#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_008 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(564,8718,29252,35160,14064) ### ### 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:=[ [0,1,2,5,143],[0,1,2,5,276],[1,2,5,276,558],[1,2,5,287,558], [0,1,2,35,173],[0,1,2,35,276],[1,2,35,276,558],[1,2,35,317,558], [0,1,2,140,143],[0,1,2,140,173],[1,2,284,287,558],[1,2,284,317,558], [0,1,4,5,143],[0,1,4,5,276],[0,1,4,276,558],[1,4,5,276,558], [1,4,5,287,558],[0,1,4,142,143],[0,1,4,142,424],[0,1,4,286,558], [1,4,286,287,558],[0,1,4,286,424],[0,1,34,35,173],[0,1,34,35,276], [0,1,34,276,558],[1,34,35,276,558],[1,34,35,317,558],[0,1,34,130,268], [0,1,34,130,412],[0,1,34,172,173],[0,1,34,172,268],[0,1,34,316,558], [1,34,316,317,558],[0,1,34,316,412],[0,1,129,130,268],[0,1,129,130,412], [0,1,129,267,268],[0,1,129,267,549],[0,1,129,411,412],[0,1,129,411,549], [0,1,139,140,143],[0,1,139,140,173],[0,1,139,142,143],[0,1,139,142,424], [0,1,139,172,173],[0,1,139,172,268],[0,1,139,267,268],[0,1,139,267,549], [0,1,139,421,424],[0,1,139,421,549],[1,283,284,287,558],[1,283,284,317,558], [0,1,283,286,558],[1,283,286,287,558],[0,1,283,286,424],[0,1,283,316,558], [1,283,316,317,558],[0,1,283,316,412],[0,1,283,411,412],[0,1,283,411,549], [0,1,283,421,424],[0,1,283,421,549],[0,2,5,26,164],[2,5,26,164,446], [0,2,5,26,308],[2,5,26,308,446],[0,2,5,143,164],[2,5,143,164,446], [2,5,143,425,446],[0,2,5,276,277],[0,2,5,277,559],[2,5,276,277,559], [2,5,276,558,559],[0,2,5,287,308],[2,5,287,308,446],[2,5,287,425,446], [0,2,5,287,559],[2,5,287,558,559],[0,2,26,29,167],[2,26,29,167,449], [0,2,26,29,311],[2,26,29,311,449],[0,2,26,164,167],[2,26,164,167,449], [2,26,164,446,449],[0,2,26,308,311],[2,26,308,311,449],[2,26,308,446,449], [0,2,29,133,271],[0,2,29,133,415],[0,2,29,167,271],[0,2,29,311,415], [0,2,35,133,271],[0,2,35,133,415],[0,2,35,173,271],[0,2,35,276,277], [0,2,35,277,559],[2,35,276,277,559],[2,35,276,558,559],[0,2,35,317,415], [0,2,35,317,559],[2,35,317,558,559],[0,2,140,143,164],[2,140,143,164,446], [2,140,143,425,446],[0,2,140,164,167],[2,140,164,167,449],[2,140,164,446,449], [0,2,140,167,271],[0,2,140,173,271],[2,140,422,425,446],[2,140,422,446,449], [0,2,284,287,308],[2,284,287,308,446],[2,284,287,425,446],[0,2,284,287,559], [2,284,287,558,559],[0,2,284,308,311],[2,284,308,311,449],[2,284,308,446,449], [0,2,284,311,415],[0,2,284,317,415],[0,2,284,317,559],[2,284,317,558,559], [2,284,422,425,446],[2,284,422,446,449],[0,3,4,5,143],[0,3,4,5,276], [0,3,4,276,558],[0,3,4,142,143],[0,3,4,142,424],[0,3,4,286,558], [0,3,4,286,424],[0,3,5,26,164],[0,3,5,26,308],[0,3,5,143,164], [0,3,5,276,277],[0,3,5,277,559],[0,3,5,287,308],[0,3,5,287,559], [0,3,24,26,164],[0,3,24,26,308],[0,3,24,162,164],[0,3,24,162,444], [0,3,24,306,308],[0,3,24,306,444],[0,3,141,142,143],[0,3,141,142,424], [0,3,141,143,164],[0,3,141,162,164],[0,3,141,162,444],[0,3,141,423,424], [0,3,141,423,444],[0,3,276,277,278],[0,3,276,278,560],[0,3,277,278,560], [0,3,277,559,560],[0,3,276,558,560],[0,3,285,286,558],[0,3,285,286