#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_005 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(314,4524,14976,17940,7176) ### ### 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:=[ [0,1,2,5,209],[0,1,2,35,239],[0,1,2,206,209],[0,1,2,206,239], [0,1,4,5,209],[0,1,4,106,208],[0,1,4,208,209],[0,1,34,35,239], [0,1,34,94,196],[0,1,34,94,298],[0,1,34,136,196],[0,1,34,238,239], [0,1,34,238,298],[0,1,93,94,196],[0,1,93,94,298],[0,1,93,195,196], [0,1,93,195,297],[0,1,93,297,298],[0,1,103,106,208],[0,1,103,136,196], [0,1,103,195,196],[0,1,103,195,297],[0,1,205,206,209],[0,1,205,206,239], [0,1,103,205,208],[0,1,205,208,209],[0,1,205,238,239],[0,1,205,238,298], [0,1,103,205,297],[0,1,205,297,298],[0,2,5,26,128],[0,2,5,26,230], [2,5,26,128,230],[0,2,5,107,128],[2,5,107,128,230],[0,2,5,209,230], [2,5,107,209,230],[0,2,26,29,131],[0,2,26,29,233],[2,26,29,131,233], [0,2,26,128,131],[2,26,128,131,233],[0,2,26,230,233],[2,26,128,230,233], [0,2,29,97,199],[0,2,29,97,301],[0,2,29,131,199],[0,2,29,233,301], [0,2,35,97,199],[0,2,35,97,301],[0,2,35,137,199],[0,2,35,239,301], [0,2,104,107,128],[2,104,107,128,230],[2,104,107,209,230],[0,2,104,128,131], [2,104,128,131,233],[2,104,128,230,233],[0,2,104,131,199],[0,2,104,137,199], [0,2,206,209,230],[2,104,206,209,230],[0,2,206,230,233],[2,104,206,230,233], [0,2,206,233,301],[0,2,206,239,301],[0,3,4,5,209],[0,3,4,106,208], [0,3,4,208,209],[0,3,5,26,128],[0,3,5,26,230],[0,3,5,107,128], [0,3,5,209,230],[0,3,24,26,128],[0,3,24,26,230],[0,3,24,126,128], [0,3,24,126,228],[0,3,24,228,230],[0,3,105,106,208],[0,3,105,107,128], [0,3,105,126,128],[0,3,105,126,228],[0,3,105,207,208],[0,3,207,208,209], [0,3,207,209,230],[0,3,105,207,228],[0,3,207,228,230],[0,24,26,29,131], [0,24,26,29,233],[0,24,26,128,131],[0,24,26,230,233],[0,24,27,29,131], [0,24,27,29,233],[0,24,27,129,131],[0,24,27,129,231],[0,24,27,231,233], [0,24,126,128,131],[0,24,126,129,131],[0,24,126,129,231],[0,24,228,230,233], [0,24,126,228,231],[0,24,228,231,233],[0,27,29,97,199],[0,27,29,97,301], [0,27,29,131,199],[0,27,29,233,301],[0,27,90,94,196],[0,27,90,94,298], [0,27,90,97,199],[0,27,90,97,301],[0,27,90,192,196],[0,27,90,192,199], [0,27,90,294,298],[0,27,90,294,301],[0,27,93,94,196],[0,27,93,94,298], [0,27,93,195,196],[0,27,93,195,297],[0,27,93,297,298],[0,27,129,131,199], [0,27,129,192,196],[0,27,129,192,199],[0,27,129,195,196],[0,27,129,195,297], [0,27,231,233,301],[0,27,231,294,298],[0,27,231,294,301],[0,27,129,231,297], [0,27,231,297,298],[0,33,34,35,239],[0,33,34,94,196],[0,33,34,94,298], [0,33,34,136,196],[0,33,34,238,239],[0,33,34,238,298],[0,33,35,97,199], [0,33,35,97,301],[0,33,35,137,199],[0,33,35,239,301],[0,33,90,94,196], [0,33,90,94,298],[0,33,90,97,199],[0,33,90,97,301],[0,33,90,192,196], [0,33,90,192,199],[0,33,90,294,298],[0,33,90,294,301],[0,33,135,136,196], [0,33,135,137,199],[0,33,135,192,196],[0,33,135,192,199],[0,33,237,238,239], [0,33,237,238,298],[0,33,237,239,301],[0,33,237,294,298],[0,33,237,294,301], [102,103,104,107,209],[102,103,104,137,239],[102,103