#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_003 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(324,4998,16772,20160,8064) ### ### 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:=[ [0,1,2,5,83],[0,1,2,5,156],[1,2,5,156,318],[1,2,5,167,318], [0,1,2,35,113],[0,1,2,35,156],[1,2,35,156,318],[1,2,35,197,318], [0,1,2,80,83],[0,1,2,80,113],[1,2,164,167,318],[1,2,164,197,318], [0,1,4,5,83],[0,1,4,5,156],[0,1,4,156,318],[1,4,5,156,318], [1,4,5,167,318],[0,1,4,82,83],[0,1,4,82,244],[0,1,4,166,318], [1,4,166,167,318],[0,1,4,166,244],[0,1,34,35,113],[0,1,34,35,156], [0,1,34,156,318],[1,34,35,156,318],[1,34,35,197,318],[0,1,34,70,148], [0,1,34,70,232],[0,1,34,112,113],[0,1,34,112,148],[0,1,34,196,318], [1,34,196,197,318],[0,1,34,196,232],[0,1,69,70,148],[0,1,69,70,232], [0,1,69,147,148],[0,1,69,147,309],[0,1,69,231,232],[0,1,69,231,309], [0,1,79,80,83],[0,1,79,80,113],[0,1,79,82,83],[0,1,79,82,244], [0,1,79,112,113],[0,1,79,112,148],[0,1,79,147,148],[0,1,79,147,309], [0,1,79,241,244],[0,1,79,241,309],[1,163,164,167,318],[1,163,164,197,318], [0,1,163,166,318],[1,163,166,167,318],[0,1,163,166,244],[0,1,163,196,318], [1,163,196,197,318],[0,1,163,196,232],[0,1,163,231,232],[0,1,163,231,309], [0,1,163,241,244],[0,1,163,241,309],[0,2,5,26,104],[2,5,26,104,266], [0,2,5,26,188],[2,5,26,188,266],[0,2,5,83,104],[2,5,83,104,266], [2,5,83,245,266],[0,2,5,156,157],[0,2,5,157,319],[2,5,156,157,319], [2,5,156,318,319],[0,2,5,167,188],[2,5,167,188,266],[2,5,167,245,266], [0,2,5,167,319],[2,5,167,318,319],[0,2,26,29,107],[2,26,29,107,269], [0,2,26,29,191],[2,26,29,191,269],[0,2,26,104,107],[2,26,104,107,269], [2,26,104,266,269],[0,2,26,188,191],[2,26,188,191,269],[2,26,188,266,269], [0,2,29,73,151],[0,2,29,73,235],[0,2,29,107,151],[0,2,29,191,235], [0,2,35,73,151],[0,2,35,73,235],[0,2,35,113,151],[0,2,35,156,157], [0,2,35,157,319],[2,35,156,157,319],[2,35,156,318,319],[0,2,35,197,235], [0,2,35,197,319],[2,35,197,318,319],[0,2,80,83,104],[2,80,83,104,266], [2,80,83,245,266],[0,2,80,104,107],[2,80,104,107,269],[2,80,104,266,269], [0,2,80,107,151],[0,2,80,113,151],[2,80,242,245,266],[2,80,242,266,269], [0,2,164,167,188],[2,164,167,188,266],[2,164,167,245,266],[0,2,164,167,319], [2,164,167,318,319],[0,2,164,188,191],[2,164,188,191,269],[2,164,188,266,269], [0,2,164,191,235],[0,2,164,197,235],[0,2,164,197,319],[2,164,197,318,319], [2,164,242,245,266],[2,164,242,266,269],[0,3,4,5,83],[0,3,4,5,156], [0,3,4,156,318],[0,3,4,82,83],[0,3,4,82,244],[0,3,4,166,318], [0,3,4,166,244],[0,3,5,26,104],[0,3,5,26,188],[0,3,5,83,104], [0,3,5,156,157],[0,3,5,157,319],[0,3,5,167,188],[0,3,5,167,319], [0,3,24,26,104],[0,3,24,26,188],[0,3,24,102,104],[0,3,24,102,264], [0,3,24,186,188],[0,3,24,186,264],[0,3,81,82,83],[0,3,81,82,244], [0,3,81,83,104],[0,3,81,102,104],[0,3,81,102,264],[0,3,81,243,244], [0,3,81,243,264],[0,3,156,157,158],[0,3,156,158,320],[0,3,157,158,320], [0,3,157,319,320],[0,3,156,318,320],[0,3,165,166,318],[0,3,165,166,244], [0,3,165,167,188],[0,3,165,167,319],[0,3,165,186,188],[0,3,165,186,264], [0,3,165,243,244],[0,3,165,243,264],[0,3,165,318,320