#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_006 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(468,7230,24260,29160,11664) ### ### 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:=[ [0,1,2,5,119],[0,1,2,5,228],[1,2,5,228,462],[1,2,5,239,462], [0,1,2,35,149],[0,1,2,35,228],[1,2,35,228,462],[1,2,35,269,462], [0,1,2,116,119],[0,1,2,116,149],[1,2,236,239,462],[1,2,236,269,462], [0,1,4,5,119],[0,1,4,5,228],[0,1,4,228,462],[1,4,5,228,462], [1,4,5,239,462],[0,1,4,118,119],[0,1,4,118,352],[0,1,4,238,462], [1,4,238,239,462],[0,1,4,238,352],[0,1,34,35,149],[0,1,34,35,228], [0,1,34,228,462],[1,34,35,228,462],[1,34,35,269,462],[0,1,34,106,220], [0,1,34,106,340],[0,1,34,148,149],[0,1,34,148,220],[0,1,34,268,462], [1,34,268,269,462],[0,1,34,268,340],[0,1,105,106,220],[0,1,105,106,340], [0,1,105,219,220],[0,1,105,219,453],[0,1,105,339,340],[0,1,105,339,453], [0,1,115,116,119],[0,1,115,116,149],[0,1,115,118,119],[0,1,115,118,352], [0,1,115,148,149],[0,1,115,148,220],[0,1,115,219,220],[0,1,115,219,453], [0,1,115,349,352],[0,1,115,349,453],[1,235,236,239,462],[1,235,236,269,462], [0,1,235,238,462],[1,235,238,239,462],[0,1,235,238,352],[0,1,235,268,462], [1,235,268,269,462],[0,1,235,268,340],[0,1,235,339,340],[0,1,235,339,453], [0,1,235,349,352],[0,1,235,349,453],[0,2,5,26,140],[2,5,26,140,374], [0,2,5,26,260],[2,5,26,260,374],[0,2,5,119,140],[2,5,119,140,374], [2,5,119,353,374],[0,2,5,228,229],[0,2,5,229,463],[2,5,228,229,463], [2,5,228,462,463],[0,2,5,239,260],[2,5,239,260,374],[2,5,239,353,374], [0,2,5,239,463],[2,5,239,462,463],[0,2,26,29,143],[2,26,29,143,377], [0,2,26,29,263],[2,26,29,263,377],[0,2,26,140,143],[2,26,140,143,377], [2,26,140,374,377],[0,2,26,260,263],[2,26,260,263,377],[2,26,260,374,377], [0,2,29,109,223],[0,2,29,109,343],[0,2,29,143,223],[0,2,29,263,343], [0,2,35,109,223],[0,2,35,109,343],[0,2,35,149,223],[0,2,35,228,229], [0,2,35,229,463],[2,35,228,229,463],[2,35,228,462,463],[0,2,35,269,343], [0,2,35,269,463],[2,35,269,462,463],[0,2,116,119,140],[2,116,119,140,374], [2,116,119,353,374],[0,2,116,140,143],[2,116,140,143,377],[2,116,140,374,377], [0,2,116,143,223],[0,2,116,149,223],[2,116,350,353,374],[2,116,350,374,377], [0,2,236,239,260],[2,236,239,260,374],[2,236,239,353,374],[0,2,236,239,463], [2,236,239,462,463],[0,2,236,260,263],[2,236,260,263,377],[2,236,260,374,377], [0,2,236,263,343],[0,2,236,269,343],[0,2,236,269,463],[2,236,269,462,463], [2,236,350,353,374],[2,236,350,374,377],[0,3,4,5,119],[0,3,4,5,228], [0,3,4,228,462],[0,3,4,118,119],[0,3,4,118,352],[0,3,4,238,462], [0,3,4,238,352],[0,3,5,26,140],[0,3,5,26,260],[0,3,5,119,140], [0,3,5,228,229],[0,3,5,229,463],[0,3,5,239,260],[0,3,5,239,463], [0,3,24,26,140],[0,3,24,26,260],[0,3,24,138,140],[0,3,24,138,372], [0,3,24,258,260],[0,3,24,258,372],[0,3,117,118,119],[0,3,117,118,352], [0,3,117,119,140],[0,3,117,138,140],[0,3,117,138,372],[0,3,117,351,352], [0,3,117,351,372],[0,3,228,229,230],[0,3,228,230,464],[0,3,229,230,464], [0,3,229,463,464],[0,3,228,462,464],[0,3,237,238,462],[0,3,237,238