,104,206,209],[102,103,104,206,239], [102,103,106,107,209],[0,102,103,106,208],[102,103,106,208,209],[102,103,136,137,239], [0,102,103,136,196],[102,103,136,196,298],[102,103,136,238,239],[102,103,136,238,298], [0,102,103,195,196],[102,103,195,196,298],[0,102,103,195,297],[102,103,195,297,298], [102,103,205,206,209],[102,103,205,206,239],[0,102,103,205,208],[102,103,205,208,209], [102,103,205,238,239],[102,103,205,238,298],[0,102,103,205,297],[102,103,205,297,298], [0,102,104,107,128],[102,104,107,128,230],[102,104,107,209,230],[0,102,104,128,131], [102,104,128,131,233],[102,104,128,230,233],[0,102,104,131,199],[102,104,131,199,301], [102,104,131,233,301],[0,102,104,137,199],[102,104,137,199,301],[102,104,137,239,301], [102,104,206,209,230],[102,104,206,230,233],[102,104,206,233,301],[102,104,206,239,301], [102,105,106,107,209],[0,102,105,106,208],[102,105,106,208,209],[0,102,105,107,128], [102,105,107,128,230],[102,105,107,209,230],[0,102,105,126,128],[102,105,126,128,230], [0,102,105,126,228],[102,105,126,228,230],[0,102,105,207,208],[102,105,207,208,209], [102,105,207,209,230],[0,102,105,207,228],[102,105,207,228,230],[0,102,126,128,131], [102,126,128,131,233],[102,126,128,230,233],[0,102,126,129,131],[102,126,129,131,233], [0,102,126,129,231],[102,126,129,231,233],[102,126,228,230,233],[0,102,126,228,231], [102,126,228,231,233],[0,102,129,131,199],[102,129,131,199,301],[102,129,131,233,301], [0,102,129,192,196],[102,129,192,196,298],[0,102,129,192,199],[102,129,192,199,301], [102,129,192,294,298],[102,129,192,294,301],[0,102,129,195,196],[102,129,195,196,298], [0,102,129,195,297],[102,129,195,297,298],[102,129,231,233,301],[102,129,231,294,298], [102,129,231,294,301],[0,102,129,231,297],[102,129,231,297,298],[102,135,136,137,239], [0,102,135,136,196],[102,135,136,196,298],[102,135,136,238,239],[102,135,136,238,298], [0,102,135,137,199],[102,135,137,199,301],[102,135,137,239,301],[0,102,135,192,196], [102,135,192,196,298],[0,102,135,192,199],[102,135,192,199,301],[102,135,192,294,298], [102,135,192,294,301],[102,135,237,238,239],[102,135,237,238,298],[102,135,237,239,301], [102,135,237,294,298],[102,135,237,294,301],[0,204,205,206,209],[102,204,205,206,209], [0,204,205,206,239],[102,204,205,206,239],[0,102,204,205,208],[0,204,205,208,209], [102,204,205,208,209],[0,204,205,238,239],[102,204,205,238,239],[0,204,205,238,298], [102,204,205,238,298],[0,102,204,205,297],[0,204,205,297,298],[102,204,205,297,298], [0,204,206,209,230],[102,204,206,209,230],[0,204,206,230,233],[102,204,206,230,233], [0,204,206,233,301],[102,204,206,233,301],[0,204,206,239,301],[102,204,206,239,301], [0,102,204,207,208],[0,204,207,208,209],[102,204,207,208,209],[0,204,207,209,230], [102,204,207,209,230],[0,102,204,207,228],[0,204,207,228,230],[102,204,207,228,230], [0,204,228,230,233],[102,204,228,230,233],[0,102,204,228,231],[0,204,228,231,233], [102,204,228,231,233],[0,204,231,233,301],[102,204,231,233,301],[0,204,231,294,298], [102,204,231,294,298],[0,204,231,294,301],[102,204,231,294,301],[0,102