],[0,3,165,319,320], [0,24,26,29,107],[0,24,26,29,191],[0,24,26,104,107],[0,24,26,188,191], [0,24,27,29,107],[0,24,27,29,191],[0,24,27,105,107],[0,24,27,105,267], [0,24,27,189,191],[0,24,27,189,267],[0,24,102,104,107],[0,24,102,105,107], [0,24,102,105,267],[0,24,102,264,267],[0,24,186,188,191],[0,24,186,189,191], [0,24,186,189,267],[0,24,186,264,267],[0,27,29,73,151],[0,27,29,73,235], [0,27,29,107,151],[0,27,29,191,235],[0,27,66,70,148],[0,27,66,70,232], [0,27,66,73,151],[0,27,66,73,235],[0,27,66,144,148],[0,27,66,144,151], [0,27,66,228,232],[0,27,66,228,235],[0,27,69,70,148],[0,27,69,70,232], [0,27,69,147,148],[0,27,69,147,309],[0,27,69,231,232],[0,27,69,231,309], [0,27,105,107,151],[0,27,105,144,148],[0,27,105,144,151],[0,27,105,147,148], [0,27,105,147,309],[0,27,105,267,309],[0,27,189,191,235],[0,27,189,228,232], [0,27,189,228,235],[0,27,189,231,232],[0,27,189,231,309],[0,27,189,267,309], [0,33,34,35,113],[0,33,34,35,156],[0,33,34,156,318],[0,33,34,70,148], [0,33,34,70,232],[0,33,34,112,113],[0,33,34,112,148],[0,33,34,196,318], [0,33,34,196,232],[0,33,35,73,151],[0,33,35,73,235],[0,33,35,113,151], [0,33,35,156,157],[0,33,35,157,319],[0,33,35,197,235],[0,33,35,197,319], [0,33,66,70,148],[0,33,66,70,232],[0,33,66,73,151],[0,33,66,73,235], [0,33,66,144,148],[0,33,66,144,151],[0,33,66,228,232],[0,33,66,228,235], [0,33,111,112,113],[0,33,111,112,148],[0,33,111,113,151],[0,33,111,144,148], [0,33,111,144,151],[0,33,156,157,158],[0,33,156,158,320],[0,33,157,158,320], [0,33,157,319,320],[0,33,156,318,320],[0,33,195,196,318],[0,33,195,196,232], [0,33,195,197,235],[0,33,195,197,319],[0,33,195,228,232],[0,33,195,228,235], [0,33,195,318,320],[0,33,195,319,320],[0,78,79,80,83],[78,79,80,83,245], [0,78,79,80,113],[78,79,80,113,275],[78,79,80,242,245],[78,79,80,242,275], [0,78,79,82,83],[78,79,82,83,245],[0,78,79,82,244],[78,79,82,244,245], [0,78,79,112,113],[78,79,112,113,275],[0,78,79,112,148],[78,79,112,148,310], [78,79,112,274,275],[78,79,112,274,310],[0,78,79,147,148],[78,79,147,148,310], [0,78,79,147,309],[78,79,147,309,310],[78,79,241,242,245],[78,79,241,242,275], [0,78,79,241,244],[78,79,241,244,245],[78,79,241,274,275],[78,79,241,274,310], [0,78,79,241,309],[78,79,241,309,310],[0,78,80,83,104],[78,80,83,104,266], [78,80,83,245,266],[0,78,80,104,107],[78,80,104,107,269],[78,80,104,266,269], [0,78,80,107,151],[78,80,107,151,313],[78,80,107,269,313],[0,78,80,113,151], [78,80,113,151,313],[78,80,113,275,313],[78,80,242,245,266],[78,80,242,266,269], [78,80,242,269,313],[78,80,242,275,313],[0,78,81,82,83],[78,81,82,83,245], [0,78,81,82,244],[78,81,82,244,245],[0,78,81,83,104],[78,81,83,104,266], [78,81,83,245,266],[0,78,81,102,104],[78,81,102,104,266],[0,78,81,102,264], [78,81,102,264,266],[0,78,81,243,244],[78,81,243,244,245],[78,81,243,245,266], [0,78,81,243,264],[78,81,243,264,266],[0,78,102,104,107],[78,102,104,107,269], [78,102,104,266,269],[0,78,102,105,107],[78,102,105,107,269],[0,78,102,105,267], [78,102,105,267,269],[78,102,264,266,269],[0,78,102,264,267],[78,102,264,267,269], [0,78,105,107,151],[78,105,107,151,313],[78,105,107,269,313],