#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_011 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(708,10950,36740,44160,17664) ### ### 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:=[ [0,1,2,5,179],[0,1,2,5,348],[1,2,5,348,702],[1,2,5,359,702], [0,1,2,35,209],[0,1,2,35,348],[1,2,35,348,702],[1,2,35,389,702], [0,1,2,176,179],[0,1,2,176,209],[1,2,356,359,702],[1,2,356,389,702], [0,1,4,5,179],[0,1,4,5,348],[0,1,4,348,702],[1,4,5,348,702], [1,4,5,359,702],[0,1,4,178,179],[0,1,4,178,532],[0,1,4,358,702], [1,4,358,359,702],[0,1,4,358,532],[0,1,34,35,209],[0,1,34,35,348], [0,1,34,348,702],[1,34,35,348,702],[1,34,35,389,702],[0,1,34,166,340], [0,1,34,166,520],[0,1,34,208,209],[0,1,34,208,340],[0,1,34,388,702], [1,34,388,389,702],[0,1,34,388,520],[0,1,165,166,340],[0,1,165,166,520], [0,1,165,339,340],[0,1,165,339,693],[0,1,165,519,520],[0,1,165,519,693], [0,1,175,176,179],[0,1,175,176,209],[0,1,175,178,179],[0,1,175,178,532], [0,1,175,208,209],[0,1,175,208,340],[0,1,175,339,340],[0,1,175,339,693], [0,1,175,529,532],[0,1,175,529,693],[1,355,356,359,702],[1,355,356,389,702], [0,1,355,358,702],[1,355,358,359,702],[0,1,355,358,532],[0,1,355,388,702], [1,355,388,389,702],[0,1,355,388,520],[0,1,355,519,520],[0,1,355,519,693], [0,1,355,529,532],[0,1,355,529,693],[0,2,5,26,200],[2,5,26,200,554], [0,2,5,26,380],[2,5,26,380,554],[0,2,5,179,200],[2,5,179,200,554], [2,5,179,533,554],[0,2,5,348,349],[0,2,5,349,703],[2,5,348,349,703], [2,5,348,702,703],[0,2,5,359,380],[2,5,359,380,554],[2,5,359,533,554], [0,2,5,359,703],[2,5,359,702,703],[0,2,26,29,203],[2,26,29,203,557], [0,2,26,29,383],[2,26,29,383,557],[0,2,26,200,203],[2,26,200,203,557], [2,26,200,554,557],[0,2,26,380,383],[2,26,380,383,557],[2,26,380,554,557], [0,2,29,169,343],[0,2,29,169,523],[0,2,29,203,343],[0,2,29,383,523], [0,2,35,169,343],[0,2,35,169,523],[0,2,35,209,343],[0,2,35,348,349], [0,2,35,349,703],[2,35,348,349,703],[2,35,348,702,703],[0,2,35,389,523], [0,2,35,389,703],[2,35,389,702,703],[0,2,176,179,200],[2,176,179,200,554], [2,176,179,533,554],[0,2,176,200,203],[2,176,200,203,557],[2,176,200,554,557], [0,2,176,203,343],[0,2,176,209,343],[2,176,530,533,554],[2,176,530,554,557], [0,2,356,359,380],[2,356,359,380,554],[2,356,359,533,554],[0,2,356,359,703], [2,356,359,702,703],[0,2,356,380,383],[2,356,380,383,557],[2,356,380,554,557], [0,2,356,383,523],[0,2,356,389,523],[0,2,356,389,703],[2,356,389,702,703], [2,356,530,533,554],[2,356,530,554,557],[0,3,4,5,179],[0,3,4,5,348], [0,3,4,348,702],[0,3,4,178,179],[0,3,4,178,532],[0,3,4,358,702], [0,3,4,358,532],[0,3,5,26,200],[0,3,5,26,380],[0,3,5,179,200], [0,3,5,348,349],[0,3,5,349,703],[0,3,5,359,380],[0,3,5,359,703], [0,3,24,26,200],[0,3,24,26,380],[0,3,24,198,200],[0,3,24,198,552], [0,3,24,378,380],[0,3,24,378,552],[0,3,177,178,179],[0,3,177,178,532], [0,3,177,179,200],[0,3,177,198,200],[0,3,177,198,552],[0,3,177,531,532], [0,3,177,531,552],[0,3,348,349,350],[0,3,348,350,704],[0,3,349,350,704], [0,3,349,703,704],[0,3,348,702,704],[0,3,357,358,702],[0,3,357,358,532], [0,3,357,359,380],[0,3,357,359,703],[0,3,357,378,380],[0,3,357,378,552], [0,3,357,531,532],[0,3,357,531,552],[0,3,357,702,704],[0,3,357,703,704], [0,24,26,29,203],[0,24,26,29,383],[0,24,26,200,203],[0,24,26,380,383], [0,24,27,29,203],[0,24,27,29,383],[0,24,27,