,424], [0,3,285,287,308],[0,3,285,287,559],[0,3,285,306,308],[0,3,285,306,444], [0,3,285,423,424],[0,3,285,423,444],[0,3,285,558,560],[0,3,285,559,560], [0,24,26,29,167],[0,24,26,29,311],[0,24,26,164,167],[0,24,26,308,311], [0,24,27,29,167],[0,24,27,29,311],[0,24,27,165,167],[0,24,27,165,447], [0,24,27,309,311],[0,24,27,309,447],[0,24,162,164,167],[0,24,162,165,167], [0,24,162,165,447],[0,24,162,444,447],[0,24,306,308,311],[0,24,306,309,311], [0,24,306,309,447],[0,24,306,444,447],[0,27,29,133,271],[0,27,29,133,415], [0,27,29,167,271],[0,27,29,311,415],[0,27,126,130,268],[0,27,126,130,412], [0,27,126,133,271],[0,27,126,133,415],[0,27,126,264,268],[0,27,126,264,271], [0,27,126,408,412],[0,27,126,408,415],[0,27,129,130,268],[0,27,129,130,412], [0,27,129,267,268],[0,27,129,267,549],[0,27,129,411,412],[0,27,129,411,549], [0,27,165,167,271],[0,27,165,264,268],[0,27,165,264,271],[0,27,165,267,268], [0,27,165,267,549],[0,27,165,447,549],[0,27,309,311,415],[0,27,309,408,412], [0,27,309,408,415],[0,27,309,411,412],[0,27,309,411,549],[0,27,309,447,549], [0,33,34,35,173],[0,33,34,35,276],[0,33,34,276,558],[0,33,34,130,268], [0,33,34,130,412],[0,33,34,172,173],[0,33,34,172,268],[0,33,34,316,558], [0,33,34,316,412],[0,33,35,133,271],[0,33,35,133,415],[0,33,35,173,271], [0,33,35,276,277],[0,33,35,277,559],[0,33,35,317,415],[0,33,35,317,559], [0,33,126,130,268],[0,33,126,130,412],[0,33,126,133,271],[0,33,126,133,415], [0,33,126,264,268],[0,33,126,264,271],[0,33,126,408,412],[0,33,126,408,415], [0,33,171,172,173],[0,33,171,172,268],[0,33,171,173,271],[0,33,171,264,268], [0,33,171,264,271],[0,33,276,277,278],[0,33,276,278,560],[0,33,277,278,560], [0,33,277,559,560],[0,33,276,558,560],[0,33,315,316,558],[0,33,315,316,412], [0,33,315,317,415],[0,33,315,317,559],[0,33,315,408,412],[0,33,315,408,415], [0,33,315,558,560],[0,33,315,559,560],[0,138,139,140,143],[138,139,140,143,425], [0,138,139,140,173],[138,139,140,173,455],[138,139,140,422,425],[138,139,140,422,455], [0,138,139,142,143],[138,139,142,143,425],[0,138,139,142,424],[138,139,142,424,425], [0,138,139,172,173],[138,139,172,173,455],[0,138,139,172,268],[138,139,172,268,550], [138,139,172,454,455],[138,139,172,454,550],[0,138,139,267,268],[138,139,267,268,550], [0,138,139,267,549],[138,139,267,549,550],[138,139,421,422,425],[138,139,421,422,455], [0,138,139,421,424],[138,139,421,424,425],[138,139,421,454,455],[138,139,421,454,550], [0,138,139,421,549],[138,139,421,549,550],[0,138,140,143,164],[138,140,143,164,446], [138,140,143,425,446],[0,138,140,164,167],[138,140,164,167,449],[138,140,164,446,449], [0,138,140,167,271],[138,140,167,271,553],[138,140,167,449,553],[0,138,140,173,271], [138,140,173,271,553],[138,140,173,455,553],[138,140,422,425,446],[138,140,422,446,449], [138,140,422,449,553],[138,140,422,455,553],[0,138,141,142,143],[138,141,142,143,425], [0,138,141,142,424],[138,141,142,424,425],[0,138,141,143,164],[138,141,143,164,446], [138,141,143,425,446],[0,138,141,162,164],[138,141,162,164,446],[0,138,141,162,444], [138,141,162