[0,78,105,144,148], [78,105,144,148,310],[0,78,105,144,151],[78,105,144,151,313],[78,105,144,306,310], [78,105,144,306,313],[0,78,105,147,148],[78,105,147,148,310],[0,78,105,147,309], [78,105,147,309,310],[78,105,267,269,313],[78,105,267,306,310],[78,105,267,306,313], [0,78,105,267,309],[78,105,267,309,310],[0,78,111,112,113],[78,111,112,113,275], [0,78,111,112,148],[78,111,112,148,310],[78,111,112,274,275],[78,111,112,274,310], [0,78,111,113,151],[78,111,113,151,313],[78,111,113,275,313],[0,78,111,144,148], [78,111,144,148,310],[0,78,111,144,151],[78,111,144,151,313],[78,111,144,306,310], [78,111,144,306,313],[78,111,273,274,275],[78,111,273,274,310],[78,111,273,275,313], [78,111,273,306,310],[78,111,273,306,313],[78,240,241,242,245],[78,240,241,242,275], [0,78,240,241,244],[78,240,241,244,245],[78,240,241,274,275],[78,240,241,274,310], [0,78,240,241,309],[78,240,241,309,310],[78,240,242,245,266],[78,240,242,266,269], [78,240,242,269,313],[78,240,242,275,313],[0,78,240,243,244],[78,240,243,244,245], [78,240,243,245,266],[0,78,240,243,264],[78,240,243,264,266],[78,240,264,266,269], [0,78,240,264,267],[78,240,264,267,269],[78,240,267,269,313],[78,240,267,306,310], [78,240,267,306,313],[0,78,240,267,309],[78,240,267,309,310],[78,240,273,274,275], [78,240,273,274,310],[78,240,273,275,313],[78,240,273,306,310],[78,240,273,306,313], [162,163,164,167,245],[162,163,164,167,318],[162,163,164,197,275],[162,163,164,197,318], [162,163,164,242,245],[162,163,164,242,275],[162,163,166,167,245],[0,162,163,166,318], [162,163,166,167,318],[0,162,163,166,244],[162,163,166,244,245],[162,163,196,197,275], [0,162,163,196,318],[162,163,196,197,318],[0,162,163,196,232],[162,163,196,232,310], [162,163,196,274,275],[162,163,196,274,310],[0,162,163,231,232],[162,163,231,232,310], [0,162,163,231,309],[162,163,231,309,310],[162,163,241,242,245],[162,163,241,242,275], [0,162,163,241,244],[162,163,241,244,245],[162,163,241,274,275],[162,163,241,274,310], [0,162,163,241,309],[162,163,241,309,310],[0,162,164,167,188],[162,164,167,188,266], [162,164,167,245,266],[0,162,164,167,319],[162,164,167,318,319],[0,162,164,188,191], [162,164,188,191,269],[162,164,188,266,269],[0,162,164,191,235],[162,164,191,235,313], [162,164,191,269,313],[0,162,164,197,235],[162,164,197,235,313],[162,164,197,275,313], [0,162,164,197,319],[162,164,197,318,319],[162,164,242,245,266],[162,164,242,266,269], [162,164,242,269,313],[162,164,242,275,313],[162,165,166,167,245],[0,162,165,166,318], [162,165,166,167,318],[0,162,165,166,244],[162,165,166,244,245],[0,162,165,167,188], [162,165,167,188,266],[162,165,167,245,266],[0,162,165,167,319],[162,165,167,318,319], [0,162,165,186,188],[162,165,186,188,266],[0,162,165,186,264],[162,165,186,264,266], [0,162,165,243,244],[162,165,243,244,245],[162,165,243,245,266],[0,162,165,243,264], [162,165,243,264,266],[0,162,165,318,320],[0,162,165,319,320],[162,165,318,319,320], [0,162,186,188,191],[162,186,188,191,269],[162,186,188,266,269],[0,162,186,189,191], [162,186,189,191,269],[0,162,186,189,267],[162,186,189,267,269],[162,186,264,266,269], [0,162,186,264