,204,231,297], [0,204,231,297,298],[102,204,231,297,298],[0,204,237,238,239],[102,204,237,238,239], [0,204,237,238,298],[102,204,237,238,298],[0,204,237,239,301],[102,204,237,239,301], [0,204,237,294,298],[102,204,237,294,298],[0,204,237,294,301],[102,204,237,294,301], [1,2,5,41,143],[1,2,5,41,245],[2,5,41,143,245],[1,2,5,107,143], [2,5,107,143,245],[1,2,5,209,245],[2,5,107,209,245],[1,2,35,97,199], [1,2,35,97,301],[1,2,35,137,199],[1,2,35,239,301],[1,2,38,41,143], [1,2,38,41,245],[2,38,41,143,245],[1,2,38,100,202],[1,2,38,100,304], [1,2,38,140,143],[2,38,140,143,245],[1,2,38,140,202],[1,2,38,242,245], [2,38,140,242,245],[1,2,38,242,304],[1,2,96,97,199],[1,2,96,97,301], [1,2,96,100,202],[1,2,96,100,304],[1,2,96,198,199],[1,2,96,198,202], [1,2,96,300,301],[1,2,96,300,304],[1,2,104,107,143],[2,104,107,143,245], [2,104,107,209,245],[1,2,104,137,199],[1,2,104,140,143],[2,104,140,143,245], [1,2,104,140,202],[2,104,140,242,245],[1,2,104,198,199],[1,2,104,198,202], [1,2,206,209,245],[2,104,206,209,245],[1,2,206,239,301],[1,2,206,242,245], [2,104,206,242,245],[1,2,206,242,304],[1,2,206,300,301],[1,2,206,300,304], [1,4,5,41,143],[1,4,5,41,245],[1,4,5,107,143],[1,4,5,209,245], [1,4,39,41,143],[1,4,39,41,245],[1,4,39,141,143],[1,4,39,141,243], [1,4,39,243,245],[1,4,106,107,143],[1,4,106,141,143],[1,4,106,141,243], [1,4,208,209,245],[1,4,106,208,243],[1,4,208,243,245],[1,34,35,97,199], [1,34,35,97,301],[1,34,35,137,199],[1,34,35,239,301],[1,34,91,94,196], [1,34,91,94,298],[1,34,91,97,199],[1,34,91,97,301],[1,34,91,193,196], [1,34,91,193,199],[1,34,91,295,298],[1,34,91,295,301],[1,34,136,137,199], [1,34,136,193,196],[1,34,136,193,199],[1,34,238,239,301],[1,34,238,295,298], [1,34,238,295,301],[1,36,38,41,143],[1,36,38,41,245],[1,36,38,100,202], [1,36,38,100,304],[1,36,38,140,143],[1,36,38,140,202],[1,36,38,242,245], [1,36,38,242,304],[1,36,39,41,143],[1,36,39,41,245],[1,36,39,141,143], [1,36,39,141,243],[1,36,39,243,245],[1,36,91,94,196],[1,36,91,94,298], [1,36,91,97,199],[1,36,91,97,301],[1,36,91,193,196],[1,36,91,193,199], [1,36,91,295,298],[1,36,91,295,301],[1,36,93,94,196],[1,36,93,94,298], [1,36,93,195,196],[1,36,93,195,297],[1,36,93,297,298],[1,36,96,97,199], [1,36,96,97,301],[1,36,96,100,202],[1,36,96,100,304],[1,36,96,198,199], [1,36,96,198,202],[1,36,96,300,301],[1,36,96,300,304],[1,36,138,140,143], [1,36,138,140,202],[1,36,138,141,143],[1,36,138,141,243],[1,36,138,193,196], [1,36,138,193,199],[1,36,138,195,196],[1,36,138,195,297],[1,36,138,198,199], [1,36,138,198,202],[1,36,240,242,245],[1,36,240,242,304],[1,36,138,240,243], [1,36,240,243,245],[1,36,240,295,298],[1,36,240,295,301],[1,36,138,240,297], [1,36,240,297,298],[1,36,240,300,301],[1,36,240,300,304],[1,103,104,107,143], [103,104,107,143,245],[103,104,107,209,245],[1,103,104,137,199],[103,104,137,199,301], [103,104,137,239,301],[1,103,104,140,143],[103,104,140,143,245],[1,103,104,140,202], [103,104,140,202,304],[103,104,140,242,245],[103,104,140,242,304],[1,103,104,198,199], [103,104,198,199,301],[1,103,104,198,202],[103,104