#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_016 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(948,14670,49220,59160,23664) ### ### 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:=[ [0,1,2,5,239],[0,1,2,5,468],[1,2,5,468,942],[1,2,5,479,942], [0,1,2,35,269],[0,1,2,35,468],[1,2,35,468,942],[1,2,35,509,942], [0,1,2,236,239],[0,1,2,236,269],[1,2,476,479,942],[1,2,476,509,942], [0,1,4,5,239],[0,1,4,5,468],[0,1,4,468,942],[1,4,5,468,942], [1,4,5,479,942],[0,1,4,238,239],[0,1,4,238,712],[0,1,4,478,942], [1,4,478,479,942],[0,1,4,478,712],[0,1,34,35,269],[0,1,34,35,468], [0,1,34,468,942],[1,34,35,468,942],[1,34,35,509,942],[0,1,34,226,460], [0,1,34,226,700],[0,1,34,268,269],[0,1,34,268,460],[0,1,34,508,942], [1,34,508,509,942],[0,1,34,508,700],[0,1,225,226,460],[0,1,225,226,700], [0,1,225,459,460],[0,1,225,459,933],[0,1,225,699,700],[0,1,225,699,933], [0,1,235,236,239],[0,1,235,236,269],[0,1,235,238,239],[0,1,235,238,712], [0,1,235,268,269],[0,1,235,268,460],[0,1,235,459,460],[0,1,235,459,933], [0,1,235,709,712],[0,1,235,709,933],[1,475,476,479,942],[1,475,476,509,942], [0,1,475,478,942],[1,475,478,479,942],[0,1,475,478,712],[0,1,475,508,942], [1,475,508,509,942],[0,1,475,508,700],[0,1,475,699,700],[0,1,475,699,933], [0,1,475,709,712],[0,1,475,709,933],[0,2,5,26,260],[2,5,26,260,734], [0,2,5,26,500],[2,5,26,500,734],[0,2,5,239,260],[2,5,239,260,734], [2,5,239,713,734],[0,2,5,468,469],[0,2,5,469,943],[2,5,468,469,943], [2,5,468,942,943],[0,2,5,479,500],[2,5,479,500,734],[2,5,479,713,734], [0,2,5,479,943],[2,5,479,942,943],[0,2,26,29,263],[2,26,29,263,737], [0,2,26,29,503],[2,26,29,503,737],[0,2,26,260,263],[2,26,260,263,737], [2,26,260,734,737],[0,2,26,500,503],[2,26,500,503,737],[2,26,500,734,737], [0,2,29,229,463],[0,2,29,229,703],[0,2,29,263,463],[0,2,29,503,703], [0,2,35,229,463],[0,2,35,229,703],[0,2,35,269,463],[0,2,35,468,469], [0,2,35,469,943],[2,35,468,469,943],[2,35,468,942,943],[0,2,35,509,703], [0,2,35,509,943],[2,35,509,942,943],[0,2,236,239,260],[2,236,239,260,734], [2,236,239,713,734],[0,2,236,260,263],[2,236,260,263,737],[2,236,260,734,737], [0,2,236,263,463],[0,2,236,269,463],[2,236,710,713,734],[2,236,710,734,737], [0,2,476,479,500],[2,476,479,500,734],[2,476,479,713,734],[0,2,476,479,943], [2,476,479,942,943],[0,2,476,500,503],[2,476,500,503,737],[2,476,500,734,737], [0,2,476,503,703],[0,2,476,509,703],[0,2,476,509,943],[2,476,509,942,943], [2,476,710,713,734],[2,476,710,734,737],[0,3,4,5,239],[0,3,4,5,468], [0,3,4,468,942],[0,3,4,238,239],[0,3,4,238,712],[0,3,4,478,942], [0,3,4,478,712],[0,3,5,26,260],[0,3,5,26,500],[0,3,5,239,260], [0,3,5,468,469],[0,3,5,469,943],[0,3,5,479,500],[0,3,5,479,943], [0,3,24,26,260],[0,3,24,26,500],[0,3,24,258,260],[0,3,24,258,732], [0,3,24,498,500],[0,3,24,498,732],[0,3,237,238,239],[0,3,237,238,712], [0,3,237,239,260],[0,3,237,258,260],[0,3,237,258,732],[0,3,237,711,712], [0,3,237,711,732],[0,3,468,469,470],[0,3,468,470,944],[0,3,469,470,944], [0,3,469,943,944],[0,3,468,942,944],[0,3,477,478,942],[0,3,477,478,712], [0,3,477,479,500],[0,3,477,479,943],[0,3,477,498,500],[0,3,477,498,732], [0,3,477,711,712],[0,3,477,711,732],[0,3,477,942,944],[0,3,477,943,944], [0,24,26,29,263],[0,24,26,29,503],[0,24,26,260,263],[0,24,26,500,503], [0,24,27,29,263],[0,24,27,29,503],[0,24,27,