,444,446],[0,138,141,423,424],[138,141,423,424,425],[138,141,423,425,446], [0,138,141,423,444],[138,141,423,444,446],[0,138,162,164,167],[138,162,164,167,449], [138,162,164,446,449],[0,138,162,165,167],[138,162,165,167,449],[0,138,162,165,447], [138,162,165,447,449],[138,162,444,446,449],[0,138,162,444,447],[138,162,444,447,449], [0,138,165,167,271],[138,165,167,271,553],[138,165,167,449,553],[0,138,165,264,268], [138,165,264,268,550],[0,138,165,264,271],[138,165,264,271,553],[138,165,264,546,550], [138,165,264,546,553],[0,138,165,267,268],[138,165,267,268,550],[0,138,165,267,549], [138,165,267,549,550],[138,165,447,449,553],[138,165,447,546,550],[138,165,447,546,553], [0,138,165,447,549],[138,165,447,549,550],[0,138,171,172,173],[138,171,172,173,455], [0,138,171,172,268],[138,171,172,268,550],[138,171,172,454,455],[138,171,172,454,550], [0,138,171,173,271],[138,171,173,271,553],[138,171,173,455,553],[0,138,171,264,268], [138,171,264,268,550],[0,138,171,264,271],[138,171,264,271,553],[138,171,264,546,550], [138,171,264,546,553],[138,171,453,454,455],[138,171,453,454,550],[138,171,453,455,553], [138,171,453,546,550],[138,171,453,546,553],[138,420,421,422,425],[138,420,421,422,455], [0,138,420,421,424],[138,420,421,424,425],[138,420,421,454,455],[138,420,421,454,550], [0,138,420,421,549],[138,420,421,549,550],[138,420,422,425,446],[138,420,422,446,449], [138,420,422,449,553],[138,420,422,455,553],[0,138,420,423,424],[138,420,423,424,425], [138,420,423,425,446],[0,138,420,423,444],[138,420,423,444,446],[138,420,444,446,449], [0,138,420,444,447],[138,420,444,447,449],[138,420,447,449,553],[138,420,447,546,550], [138,420,447,546,553],[0,138,420,447,549],[138,420,447,549,550],[138,420,453,454,455], [138,420,453,454,550],[138,420,453,455,553],[138,420,453,546,550],[138,420,453,546,553], [282,283,284,287,425],[282,283,284,287,558],[282,283,284,317,455],[282,283,284,317,558], [282,283,284,422,425],[282,283,284,422,455],[282,283,286,287,425],[0,282,283,286,558], [282,283,286,287,558],[0,282,283,286,424],[282,283,286,424,425],[282,283,316,317,455], [0,282,283,316,558],[282,283,316,317,558],[0,282,283,316,412],[282,283,316,412,550], [282,283,316,454,455],[282,283,316,454,550],[0,282,283,411,412],[282,283,411,412,550], [0,282,283,411,549],[282,283,411,549,550],[282,283,421,422,425],[282,283,421,422,455], [0,282,283,421,424],[282,283,421,424,425],[282,283,421,454,455],[282,283,421,454,550], [0,282,283,421,549],[282,283,421,549,550],[0,282,284,287,308],[282,284,287,308,446], [282,284,287,425,446],[0,282,284,287,559],[282,284,287,558,559],[0,282,284,308,311], [282,284,308,311,449],[282,284,308,446,449],[0,282,284,311,415],[282,284,311,415,553], [282,284,311,449,553],[0,282,284,317,415],[282,284,317,415,553],[282,284,317,455,553], [0,282,284,317,559],[282,284,317,558,559],[282,284,422,425,446],[282,284,422,446,449], [282,284,422,449,553],[282,284,422,455,553],[282,285,286,287,425],[0,282,285,286,558], [282,285,286,287,558],[0,282,285,286,424],[282,285,286,424,425],[0,282,285,287,308], [282