,198,202,304],[103,104,198,300,301], [103,104,198,300,304],[103,104,206,209,245],[103,104,206,239,301],[103,104,206,242,245], [103,104,206,242,304],[103,104,206,300,301],[103,104,206,300,304],[1,103,106,107,143], [103,106,107,143,245],[103,106,107,209,245],[1,103,106,141,143],[103,106,141,143,245], [1,103,106,141,243],[103,106,141,243,245],[103,106,208,209,245],[1,103,106,208,243], [103,106,208,243,245],[1,103,136,137,199],[103,136,137,199,301],[103,136,137,239,301], [1,103,136,193,196],[103,136,193,196,298],[1,103,136,193,199],[103,136,193,199,301], [103,136,193,295,298],[103,136,193,295,301],[103,136,238,239,301],[103,136,238,295,298], [103,136,238,295,301],[1,103,138,140,143],[103,138,140,143,245],[1,103,138,140,202], [103,138,140,202,304],[103,138,140,242,245],[103,138,140,242,304],[1,103,138,141,143], [103,138,141,143,245],[1,103,138,141,243],[103,138,141,243,245],[1,103,138,193,196], [103,138,193,196,298],[1,103,138,193,199],[103,138,193,199,301],[103,138,193,295,298], [103,138,193,295,301],[1,103,138,195,196],[103,138,195,196,298],[1,103,138,195,297], [103,138,195,297,298],[1,103,138,198,199],[103,138,198,199,301],[1,103,138,198,202], [103,138,198,202,304],[103,138,198,300,301],[103,138,198,300,304],[103,138,240,242,245], [103,138,240,242,304],[1,103,138,240,243],[103,138,240,243,245],[103,138,240,295,298], [103,138,240,295,301],[1,103,138,240,297],[103,138,240,297,298],[103,138,240,300,301], [103,138,240,300,304],[1,205,206,209,245],[103,205,206,209,245],[1,205,206,239,301], [103,205,206,239,301],[1,205,206,242,245],[103,205,206,242,245],[1,205,206,242,304], [103,205,206,242,304],[1,205,206,300,301],[103,205,206,300,301],[1,205,206,300,304], [103,205,206,300,304],[1,205,208,209,245],[103,205,208,209,245],[1,103,205,208,243], [1,205,208,243,245],[103,205,208,243,245],[1,205,238,239,301],[103,205,238,239,301], [1,205,238,295,298],[103,205,238,295,298],[1,205,238,295,301],[103,205,238,295,301], [1,205,240,242,245],[103,205,240,242,245],[1,205,240,242,304],[103,205,240,242,304], [1,103,205,240,243],[1,205,240,243,245],[103,205,240,243,245],[1,205,240,295,298], [103,205,240,295,298],[1,205,240,295,301],[103,205,240,295,301],[1,103,205,240,297], [1,205,240,297,298],[103,205,240,297,298],[1,205,240,300,301],[103,205,240,300,301], [1,205,240,300,304],[103,205,240,300,304],[2,29,96,97,199],[2,29,96,97,301], [2,29,96,100,202],[2,29,96,100,304],[2,29,96,198,199],[2,29,96,198,202], [2,29,96,300,301],[2,29,96,300,304],[2,29,98,100,202],[2,29,98,100,304], [2,29,98,200,202],[2,29,98,200,302],[2,29,98,302,304],[2,29,131,198,199], [2,29,131,198,202],[2,29,131,200,202],[2,29,131,200,302],[2,29,233,300,301], [2,29,233,300,304],[2,29,131,233,302],[2,29,233,302,304],[2,38,98,100,202], [2,38,98,100,304],[2,38,98,200,202],[2,38,98,200,302],[2,38,98,302,304], [2,38,140,200,202],[2,38,140,200,302],[2,38,140,242,302],[2,38,242,302,304], [2,104,131,198,199],[104,131,198,199,301],[2,104,131,198,202],[104,131,198,202,304], [104,131,198,300,301],[104,131,198,300,304],[2,104,131,200,202],[104,131,200