261,263],[0,24,27,261,735], [0,24,27,501,503],[0,24,27,501,735],[0,24,258,260,263],[0,24,258,261,263], [0,24,258,261,735],[0,24,258,732,735],[0,24,498,500,503],[0,24,498,501,503], [0,24,498,501,735],[0,24,498,732,735],[0,27,29,229,463],[0,27,29,229,703], [0,27,29,263,463],[0,27,29,503,703],[0,27,222,226,460],[0,27,222,226,700], [0,27,222,229,463],[0,27,222,229,703],[0,27,222,456,460],[0,27,222,456,463], [0,27,222,696,700],[0,27,222,696,703],[0,27,225,226,460],[0,27,225,226,700], [0,27,225,459,460],[0,27,225,459,933],[0,27,225,699,700],[0,27,225,699,933], [0,27,261,263,463],[0,27,261,456,460],[0,27,261,456,463],[0,27,261,459,460], [0,27,261,459,933],[0,27,261,735,933],[0,27,501,503,703],[0,27,501,696,700], [0,27,501,696,703],[0,27,501,699,700],[0,27,501,699,933],[0,27,501,735,933], [0,33,34,35,269],[0,33,34,35,468],[0,33,34,468,942],[0,33,34,226,460], [0,33,34,226,700],[0,33,34,268,269],[0,33,34,268,460],[0,33,34,508,942], [0,33,34,508,700],[0,33,35,229,463],[0,33,35,229,703],[0,33,35,269,463], [0,33,35,468,469],[0,33,35,469,943],[0,33,35,509,703],[0,33,35,509,943], [0,33,222,226,460],[0,33,222,226,700],[0,33,222,229,463],[0,33,222,229,703], [0,33,222,456,460],[0,33,222,456,463],[0,33,222,696,700],[0,33,222,696,703], [0,33,267,268,269],[0,33,267,268,460],[0,33,267,269,463],[0,33,267,456,460], [0,33,267,456,463],[0,33,468,469,470],[0,33,468,470,944],[0,33,469,470,944], [0,33,469,943,944],[0,33,468,942,944],[0,33,507,508,942],[0,33,507,508,700], [0,33,507,509,703],[0,33,507,509,943],[0,33,507,696,700],[0,33,507,696,703], [0,33,507,942,944],[0,33,507,943,944],[0,234,235,236,239],[234,235,236,239,713], [0,234,235,236,269],[234,235,236,269,743],[234,235,236,710,713],[234,235,236,710,743], [0,234,235,238,239],[234,235,238,239,713],[0,234,235,238,712],[234,235,238,712,713], [0,234,235,268,269],[234,235,268,269,743],[0,234,235,268,460],[234,235,268,460,934], [234,235,268,742,743],[234,235,268,742,934],[0,234,235,459,460],[234,235,459,460,934], [0,234,235,459,933],[234,235,459,933,934],[234,235,709,710,713],[234,235,709,710,743], [0,234,235,709,712],[234,235,709,712,713],[234,235,709,742,743],[234,235,709,742,934], [0,234,235,709,933],[234,235,709,933,934],[0,234,236,239,260],[234,236,239,260,734], [234,236,239,713,734],[0,234,236,260,263],[234,236,260,263,737],[234,236,260,734,737], [0,234,236,263,463],[234,236,263,463,937],[234,236,263,737,937],[0,234,236,269,463], [234,236,269,463,937],[234,236,269,743,937],[234,236,710,713,734],[234,236,710,734,737], [234,236,710,737,937],[234,236,710,743,937],[0,234,237,238,239],[234,237,238,239,713], [0,234,237,238,712],[234,237,238,712,713],[0,234,237,239,260],[234,237,239,260,734], [234,237,239,713,734],[0,234,237,258,260],[234,237,258,260,734],[0,234,237,258,732], [234,237,258,732,734],[0,234,237,711,712],[234,237,711,712,713],[234,237,711,713,734], [0,234,237,711,732],[234,237,711,732,734],[0,234,258,260,263],[234,258,260,263,737], [234,258,260,734,737],[0,234,258,261,263],[234,258,261,263,737],[0,234,258,261,735], [234,258,261,735,737],[234,258,732,734,737],[0,234,258,732,735],[234,258,732,735,737], [0,234,261,263,463],[234,261,263,463,937],[234,261,263,737,937],[0,234,261,456,460], [234,261,456,460,934],[0,234,261,456,463],[234,261,456,463,937],[234,261,456,930,934], [234,261,456,930,937],[0,234,261,459