,267],[162,186,264,267,269],[0,162,189,191,235],[162,189,191,235,313], [162,189,191,269,313],[0,162,189,228,232],[162,189,228,232,310],[0,162,189,228,235], [162,189,228,235,313],[162,189,228,306,310],[162,189,228,306,313],[0,162,189,231,232], [162,189,231,232,310],[0,162,189,231,309],[162,189,231,309,310],[162,189,267,269,313], [162,189,267,306,310],[162,189,267,306,313],[0,162,189,267,309],[162,189,267,309,310], [162,195,196,197,275],[0,162,195,196,318],[162,195,196,197,318],[0,162,195,196,232], [162,195,196,232,310],[162,195,196,274,275],[162,195,196,274,310],[0,162,195,197,235], [162,195,197,235,313],[162,195,197,275,313],[0,162,195,197,319],[162,195,197,318,319], [0,162,195,228,232],[162,195,228,232,310],[0,162,195,228,235],[162,195,228,235,313], [162,195,228,306,310],[162,195,228,306,313],[162,195,273,274,275],[162,195,273,274,310], [162,195,273,275,313],[162,195,273,306,310],[162,195,273,306,313],[0,162,195,318,320], [0,162,195,319,320],[162,195,318,319,320],[162,240,241,242,245],[162,240,241,242,275], [0,162,240,241,244],[162,240,241,244,245],[162,240,241,274,275],[162,240,241,274,310], [0,162,240,241,309],[162,240,241,309,310],[162,240,242,245,266],[162,240,242,266,269], [162,240,242,269,313],[162,240,242,275,313],[0,162,240,243,244],[162,240,243,244,245], [162,240,243,245,266],[0,162,240,243,264],[162,240,243,264,266],[162,240,264,266,269], [0,162,240,264,267],[162,240,264,267,269],[162,240,267,269,313],[162,240,267,306,310], [162,240,267,306,313],[0,162,240,267,309],[162,240,267,309,310],[162,240,273,274,275], [162,240,273,274,310],[162,240,273,275,313],[162,240,273,306,310],[162,240,273,306,313], [1,2,5,41,119],[2,5,41,119,281],[1,2,5,41,203],[2,5,41,203,281], [1,2,5,83,119],[2,5,83,119,281],[2,5,83,245,281],[1,2,5,167,203], [2,5,167,203,281],[2,5,167,245,281],[1,2,35,73,151],[1,2,35,73,235], [1,2,35,113,151],[1,2,35,197,235],[1,2,38,41,119],[2,38,41,119,281], [1,2,38,41,203],[2,38,41,203,281],[1,2,38,76,154],[1,2,38,76,238], [1,2,38,116,119],[2,38,116,119,281],[1,2,38,116,154],[2,38,116,278,281], [1,2,38,200,203],[2,38,200,203,281],[1,2,38,200,238],[2,38,200,278,281], [1,2,72,73,151],[1,2,72,73,235],[1,2,72,76,154],[1,2,72,76,238], [1,2,72,150,151],[1,2,72,150,154],[1,2,72,234,235],[1,2,72,234,238], [1,2,80,83,119],[2,80,83,119,281],[2,80,83,245,281],[1,2,80,113,151], [1,2,80,116,119],[2,80,116,119,281],[1,2,80,116,154],[2,80,116,278,281], [1,2,80,150,151],[1,2,80,150,154],[2,80,242,245,281],[2,80,242,278,281], [1,2,164,167,203],[2,164,167,203,281],[2,164,167,245,281],[1,2,164,197,235], [1,2,164,200,203],[2,164,200,203,281],[1,2,164,200,238],[2,164,200,278,281], [1,2,164,234,235],[1,2,164,234,238],[2,164,242,245,281],[2,164,242,278,281], [1,4,5,41,119],[1,4,5,41,203],[1,4,5,83,119],[1,4,5,167,203], [1,4,39,41,119],[1,4,39,41,203],[1,4,39,117,119],[1,4,39,117,279], [1,4,39,201,203],[1,4,39,201,279],[1,4,82,83,119],[1,4,82,117,119], [1,4,82,117,279],[1,4,82,244,279],[1,4,166,167,203],[1,4,166,201,203], [1,4,166,201,279],[1,4,166,244,279],[1,34,35,73,151],[1,34,35,73,235], 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