,352], [0,3,237,239,260],[0,3,237,239,463],[0,3,237,258,260],[0,3,237,258,372], [0,3,237,351,352],[0,3,237,351,372],[0,3,237,462,464],[0,3,237,463,464], [0,24,26,29,143],[0,24,26,29,263],[0,24,26,140,143],[0,24,26,260,263], [0,24,27,29,143],[0,24,27,29,263],[0,24,27,141,143],[0,24,27,141,375], [0,24,27,261,263],[0,24,27,261,375],[0,24,138,140,143],[0,24,138,141,143], [0,24,138,141,375],[0,24,138,372,375],[0,24,258,260,263],[0,24,258,261,263], [0,24,258,261,375],[0,24,258,372,375],[0,27,29,109,223],[0,27,29,109,343], [0,27,29,143,223],[0,27,29,263,343],[0,27,102,106,220],[0,27,102,106,340], [0,27,102,109,223],[0,27,102,109,343],[0,27,102,216,220],[0,27,102,216,223], [0,27,102,336,340],[0,27,102,336,343],[0,27,105,106,220],[0,27,105,106,340], [0,27,105,219,220],[0,27,105,219,453],[0,27,105,339,340],[0,27,105,339,453], [0,27,141,143,223],[0,27,141,216,220],[0,27,141,216,223],[0,27,141,219,220], [0,27,141,219,453],[0,27,141,375,453],[0,27,261,263,343],[0,27,261,336,340], [0,27,261,336,343],[0,27,261,339,340],[0,27,261,339,453],[0,27,261,375,453], [0,33,34,35,149],[0,33,34,35,228],[0,33,34,228,462],[0,33,34,106,220], [0,33,34,106,340],[0,33,34,148,149],[0,33,34,148,220],[0,33,34,268,462], [0,33,34,268,340],[0,33,35,109,223],[0,33,35,109,343],[0,33,35,149,223], [0,33,35,228,229],[0,33,35,229,463],[0,33,35,269,343],[0,33,35,269,463], [0,33,102,106,220],[0,33,102,106,340],[0,33,102,109,223],[0,33,102,109,343], [0,33,102,216,220],[0,33,102,216,223],[0,33,102,336,340],[0,33,102,336,343], [0,33,147,148,149],[0,33,147,148,220],[0,33,147,149,223],[0,33,147,216,220], [0,33,147,216,223],[0,33,228,229,230],[0,33,228,230,464],[0,33,229,230,464], [0,33,229,463,464],[0,33,228,462,464],[0,33,267,268,462],[0,33,267,268,340], [0,33,267,269,343],[0,33,267,269,463],[0,33,267,336,340],[0,33,267,336,343], [0,33,267,462,464],[0,33,267,463,464],[0,114,115,116,119],[114,115,116,119,353], [0,114,115,116,149],[114,115,116,149,383],[114,115,116,350,353],[114,115,116,350,383], [0,114,115,118,119],[114,115,118,119,353],[0,114,115,118,352],[114,115,118,352,353], [0,114,115,148,149],[114,115,148,149,383],[0,114,115,148,220],[114,115,148,220,454], [114,115,148,382,383],[114,115,148,382,454],[0,114,115,219,220],[114,115,219,220,454], [0,114,115,219,453],[114,115,219,453,454],[114,115,349,350,353],[114,115,349,350,383], [0,114,115,349,352],[114,115,349,352,353],[114,115,349,382,383],[114,115,349,382,454], [0,114,115,349,453],[114,115,349,453,454],[0,114,116,119,140],[114,116,119,140,374], [114,116,119,353,374],[0,114,116,140,143],[114,116,140,143,377],[114,116,140,374,377], [0,114,116,143,223],[114,116,143,223,457],[114,116,143,377,457],[0,114,116,149,223], [114,116,149,223,457],[114,116,149,383,457],[114,116,350,353,374],[114,116,350,374,377], [114,116,350,377,457],[114,116,350,383,457],[0,114,117,118,119],[114,117,118,119,353], [0,114,117,118,352],[114,117,118,352,353],[0,114,117,119,140],[114,117,119,140,374], [114,117,119,353,374],[0,114,117,138,140],[114,117,138,140,374],[0,114,117,138,372], [114,117,138