,460],[234,261,459,460,934],[0,234,261,459,933], [234,261,459,933,934],[234,261,735,737,937],[234,261,735,930,934],[234,261,735,930,937], [0,234,261,735,933],[234,261,735,933,934],[0,234,267,268,269],[234,267,268,269,743], [0,234,267,268,460],[234,267,268,460,934],[234,267,268,742,743],[234,267,268,742,934], [0,234,267,269,463],[234,267,269,463,937],[234,267,269,743,937],[0,234,267,456,460], [234,267,456,460,934],[0,234,267,456,463],[234,267,456,463,937],[234,267,456,930,934], [234,267,456,930,937],[234,267,741,742,743],[234,267,741,742,934],[234,267,741,743,937], [234,267,741,930,934],[234,267,741,930,937],[234,708,709,710,713],[234,708,709,710,743], [0,234,708,709,712],[234,708,709,712,713],[234,708,709,742,743],[234,708,709,742,934], [0,234,708,709,933],[234,708,709,933,934],[234,708,710,713,734],[234,708,710,734,737], [234,708,710,737,937],[234,708,710,743,937],[0,234,708,711,712],[234,708,711,712,713], [234,708,711,713,734],[0,234,708,711,732],[234,708,711,732,734],[234,708,732,734,737], [0,234,708,732,735],[234,708,732,735,737],[234,708,735,737,937],[234,708,735,930,934], [234,708,735,930,937],[0,234,708,735,933],[234,708,735,933,934],[234,708,741,742,743], [234,708,741,742,934],[234,708,741,743,937],[234,708,741,930,934],[234,708,741,930,937], [474,475,476,479,713],[474,475,476,479,942],[474,475,476,509,743],[474,475,476,509,942], [474,475,476,710,713],[474,475,476,710,743],[474,475,478,479,713],[0,474,475,478,942], [474,475,478,479,942],[0,474,475,478,712],[474,475,478,712,713],[474,475,508,509,743], [0,474,475,508,942],[474,475,508,509,942],[0,474,475,508,700],[474,475,508,700,934], [474,475,508,742,743],[474,475,508,742,934],[0,474,475,699,700],[474,475,699,700,934], [0,474,475,699,933],[474,475,699,933,934],[474,475,709,710,713],[474,475,709,710,743], [0,474,475,709,712],[474,475,709,712,713],[474,475,709,742,743],[474,475,709,742,934], [0,474,475,709,933],[474,475,709,933,934],[0,474,476,479,500],[474,476,479,500,734], [474,476,479,713,734],[0,474,476,479,943],[474,476,479,942,943],[0,474,476,500,503], [474,476,500,503,737],[474,476,500,734,737],[0,474,476,503,703],[474,476,503,703,937], [474,476,503,737,937],[0,474,476,509,703],[474,476,509,703,937],[474,476,509,743,937], [0,474,476,509,943],[474,476,509,942,943],[474,476,710,713,734],[474,476,710,734,737], [474,476,710,737,937],[474,476,710,743,937],[474,477,478,479,713],[0,474,477,478,942], [474,477,478,479,942],[0,474,477,478,712],[474,477,478,712,713],[0,474,477,479,500], [474,477,479,500,734],[474,477,479,713,734],[0,474,477,479,943],[474,477,479,942,943], [0,474,477,498,500],[474,477,498,500,734],[0,474,477,498,732],[474,477,498,732,734], [0,474,477,711,712],[474,477,711,712,713],[474,477,711,713,734],[0,474,477,711,732], [474,477,711,732,734],[0,474,477,942,944],[0,474,477,943,944],[474,477,942,943,944], [0,474,498,500,503],[474,498,500,503,737],[474,498,500,734,737],[0,474,498,501,503], [474,498,501,503,737],[0,474,498,501,735],[474,498,501,735,737],[474,498,732,734,737], [0,474,498,732,735],[474,498,732,735,737],[0,474,501,503,703],[474,501,503,703,937], [474,501,503,737,937],[0,474,501,696,700],[474,501,696,700,934],[0,474,501,696,703], [474,501,696,703,937],[474,501,696,930,934],[474,501,696,930,937],[0,474,501,699,700], [474,501,699,700,934],[0,474,501,699,933],