201,203],[0,24,27,201,555], [0,24,27,381,383],[0,24,27,381,555],[0,24,198,200,203],[0,24,198,201,203], [0,24,198,201,555],[0,24,198,552,555],[0,24,378,380,383],[0,24,378,381,383], [0,24,378,381,555],[0,24,378,552,555],[0,27,29,169,343],[0,27,29,169,523], [0,27,29,203,343],[0,27,29,383,523],[0,27,162,166,340],[0,27,162,166,520], [0,27,162,169,343],[0,27,162,169,523],[0,27,162,336,340],[0,27,162,336,343], [0,27,162,516,520],[0,27,162,516,523],[0,27,165,166,340],[0,27,165,166,520], [0,27,165,339,340],[0,27,165,339,693],[0,27,165,519,520],[0,27,165,519,693], [0,27,201,203,343],[0,27,201,336,340],[0,27,201,336,343],[0,27,201,339,340], [0,27,201,339,693],[0,27,201,555,693],[0,27,381,383,523],[0,27,381,516,520], [0,27,381,516,523],[0,27,381,519,520],[0,27,381,519,693],[0,27,381,555,693], [0,33,34,35,209],[0,33,34,35,348],[0,33,34,348,702],[0,33,34,166,340], [0,33,34,166,520],[0,33,34,208,209],[0,33,34,208,340],[0,33,34,388,702], [0,33,34,388,520],[0,33,35,169,343],[0,33,35,169,523],[0,33,35,209,343], [0,33,35,348,349],[0,33,35,349,703],[0,33,35,389,523],[0,33,35,389,703], [0,33,162,166,340],[0,33,162,166,520],[0,33,162,169,343],[0,33,162,169,523], [0,33,162,336,340],[0,33,162,336,343],[0,33,162,516,520],[0,33,162,516,523], [0,33,207,208,209],[0,33,207,208,340],[0,33,207,209,343],[0,33,207,336,340], [0,33,207,336,343],[0,33,348,349,350],[0,33,348,350,704],[0,33,349,350,704], [0,33,349,703,704],[0,33,348,702,704],[0,33,387,388,702],[0,33,387,388,520], [0,33,387,389,523],[0,33,387,389,703],[0,33,387,516,520],[0,33,387,516,523], [0,33,387,702,704],[0,33,387,703,704],[0,174,175,176,179],[174,175,176,179,533], [0,174,175,176,209],[174,175,176,209,563],[174,175,176,530,533],[174,175,176,530,563], [0,174,175,178,179],[174,175,178,179,533],[0,174,175,178,532],[174,175,178,532,533], [0,174,175,208,209],[174,175,208,209,563],[0,174,175,208,340],[174,175,208,340,694], [174,175,208,562,563],[174,175,208,562,694],[0,174,175,339,340],[174,175,339,340,694], [0,174,175,339,693],[174,175,339,693,694],[174,175,529,530,533],[174,175,529,530,563], [0,174,175,529,532],[174,175,529,532,533],[174,175,529,562,563],[174,175,529,562,694], [0,174,175,529,693],[174,175,529,693,694],[0,174,176,179,200],[174,176,179,200,554], [174,176,179,533,554],[0,174,176,200,203],[174,176,200,203,557],[174,176,200,554,557], [0,174,176,203,343],[174,176,203,343,697],[174,176,203,557,697],[0,174,176,209,343], [174,176,209,343,697],[174,176,209,563,697],[174,176,530,533,554],[174,176,530,554,557], [174,176,530,557,697],[174,176,530,563,697],[0,174,177,178,179],[174,177,178,179,533], [0,174,177,178,532],[174,177,178,532,533],[0,174,177,179,200],[174,177,179,200,554], [174,177,179,533,554],[0,174,177,198,200],[174,177,198,200,554],[0,174,177,198,552], [174,177,198,552,554],[0,174,177,531,532],[174,177,531,532,533],[174,177,531,533,554], [0,174,177,531,552],[174,177,531,552,554],[0,174,198,200,203],[174,198,200,203,557], [174,198,200,554,557],[0,174,198,201,203],[174,198,201,203,557],[0,174,198,201,555], [174,198,201,555,557],[174,198,552,554,557],[0,174,198,552,555],[174,198,552,555,557], [0,174,201,203,343],[174,201,203,343,697],[174,201,203,557,697],[0,174,201,336,340], [174,201,336,340,694],[0,174,201,336,343],[174,201,336,343,697],[174,201,336,690,694], [174,201,336,690,697],[0,174,201,339