,372,374],[0,114,117,351,352],[114,117,351,352,353],[114,117,351,353,374], [0,114,117,351,372],[114,117,351,372,374],[0,114,138,140,143],[114,138,140,143,377], [114,138,140,374,377],[0,114,138,141,143],[114,138,141,143,377],[0,114,138,141,375], [114,138,141,375,377],[114,138,372,374,377],[0,114,138,372,375],[114,138,372,375,377], [0,114,141,143,223],[114,141,143,223,457],[114,141,143,377,457],[0,114,141,216,220], [114,141,216,220,454],[0,114,141,216,223],[114,141,216,223,457],[114,141,216,450,454], [114,141,216,450,457],[0,114,141,219,220],[114,141,219,220,454],[0,114,141,219,453], [114,141,219,453,454],[114,141,375,377,457],[114,141,375,450,454],[114,141,375,450,457], [0,114,141,375,453],[114,141,375,453,454],[0,114,147,148,149],[114,147,148,149,383], [0,114,147,148,220],[114,147,148,220,454],[114,147,148,382,383],[114,147,148,382,454], [0,114,147,149,223],[114,147,149,223,457],[114,147,149,383,457],[0,114,147,216,220], [114,147,216,220,454],[0,114,147,216,223],[114,147,216,223,457],[114,147,216,450,454], [114,147,216,450,457],[114,147,381,382,383],[114,147,381,382,454],[114,147,381,383,457], [114,147,381,450,454],[114,147,381,450,457],[114,348,349,350,353],[114,348,349,350,383], [0,114,348,349,352],[114,348,349,352,353],[114,348,349,382,383],[114,348,349,382,454], [0,114,348,349,453],[114,348,349,453,454],[114,348,350,353,374],[114,348,350,374,377], [114,348,350,377,457],[114,348,350,383,457],[0,114,348,351,352],[114,348,351,352,353], [114,348,351,353,374],[0,114,348,351,372],[114,348,351,372,374],[114,348,372,374,377], [0,114,348,372,375],[114,348,372,375,377],[114,348,375,377,457],[114,348,375,450,454], [114,348,375,450,457],[0,114,348,375,453],[114,348,375,453,454],[114,348,381,382,383], [114,348,381,382,454],[114,348,381,383,457],[114,348,381,450,454],[114,348,381,450,457], [234,235,236,239,353],[234,235,236,239,462],[234,235,236,269,383],[234,235,236,269,462], [234,235,236,350,353],[234,235,236,350,383],[234,235,238,239,353],[0,234,235,238,462], [234,235,238,239,462],[0,234,235,238,352],[234,235,238,352,353],[234,235,268,269,383], [0,234,235,268,462],[234,235,268,269,462],[0,234,235,268,340],[234,235,268,340,454], [234,235,268,382,383],[234,235,268,382,454],[0,234,235,339,340],[234,235,339,340,454], [0,234,235,339,453],[234,235,339,453,454],[234,235,349,350,353],[234,235,349,350,383], [0,234,235,349,352],[234,235,349,352,353],[234,235,349,382,383],[234,235,349,382,454], [0,234,235,349,453],[234,235,349,453,454],[0,234,236,239,260],[234,236,239,260,374], [234,236,239,353,374],[0,234,236,239,463],[234,236,239,462,463],[0,234,236,260,263], [234,236,260,263,377],[234,236,260,374,377],[0,234,236,263,343],[234,236,263,343,457], [234,236,263,377,457],[0,234,236,269,343],[234,236,269,343,457],[234,236,269,383,457], [0,234,236,269,463],[234,236,269,462,463],[234,236,350,353,374],[234,236,350,374,377], [234,236,350,377,457],[234,236,350,383,457],[234,237,238,239,353],[0,234,237,238,462], [234,237,238,239,462],[0,234,237,238,352],[234,237,238,352,353],[0,234,237,239,260], [234