,285,287,308,446],[282,285,287,425,446],[0,282,285,287,559],[282,285,287,558,559], [0,282,285,306,308],[282,285,306,308,446],[0,282,285,306,444],[282,285,306,444,446], [0,282,285,423,424],[282,285,423,424,425],[282,285,423,425,446],[0,282,285,423,444], [282,285,423,444,446],[0,282,285,558,560],[0,282,285,559,560],[282,285,558,559,560], [0,282,306,308,311],[282,306,308,311,449],[282,306,308,446,449],[0,282,306,309,311], [282,306,309,311,449],[0,282,306,309,447],[282,306,309,447,449],[282,306,444,446,449], [0,282,306,444,447],[282,306,444,447,449],[0,282,309,311,415],[282,309,311,415,553], [282,309,311,449,553],[0,282,309,408,412],[282,309,408,412,550],[0,282,309,408,415], [282,309,408,415,553],[282,309,408,546,550],[282,309,408,546,553],[0,282,309,411,412], [282,309,411,412,550],[0,282,309,411,549],[282,309,411,549,550],[282,309,447,449,553], [282,309,447,546,550],[282,309,447,546,553],[0,282,309,447,549],[282,309,447,549,550], [282,315,316,317,455],[0,282,315,316,558],[282,315,316,317,558],[0,282,315,316,412], [282,315,316,412,550],[282,315,316,454,455],[282,315,316,454,550],[0,282,315,317,415], [282,315,317,415,553],[282,315,317,455,553],[0,282,315,317,559],[282,315,317,558,559], [0,282,315,408,412],[282,315,408,412,550],[0,282,315,408,415],[282,315,408,415,553], [282,315,408,546,550],[282,315,408,546,553],[282,315,453,454,455],[282,315,453,454,550], [282,315,453,455,553],[282,315,453,546,550],[282,315,453,546,553],[0,282,315,558,560], [0,282,315,559,560],[282,315,558,559,560],[282,420,421,422,425],[282,420,421,422,455], [0,282,420,421,424],[282,420,421,424,425],[282,420,421,454,455],[282,420,421,454,550], [0,282,420,421,549],[282,420,421,549,550],[282,420,422,425,446],[282,420,422,446,449], [282,420,422,449,553],[282,420,422,455,553],[0,282,420,423,424],[282,420,423,424,425], [282,420,423,425,446],[0,282,420,423,444],[282,420,423,444,446],[282,420,444,446,449], [0,282,420,444,447],[282,420,444,447,449],[282,420,447,449,553],[282,420,447,546,550], [282,420,447,546,553],[0,282,420,447,549],[282,420,447,549,550],[282,420,453,454,455], [282,420,453,454,550],[282,420,453,455,553],[282,420,453,546,550],[282,420,453,546,553], [1,2,5,41,179],[2,5,41,179,461],[1,2,5,41,323],[2,5,41,323,461], [1,2,5,143,179],[2,5,143,179,461],[2,5,143,425,461],[1,2,5,287,323], [2,5,287,323,461],[2,5,287,425,461],[1,2,35,133,271],[1,2,35,133,415], [1,2,35,173,271],[1,2,35,317,415],[1,2,38,41,179],[2,38,41,179,461], [1,2,38,41,323],[2,38,41,323,461],[1,2,38,136,274],[1,2,38,136,418], [1,2,38,176,179],[2,38,176,179,461],[1,2,38,176,274],[2,38,176,458,461], [1,2,38,320,323],[2,38,320,323,461],[1,2,38,320,418],[2,38,320,458,461], [1,2,132,133,271],[1,2,132,133,415],[1,2,132,136,274],[1,2,132,136,418], [1,2,132,270,271],[1,2,132,270,274],[1,2,132,414,415],[1,2,132,414,418], [1,2,140,143,179],[2,140,143,179,461],[2,140,143,425,461],[1,2,140,173,271], [1,2,140,176,179],[2,140,176,179,461],[1,2,140,176,274],[2,140,176,458,461], [1,2,140,270,271],[1,2,140,270,274],[2,140,422,425,461],[2,140,422,458,461], [1,2,284,287,323],[2,284,287,323,461],[2,284,287,425,461],[1,2,284,317,415], [1,2,284,320,323],[2,284,320,323,461],[1,2,284,320,418],[2,284,320,458,461], [1,2,284,414,415],[1,2,284,414,418],[2,284,422,425,461],[2,284,422,458,461], [1,4,5,41,179],[1,4,5,41,323],[1,4,5,143,179],[1,4,5,287,323], [1,4,39,41,179],[1,4,39,41,323],[1,4,39,177,179],[1,4,39,177,459], [1,4,39,321,323],[1,4,39,321,459],[1,4,142,143,179],[1,4,142,177,179], [1,4,142,177,459],[1,4,142,424,459],[1,4,286,287,323],[1,4,286,321,323], [1,4,286,321,459],[1,4,286,424,459],[1,34,35,133,271],[1,34,35,133,415], [1,34,35,173,271],[1,34,35,317,415],[1,34,127,130,268],[1,34,127,130,412], [1,34,127,133,271],[1,34,127,133,415],[1,34,127,265,268],[1,34,127,265,271], [1,34,127,409,412],[1,34,127,409,415],[1,34,172,173,271],[1,34,172,265,268], [1,34,172,265,271],[1,34,316,317,415],[1,34,316,409,412],[1,34,316,409,415], [1,36,38,41,179],[1,36,38,41,323],[1,36,38,136,274],[1,36,38,136,418], [1,36,38,176,179],[1,36,38,176,274],[1,36,38,320,323],[1,36,38,320,418], [1,36,39,41,179],[1,36,39,41,323],[1,36,39,177,179],[1,36,39,177,459], [1,36,39,321,323],[1,36,39,321,459],[1,36,127,130,268],[1,36,127,130,412], [1,36,127,133,271],[1,36,127,133,415],[1,36,127,265,268],[1,36,127,265,271], [1,36,127,409,412],[1,36,127,409,415],[1,36,129,130,268],[1,36,129,130,412], [1,36,129,267,268],[1,36,129,267,549],[1,36,129,411,412],[1,36,129,411,549], [1,36,132,133,271],[1,36,132,133,415],[1,36,132,136,274],[1,36,132,136,418], [1,36,132,270,271],[1,36,132,270,274],[1,36,132,414,415],[1,36,132,414,418], [1,36,174,176,179],[1,36,174,176,274],[1,36,174,177,179],[1,36,174,177,459], [1,36,174,265,268],[1,36,174,265,271],[1,36,174,267,268],[1,36,174,267,549], [1,36,174,270,271],[1,36,174,270,274],[1,36,174,456,459],[1,36,174,456,549], [1,36,318,320,323],[1,36,318,320,418],[1,36,318,321,323],[1,36,318,321,459], [1,36,318,409,412],[1,36,318,409,415],[1,36,318,411,412],[1,36,318,411,549], [1,36,318,414,415],[1,36,318,414,418],[1,36,318,456,459],[1,36,318,456,549], [1,139,140,143,179],[139,140,143,179,461],[139,140,143,425,461],[1,139,140,173,271], [139,140,173,271,553],[139,140,173,455,553],[1,139,140,176,179],[139,140,176,179,461], [1,139,140,176,274],[139,140,176,274,556],[139,140,176,458,461],[139,140,176,458,556], [1,139,140,270,271],[139,140,270,271,553],[1,139,140,270,274],[139,140,270,274,556], [139,140,270,552,553],[139,140,270,552,556],[139,140,422,425,461],[139,140,422,455,553], [139,140,422,458,461],[139,140,422,458,556],[139,140,422,552,553],[139,140,422,552,556], [1,139,142,143,179],[139,142,143,179,461],[139,142,143,425,461],[1,139,142,177,179], [139,142,177,179,461],[1,139,142,177,459],[139,142,177,459,461],[139,142,424,425,461], [1,139,142,424,459],[139,142,424,459,461],[1,139,172,173,271],[139,172,173,271,553], [139,172,173,455,553],[1,139,172,265,268],[139,172,265,268,550],[1,139,172,265,271], [139,172,265,271,553],[139,172,265,547,550],[139,172,265,547,553],[139,172,454,455,553], 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