,340],[174,201,339,340,694],[0,174,201,339,693], [174,201,339,693,694],[174,201,555,557,697],[174,201,555,690,694],[174,201,555,690,697], [0,174,201,555,693],[174,201,555,693,694],[0,174,207,208,209],[174,207,208,209,563], [0,174,207,208,340],[174,207,208,340,694],[174,207,208,562,563],[174,207,208,562,694], [0,174,207,209,343],[174,207,209,343,697],[174,207,209,563,697],[0,174,207,336,340], [174,207,336,340,694],[0,174,207,336,343],[174,207,336,343,697],[174,207,336,690,694], [174,207,336,690,697],[174,207,561,562,563],[174,207,561,562,694],[174,207,561,563,697], [174,207,561,690,694],[174,207,561,690,697],[174,528,529,530,533],[174,528,529,530,563], [0,174,528,529,532],[174,528,529,532,533],[174,528,529,562,563],[174,528,529,562,694], [0,174,528,529,693],[174,528,529,693,694],[174,528,530,533,554],[174,528,530,554,557], [174,528,530,557,697],[174,528,530,563,697],[0,174,528,531,532],[174,528,531,532,533], [174,528,531,533,554],[0,174,528,531,552],[174,528,531,552,554],[174,528,552,554,557], [0,174,528,552,555],[174,528,552,555,557],[174,528,555,557,697],[174,528,555,690,694], [174,528,555,690,697],[0,174,528,555,693],[174,528,555,693,694],[174,528,561,562,563], [174,528,561,562,694],[174,528,561,563,697],[174,528,561,690,694],[174,528,561,690,697], [354,355,356,359,533],[354,355,356,359,702],[354,355,356,389,563],[354,355,356,389,702], [354,355,356,530,533],[354,355,356,530,563],[354,355,358,359,533],[0,354,355,358,702], [354,355,358,359,702],[0,354,355,358,532],[354,355,358,532,533],[354,355,388,389,563], [0,354,355,388,702],[354,355,388,389,702],[0,354,355,388,520],[354,355,388,520,694], [354,355,388,562,563],[354,355,388,562,694],[0,354,355,519,520],[354,355,519,520,694], [0,354,355,519,693],[354,355,519,693,694],[354,355,529,530,533],[354,355,529,530,563], [0,354,355,529,532],[354,355,529,532,533],[354,355,529,562,563],[354,355,529,562,694], [0,354,355,529,693],[354,355,529,693,694],[0,354,356,359,380],[354,356,359,380,554], [354,356,359,533,554],[0,354,356,359,703],[354,356,359,702,703],[0,354,356,380,383], [354,356,380,383,557],[354,356,380,554,557],[0,354,356,383,523],[354,356,383,523,697], [354,356,383,557,697],[0,354,356,389,523],[354,356,389,523,697],[354,356,389,563,697], [0,354,356,389,703],[354,356,389,702,703],[354,356,530,533,554],[354,356,530,554,557], [354,356,530,557,697],[354,356,530,563,697],[354,357,358,359,533],[0,354,357,358,702], [354,357,358,359,702],[0,354,357,358,532],[354,357,358,532,533],[0,354,357,359,380], [354,357,359,380,554],[354,357,359,533,554],[0,354,357,359,703],[354,357,359,702,703], [0,354,357,378,380],[354,357,378,380,554],[0,354,357,378,552],[354,357,378,552,554], [0,354,357,531,532],[354,357,531,532,533],[354,357,531,533,554],[0,354,357,531,552], [354,357,531,552,554],[0,354,357,702,704],[0,354,357,703,704],[354,357,702,703,704], [0,354,378,380,383],[354,378,380,383,557],[354,378,380,554,557],[0,354,378,381,383], [354,378,381,383,557],[0,354,378,381,555],[354,378,381,555,557],[354,378,552,554,557], [0,354,378,552,555],[354,378,552,555,557],[0,354,381,383,523],[354,381,383,523,697], [354,381,383,557,697],[0,354,381,516,520],[354,381,516,520,694],[0,354,381,516,523], [354,381,516,523,697],[354,381,516,690,694],[354,381,516,690,697],[0,354,381,519,520], [354,381,519,520,694],[0,354,381,519,693],