,237,239,260,374],[234,237,239,353,374],[0,234,237,239,463],[234,237,239,462,463], [0,234,237,258,260],[234,237,258,260,374],[0,234,237,258,372],[234,237,258,372,374], [0,234,237,351,352],[234,237,351,352,353],[234,237,351,353,374],[0,234,237,351,372], [234,237,351,372,374],[0,234,237,462,464],[0,234,237,463,464],[234,237,462,463,464], [0,234,258,260,263],[234,258,260,263,377],[234,258,260,374,377],[0,234,258,261,263], [234,258,261,263,377],[0,234,258,261,375],[234,258,261,375,377],[234,258,372,374,377], [0,234,258,372,375],[234,258,372,375,377],[0,234,261,263,343],[234,261,263,343,457], [234,261,263,377,457],[0,234,261,336,340],[234,261,336,340,454],[0,234,261,336,343], [234,261,336,343,457],[234,261,336,450,454],[234,261,336,450,457],[0,234,261,339,340], [234,261,339,340,454],[0,234,261,339,453],[234,261,339,453,454],[234,261,375,377,457], [234,261,375,450,454],[234,261,375,450,457],[0,234,261,375,453],[234,261,375,453,454], [234,267,268,269,383],[0,234,267,268,462],[234,267,268,269,462],[0,234,267,268,340], [234,267,268,340,454],[234,267,268,382,383],[234,267,268,382,454],[0,234,267,269,343], [234,267,269,343,457],[234,267,269,383,457],[0,234,267,269,463],[234,267,269,462,463], [0,234,267,336,340],[234,267,336,340,454],[0,234,267,336,343],[234,267,336,343,457], [234,267,336,450,454],[234,267,336,450,457],[234,267,381,382,383],[234,267,381,382,454], [234,267,381,383,457],[234,267,381,450,454],[234,267,381,450,457],[0,234,267,462,464], [0,234,267,463,464],[234,267,462,463,464],[234,348,349,350,353],[234,348,349,350,383], [0,234,348,349,352],[234,348,349,352,353],[234,348,349,382,383],[234,348,349,382,454], [0,234,348,349,453],[234,348,349,453,454],[234,348,350,353,374],[234,348,350,374,377], [234,348,350,377,457],[234,348,350,383,457],[0,234,348,351,352],[234,348,351,352,353], [234,348,351,353,374],[0,234,348,351,372],[234,348,351,372,374],[234,348,372,374,377], [0,234,348,372,375],[234,348,372,375,377],[234,348,375,377,457],[234,348,375,450,454], [234,348,375,450,457],[0,234,348,375,453],[234,348,375,453,454],[234,348,381,382,383], [234,348,381,382,454],[234,348,381,383,457],[234,348,381,450,454],[234,348,381,450,457], [1,2,5,41,155],[2,5,41,155,389],[1,2,5,41,275],[2,5,41,275,389], [1,2,5,119,155],[2,5,119,155,389],[2,5,119,353,389],[1,2,5,239,275], [2,5,239,275,389],[2,5,239,353,389],[1,2,35,109,223],[1,2,35,109,343], [1,2,35,149,223],[1,2,35,269,343],[1,2,38,41,155],[2,38,41,155,389], [1,2,38,41,275],[2,38,41,275,389],[1,2,38,112,226],[1,2,38,112,346], [1,2,38,152,155],[2,38,152,155,389],[1,2,38,152,226],[2,38,152,386,389], [1,2,38,272,275],[2,38,272,275,389],[1,2,38,272,346],[2,38,272,386,389], [1,2,108,109,223],[1,2,108,109,343],[1,2,108,112,226],[1,2,108,112,346], [1,2,108,222,223],[1,2,108,222,226],[1,2,108,342,343],[1,2,108,342,346], [1,2,116,119,155],[2,116,119,155,389],[2,116,119,353,389],[1,2,116,149,223], [1,2,116,152,155],[2,116,152,155,389],[1,2,116,152,226],[2,116,152,386,389], [1,2,116,222,223],[1,2,116,222,226],[2,116,350,353,389],[2,116,350,386,389], [1,2,236,239,275],[2,236,239,275,389],[2,236,239,353,389],[1,2,236,269,343], [1,2,236,272,275],[2,236,272,275,389],[1,2,236,272,346],[2,236,272,386,389], [1,2,236,342,343],[1,2,236,342,346],[2,236,350,353,389],[2,236,350,386,389], [1,4,5,41,155],[1,4,5,41,275],[1,4,5,119,155],[1,4,5,239,275], [1,4,39,41,155],[1,4,39,41,275],[1,4,39,153,155],[1,4,39,153,387], [1,4,39,273,275],[1,4,39,273,387],[1,4,118,119,155],[1,4,118,153,155], [1,4,118,153,387],[1,4,118,352,387],[1,4,238,239,275],[1,4,238,273,275], [1,4,238,273,387],[1,4,238,352,387],[1,34,35,109,223],[1,34,35,109,343], [1,34,35,149,223],[1,34,35,269,343],[1,34,103,106,220],[1,34,103,106,340], [1,34,103,109,223],[1,34,103,109,343],[1,34,103,217,220],[1,34,103,217,223], [1,34,103,337,340],[1,34,103,337,343],[1,34,148,149,223],[1,34,148,217,220], [1,34,148,217,223],[1,34,268,269,343],[1,34,268,337,340],[1,34,268,337,343], [1,36,38,41,155],[1,36,38,41,275],[1,36,38,112,226],[1,36,38,112,346], [1,36,38,152,155],[1,36,38,152,226],[1,36,38,272,275],[1,36,38,272,346], [1,36,39,41,155],[1,36,39,41,275],[1,36,39,153,155],[1,36,39,153,387], [1,36,39,273,275],[1,36,39,273,387],[1,36,103,106,220],[1,36,103,106,340], [1,36,103,109,223],[1,36,103,109,343],[1,36,103,217,220],[1,36,103,217,223], [1,36,103,337,340],[1,36,103,337,343],[1,36,105,106,220],[1,36,105,106,340], [1,36,105,219,220],[1,36,105,219,453],[1,36,105,339,340],[1,36,105,339,453], [1,36,108,109,223],[1,36,108,109,343],[1,36,108,112,226],[1,36,108,112,346], [1,36,108,222,223],[1,36,108,222,226],[1,36,108,342,343],[1,36,108,342,346], [1,36,150,152,155],[1,36,150,152,226],[1,36,150,153,155],[1,36,150,153,387], [1,36,150,217,220],[1,36,150,217,223],[1,36,150,219,220],[1,36,150,219,453], [1,36,150,222,223],[1,36,150,222,226],[1,36,150,384,387],[1,36,150,384,453], [1,36,270,272,275],[1,36,270,272,346],[1,36,270,273,275],[1,36,270,273,387], [1,36,270,337,340],[1,36,270,337,343],[1,36,270,339,340],[1,36,270,339,453], [1,36,270,342,343],[1,36,270,342,346],[1,36,270,384,387],[1,36,270,384,453], [1,115,116,119,155],[115,116,119,155,389],[115,116,119,353,389],[1,115,116,149,223], [115,116,149,223,457],[115,116,149,383,457],[1,115,116,152,155],[115,116,152,155,389], [1,115,116,152,226],[115,116,152,226,460],[115,116,152,386,389],[115,116,152,386,460], [1,115,116,222,223],[115,116,222,223,457],[1,115,116,222,226],[115,116,222,226,460], [115,116,222,456,457],[115,116,222,456,460],[115,116,350,353,389],[115,116,350,383,457], [115,116,350,386,389],[115,116,350,386,460],[115,116,350,456,457],[115,116,350,456,460], [1,115,118,119,155],[115,118,119,155,389],[115,118,119,353,389],[1,115,118,153,155], [115,118,153,155,389],[1,115,118,153,387],[115,118,153,387,389],[115,118,352,353,389], [1,115,118,352,387],[115,118,352,387,389],[1,115,148,149,223],[115,148,149,223,457], [115,148,149,383,457],[1,115,148,217,220],[115,148,217,220,454],[1,115,148,217,223], [115,148,217,223,457],[115,148,217,451,454],[115,148,217,451,457],[115,148,382,383,457], 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