281,374],[128,155,281,374,376],[2,128,164,248,250],[128,164,248,250,376], [2,128,164,248,374],[128,164,248,374,376],[2,128,164,290,374],[128,164,290,374,376], [2,254,281,372,373],[128,254,281,372,373],[2,254,281,372,376],[128,254,281,372,376], [2,128,254,281,374],[2,254,281,374,376],[128,254,281,374,376],[2,128,254,290,374], [2,254,290,374,376],[128,254,290,374,376],[3,4,5,8,260],[3,4,5,257,260], [3,4,7,8,260],[3,4,7,118,244],[3,4,7,118,370],[3,4,7,133,244], [3,4,7,259,260],[3,4,7,259,370],[3,4,117,118,244],[3,4,117,118,370], [3,4,117,243,244],[3,4,117,243,369],[3,4,117,369,370],[3,4,130,133,244], [3,4,130,243,244],[3,4,130,243,369],[3,4,256,257,260],[3,4,256,259,260], [3,4,256,259,370],[3,4,130,256,369],[3,4,256,369,370],[3,5,8,23,149], [3,5,8,23,275],[5,8,23,149,275],[3,5,8,134,149],[5,8,134,149,275], [3,5,8,260,275],[5,8,134,260,275],[3,5,23,26,152],[3,5,23,26,278], 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[75,77,203,206,382],[76,77,203,206,382],[76,79,80,206,382],[75,76,79,205,382], [76,79,205,206,382],[76,202,203,206,382],[75,76,202,205,382],[76,202,205,206,382], [75,78,80,206,382],[75,78,79,205,382],[75,78,204,205,382],[75,78,204,206,382], [75,201,203,206,382],[201,202,203,206,382],[75,201,202,205,382],[201,202,205,206,382], [75,201,204,205,382],[75,201,204,206,382],[201,204,205,206,382],[78,80,83,209,382], [79,80,83,209,382],[78,80,206,209,382],[79,80,206,209,382],[79,82,83,209,382], [78,79,82,208,382],[79,82,208,209,382],[79,205,206,209,382],[78,79,205,208,382], [79,205,208,209,382],[78,81,83,209,382],[78,81,82,208,382],[78,81,207,208,382], [78,81,207,209,382],[78,204,206,209,382],[204,205,206,209,382],[78,204,205,208,382], [204,205,208,209,382],[78,204,207,208,382],[78,204,207,209,382],[204,207,208,209,382], [81,83,86,212,382],[82,83,86,212,382],[81,83,209,212,382],[82,83,209,212,382], [82,85,86,212,382],[81,82,85,211,382],[82,85,211,212,382],[82,208,209,212,382], [81,82,208,211,382],[82,208,211,212,382],[81,84,86,212,382],[81,84,85,211,382], [81,84,210,211,382],[81,84,210,212,382],[81,207,209,212,382],[207,208,209,212,382], [81,207,208,211,382],[207,208,211,212,382],[81,207,210,211,382],[81,207,210,212,382], [207,210,211,212,382],[84,86,89,215,382],[85,86,89,215,382],[84,86,212,215,382], [85,86,212,215,382],[85,88,89,215,382],[84,85,88,214,382],[85,88,214,215,382], [85,211,212,215,382],[84,85,211,214,382],[85,211,214,215,382],[84,87,89,215,382], [84,87,88,214,382],[84,87,213,214,382],[84,87,213,215,382],[84,210,212,215,382], [210,211,212,215,382],[84,210,211,214,382],[210,211,214,215,382],[84,210,213,214,382], [84,210,213,215,382],[210,213,214,215,382],[87,89,92,218,382],[88,89,92,218,382], [87,89,215,218,382],[88,89,215,218,382],[88,91,92,218,382],[87,88,91,217,382], [88,91,217,218,382],[88,214,215,218,382],[87,88,214,217,382],[88,214,217,218,382], [87,90,92,218,382],[87,90,91,217,382],[87,90,216,217,382],[87,90,216,218,382], 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