[474,501,699,933,934],[474,501,735,737,937], [474,501,735,930,934],[474,501,735,930,937],[0,474,501,735,933],[474,501,735,933,934], [474,507,508,509,743],[0,474,507,508,942],[474,507,508,509,942],[0,474,507,508,700], [474,507,508,700,934],[474,507,508,742,743],[474,507,508,742,934],[0,474,507,509,703], [474,507,509,703,937],[474,507,509,743,937],[0,474,507,509,943],[474,507,509,942,943], [0,474,507,696,700],[474,507,696,700,934],[0,474,507,696,703],[474,507,696,703,937], [474,507,696,930,934],[474,507,696,930,937],[474,507,741,742,743],[474,507,741,742,934], [474,507,741,743,937],[474,507,741,930,934],[474,507,741,930,937],[0,474,507,942,944], [0,474,507,943,944],[474,507,942,943,944],[474,708,709,710,713],[474,708,709,710,743], [0,474,708,709,712],[474,708,709,712,713],[474,708,709,742,743],[474,708,709,742,934], [0,474,708,709,933],[474,708,709,933,934],[474,708,710,713,734],[474,708,710,734,737], [474,708,710,737,937],[474,708,710,743,937],[0,474,708,711,712],[474,708,711,712,713], [474,708,711,713,734],[0,474,708,711,732],[474,708,711,732,734],[474,708,732,734,737], [0,474,708,732,735],[474,708,732,735,737],[474,708,735,737,937],[474,708,735,930,934], [474,708,735,930,937],[0,474,708,735,933],[474,708,735,933,934],[474,708,741,742,743], [474,708,741,742,934],[474,708,741,743,937],[474,708,741,930,934],[474,708,741,930,937], [1,2,5,41,275],[2,5,41,275,749],[1,2,5,41,515],[2,5,41,515,749], [1,2,5,239,275],[2,5,239,275,749],[2,5,239,713,749],[1,2,5,479,515], [2,5,479,515,749],[2,5,479,713,749],[1,2,35,229,463],[1,2,35,229,703], [1,2,35,269,463],[1,2,35,509,703],[1,2,38,41,275],[2,38,41,275,749], [1,2,38,41,515],[2,38,41,515,749],[1,2,38,232,466],[1,2,38,232,706], [1,2,38,272,275],[2,38,272,275,749],[1,2,38,272,466],[2,38,272,746,749], [1,2,38,512,515],[2,38,512,515,749],[1,2,38,512,706],[2,38,512,746,749], [1,2,228,229,463],[1,2,228,229,703],[1,2,228,232,466],[1,2,228,232,706], [1,2,228,462,463],[1,2,228,462,466],[1,2,228,702,703],[1,2,228,702,706], [1,2,236,239,275],[2,236,239,275,749],[2,236,239,713,749],[1,2,236,269,463], [1,2,236,272,275],[2,236,272,275,749],[1,2,236,272,466],[2,236,272,746,749], [1,2,236,462,463],[1,2,236,462,466],[2,236,710,713,749],[2,236,710,746,749], [1,2,476,479,515],[2,476,479,515,749],[2,476,479,713,749],[1,2,476,509,703], [1,2,476,512,515],[2,476,512,515,749],[1,2,476,512,706],[2,476,512,746,749], [1,2,476,702,703],[1,2,476,702,706],[2,476,710,713,749],[2,476,710,746,749], [1,4,5,41,275],[1,4,5,41,515],[1,4,5,239,275],[1,4,5,479,515], [1,4,39,41,275],[1,4,39,41,515],[1,4,39,273,275],[1,4,39,273,747], [1,4,39,513,515],[1,4,39,513,747],[1,4,238,239,275],[1,4,238,273,275], [1,4,238,273,747],[1,4,238,712,747],[1,4,478,479,515],[1,4,478,513,515], [1,4,478,513,747],[1,4,478,712,747],[1,34,35,229,463],[1,34,35,229,703], [1,34,35,269,463],[1,34,35,509,703],[1,34,223,226,460],[1,34,223,226,700], [1,34,223,229,463],[1,34,223,229,703],[1,34,223,457,460],[1,34,223,457,463], [1,34,223,697,700],[1,34,223,697,703],[1,34,268,269,463],[1,34,268,457,460], [1,34,268,457,463],[1,34,508,509,703],[1,34,508,697,700],[1,34,508,697,703], [1,36,38,41,275],[1,36,38,41,515],[1,36,38,232,466],[1,36,38,232,706], [1,36,38,272,275],[1,36,38,272,466],[1,36,38,512,515],[1,36,38,512,706], 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