,202,304], [2,104,131,200,302],[104,131,200,302,304],[104,131,233,300,301],[104,131,233,300,304], [2,104,131,233,302],[104,131,233,302,304],[2,104,140,200,202],[104,140,200,202,304], [2,104,140,200,302],[104,140,200,302,304],[2,104,140,242,302],[104,140,242,302,304], [2,206,233,300,301],[104,206,233,300,301],[2,206,233,300,304],[104,206,233,300,304], [2,104,206,233,302],[2,206,233,302,304],[104,206,233,302,304],[2,104,206,242,302], [2,206,242,302,304],[104,206,242,302,304],[3,4,5,8,212],[3,4,5,209,212], [3,4,7,8,212],[3,4,7,94,196],[3,4,7,94,298],[3,4,7,109,196], [3,4,7,211,212],[3,4,7,211,298],[3,4,93,94,196],[3,4,93,94,298], [3,4,93,195,196],[3,4,93,195,297],[3,4,93,297,298],[3,4,106,109,196], [3,4,106,195,196],[3,4,106,195,297],[3,4,208,209,212],[3,4,208,211,212], [3,4,208,211,298],[3,4,106,208,297],[3,4,208,297,298],[3,5,8,23,125], [3,5,8,23,227],[5,8,23,125,227],[3,5,8,110,125],[5,8,110,125,227], [3,5,8,212,227],[5,8,110,212,227],[3,5,23,26,128],[3,5,23,26,230], [5,23,26,128,230],[3,5,23,125,128],[5,23,125,128,230],[3,5,23,227,230], [5,23,125,227,230],[3,5,107,110,125],[5,107,110,125,227],[5,107,110,212,227], [3,5,107,125,128],[5,107,125,128,230],[5,107,125,227,230],[3,5,209,212,227], [5,107,209,212,227],[3,5,209,227,230],[5,107,209,227,230],[3,6,7,8,212], [3,6,7,94,196],[3,6,7,94,298],[3,6,7,109,196],[3,6,7,211,212], [3,6,7,211,298],[3,6,8,23,125],[3,6,8,23,227],[3,6,8,110,125], [3,6,8,212,227],[3,6,21,23,125],[3,6,21,23,227],[3,6,21,94,196], [3,6,21,94,298],[3,6,21,123,125],[3,6,21,123,196],[3,6,21,225,227], [3,6,21,225,298],[3,6,108,109,196],[3,6,108,110,125],[3,6,108,123,125], [3,6,108,123,196],[3,6,210,211,212],[3,6,210,211,298],[3,6,210,212,227], [3,6,210,225,227],[3,6,210,225,298],[3,21,23,26,128],[3,21,23,26,230], [3,21,23,125,128],[3,21,23,227,230],[3,21,24,26,128],[3,21,24,26,230], [3,21,24,94,196],[3,21,24,94,298],[3,21,24,126,128],[3,21,24,126,196], [3,21,24,228,230],[3,21,24,228,298],[3,21,123,125,128],[3,21,123,126,128], [3,21,123,126,196],[3,21,225,227,230],[3,21,225,228,230],[3,21,225,228,298], [3,24,93,94,196],[3,24,93,94,298],[3,24,93,195,196],[3,24,93,195,297], [3,24,93,297,298],[3,24,126,195,196],[3,24,126,195,297],[3,24,126,228,297], [3,24,228,297,298],[105,106,107,110,212],[105,106,107,209,212],[105,106,109,110,212], [3,105,106,109,196],[105,106,109,196,298],[105,106,109,211,212],[105,106,109,211,298], [3,105,106,195,196],[105,106,195,196,298],[3,105,106,195,297],[105,106,195,297,298], [105,106,208,209,212],[105,106,208,211,212],[105,106,208,211,298],[3,105,106,208,297], [105,106,208,297,298],[3,105,107,110,125],[105,107,110,125,227],[105,107,110,212,227], [3,105,107,125,128],[105,107,125,128,230],[105,107,125,227,230],[105,107,209,212,227], [105,107,209,227,230],[105,108,109,110,212],[3,105,108,109,196],[105,108,109,196,298], [105,108,109,211,212],[105,108,109,211,298],[3,105,108,110,125],[105,108,110,125,227], [105,108,110,212,227],[3,105,108,123,125],[105,108,123,125,227],[3,105,108,123,196], 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