[354,381,519,693,694],[354,381,555,557,697], [354,381,555,690,694],[354,381,555,690,697],[0,354,381,555,693],[354,381,555,693,694], [354,387,388,389,563],[0,354,387,388,702],[354,387,388,389,702],[0,354,387,388,520], [354,387,388,520,694],[354,387,388,562,563],[354,387,388,562,694],[0,354,387,389,523], [354,387,389,523,697],[354,387,389,563,697],[0,354,387,389,703],[354,387,389,702,703], [0,354,387,516,520],[354,387,516,520,694],[0,354,387,516,523],[354,387,516,523,697], [354,387,516,690,694],[354,387,516,690,697],[354,387,561,562,563],[354,387,561,562,694], [354,387,561,563,697],[354,387,561,690,694],[354,387,561,690,697],[0,354,387,702,704], [0,354,387,703,704],[354,387,702,703,704],[354,528,529,530,533],[354,528,529,530,563], [0,354,528,529,532],[354,528,529,532,533],[354,528,529,562,563],[354,528,529,562,694], [0,354,528,529,693],[354,528,529,693,694],[354,528,530,533,554],[354,528,530,554,557], [354,528,530,557,697],[354,528,530,563,697],[0,354,528,531,532],[354,528,531,532,533], [354,528,531,533,554],[0,354,528,531,552],[354,528,531,552,554],[354,528,552,554,557], [0,354,528,552,555],[354,528,552,555,557],[354,528,555,557,697],[354,528,555,690,694], [354,528,555,690,697],[0,354,528,555,693],[354,528,555,693,694],[354,528,561,562,563], [354,528,561,562,694],[354,528,561,563,697],[354,528,561,690,694],[354,528,561,690,697], [1,2,5,41,215],[2,5,41,215,569],[1,2,5,41,395],[2,5,41,395,569], [1,2,5,179,215],[2,5,179,215,569],[2,5,179,533,569],[1,2,5,359,395], [2,5,359,395,569],[2,5,359,533,569],[1,2,35,169,343],[1,2,35,169,523], [1,2,35,209,343],[1,2,35,389,523],[1,2,38,41,215],[2,38,41,215,569], [1,2,38,41,395],[2,38,41,395,569],[1,2,38,172,346],[1,2,38,172,526], [1,2,38,212,215],[2,38,212,215,569],[1,2,38,212,346],[2,38,212,566,569], [1,2,38,392,395],[2,38,392,395,569],[1,2,38,392,526],[2,38,392,566,569], [1,2,168,169,343],[1,2,168,169,523],[1,2,168,172,346],[1,2,168,172,526], [1,2,168,342,343],[1,2,168,342,346],[1,2,168,522,523],[1,2,168,522,526], [1,2,176,179,215],[2,176,179,215,569],[2,176,179,533,569],[1,2,176,209,343], [1,2,176,212,215],[2,176,212,215,569],[1,2,176,212,346],[2,176,212,566,569], [1,2,176,342,343],[1,2,176,342,346],[2,176,530,533,569],[2,176,530,566,569], [1,2,356,359,395],[2,356,359,395,569],[2,356,359,533,569],[1,2,356,389,523], [1,2,356,392,395],[2,356,392,395,569],[1,2,356,392,526],[2,356,392,566,569], [1,2,356,522,523],[1,2,356,522,526],[2,356,530,533,569],[2,356,530,566,569], [1,4,5,41,215],[1,4,5,41,395],[1,4,5,179,215],[1,4,5,359,395], [1,4,39,41,215],[1,4,39,41,395],[1,4,39,213,215],[1,4,39,213,567], [1,4,39,393,395],[1,4,39,393,567],[1,4,178,179,215],[1,4,178,213,215], [1,4,178,213,567],[1,4,178,532,567],[1,4,358,359,395],[1,4,358,393,395], [1,4,358,393,567],[1,4,358,532,567],[1,34,35,169,343],[1,34,35,169,523], [1,34,35,209,343],[1,34,35,389,523],[1,34,163,166,340],[1,34,163,166,520], [1,34,163,169,343],[1,34,163,169,523],[1,34,163,337,340],[1,34,163,337,343], [1,34,163,517,520],[1,34,163,517,523],[1,34,208,209,343],[1,34,208,337,340], [1,34,208,337,343],[1,34,388,389,523],[1,34,388,517,520],[1,34,388,517,523], [1,36,38,41,215],[1,36,38,41,395],[1,36,38,172,346],[1,36,38,172,526], [1,36,38,212,215],[1,36,38,212,346],[1,36,38,392,395],[1,36,38,392,526], 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