#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_012 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(752,11334,37836,45420,18168) ### ### 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:=[ [0,1,2,5,377],[0,1,2,35,407],[0,1,2,374,377],[0,1,2,374,407], [0,1,4,5,377],[0,1,4,190,562],[0,1,4,376,377],[0,1,4,376,562], [0,1,34,35,407],[0,1,34,178,364],[0,1,34,178,550],[0,1,34,220,364], [0,1,34,406,407],[0,1,34,406,550],[0,1,177,178,364],[0,1,177,178,550], [0,1,177,363,364],[0,1,177,363,735],[0,1,177,549,550],[0,1,177,549,735], [0,1,187,190,562],[0,1,187,220,364],[0,1,187,363,364],[0,1,187,363,735], [0,1,187,559,562],[0,1,187,559,735],[0,1,373,374,377],[0,1,373,374,407], [0,1,373,376,377],[0,1,373,376,562],[0,1,373,406,407],[0,1,373,406,550], [0,1,373,549,550],[0,1,373,549,735],[0,1,373,559,562],[0,1,373,559,735], [0,2,5,26,212],[2,5,26,212,584],[0,2,5,26,398],[2,5,26,398,584], [0,2,5,191,212],[2,5,191,212,584],[2,5,191,563,584],[0,2,5,377,398], [2,5,377,398,584],[2,5,377,563,584],[0,2,26,29,215],[2,26,29,215,587], [0,2,26,29,401],[2,26,29,401,587],[0,2,26,212,215],[2,26,212,215,587], [2,26,212,584,587],[0,2,26,398,401],[2,26,398,401,587],[2,26,398,584,587], [0,2,29,181,367],[0,2,29,181,553],[0,2,29,215,367],[0,2,29,401,553], [0,2,35,181,367],[0,2,35,181,553],[0,2,35,221,367],[0,2,35,407,553], [0,2,188,191,212],[2,188,191,212,584],[2,188,191,563,584],[0,2,188,212,215], [2,188,212,215,587],[2,188,212,584,587],[0,2,188,215,367],[0,2,188,221,367], [2,188,560,563,584],[2,188,560,584,587],[0,2,374,377,398],[2,374,377,398,584], [2,374,377,563,584],[0,2,374,398,401],[2,374,398,401,587],[2,374,398,584,587], [0,2,374,401,553],[0,2,374,407,553],[2,374,560,563,584],[2,374,560,584,587], [0,3,4,5,377],[0,3,4,190,562],[0,3,4,376,377],[0,3,4,376,562], [0,3,5,26,212],[0,3,5,26,398],[0,3,5,191,212],[0,3,5,377,398], [0,3,24,26,212],[0,3,24,26,398],[0,3,24,210,212],[0,3,24,210,582], [0,3,24,396,398],[0,3,24,396,582],[0,3,189,190,562],[0,3,189,191,212], [0,3,189,210,212],[0,3,189,210,582],[0,3,189,561,562],[0,3,189,561,582], [0,3,375,376,377],[0,3,375,376,562],[0,3,375,377,398],[0,3,375,396,398], [0,3,375,396,582],[0,3,375,561,562],[0,3,375,561,582],[0,24,26,29,215], [0,24,26,29,401],[0,24,26,212,215],[0,24,26,398,401],[0,24,27,29,215], [0,24,27,29,401],[0,24,27,213,215],[0,24,27,213,585],[0,24,27,399,401], [0,24,27,399,585],[0,24,210,212,215],[0,24,210,213,215],[0,24,210,213,585], [0,24,210,582,585],[0,24,396,398,401],[0,24,396,399,401],[0,24,396,399,585], [0,24,396,582,585],[0,27,29,181,367],[0,27,29,181,553],[0,27,29,215,367], [0,27,29,401,553],[0,27,174,178,364],[0,27,174,178,550],[0,27,174,181,367], [0,27,174,181,553],[0,27,174,360,364],[0,27,174,360,367],[0,27,174,546,550], [0,27,174,546,553],[0,27,177,178,364],[0,27,177,178,550],[0,27,177,363,364], [0,27,177,363,735],[0,27,177,549,550],[0,27,177,549,735],[0,27,213,215,367], [0,27,213,360,364],[0,27,213,360,367],[0,27,213,363,364],[0,27,213,363,735], [0,27,213,585,735],[0,27,399,401,553],[0,27,399,546,550],[0,27,399,546,553], [0,27,399,549,550],[0,27,399,549,735],[0,27,399,585,735],[0,33,34,35,407], [0,33,34,178,364],[0,33,34,178,550],[0,33,34,220,364],[0,33,34,406,407], [0,33,34,406,550],[0,33,35,181,367],[0,33,35,181,553],[0,33,35,221,367], [0,33,35,407,553],[0,33,174,178,364],[0,33,174,178,550],[0,33,174,181,367], [0,33,174,181,553],[0,33,174,360,364],[0,33,174,360,367],[0,33,174,546,550], [0,33,174,546,553],[0,33,219,220,364],[0,33,219,221,367],[0,33,219,360,364], [0,33,219,360,367],[0,33,405,406,407],[0,33,405,406,550],[0,33,405,407,553], [0,33,405,546,550],[0,33,405,546,553],[186,187,188,191,563],[186,187,188,221,593], [186,187,188,560,563],[186,187,188,560,593],[186,187,190,191,563],[0,186,187,190,562], [186,187,190,562,563],[186,187,220,221,593],[0,186,187,220,364],[186,187,220,364,736], [186,187,220,592,593],[186,187,220,592,736],[0,186,187,363,364],[186,187,363,364,736], [0,186,187,363,735],[186,187,363,735,736],[186,187,559,560,563],[186,187,559,560,593], [0,186,187,559,562],[186,187,559,562,563],[186,187,559,592,593],[186,187,559,592,736], [0,186,187,559,735],[186,187,559,735,736],[0,186,188,191,212],[186,188,191,212,584], [186,188,191,563,584],[0,186,188,212,215],[186,188,212,215,587],[186,188,212,584,587], [0,186,188,215,367],[186,188,215,367,739],[186,188,215,587,739],[0,186,188,221,367], [186,188,221,367,739],[186,188,221,593,739],[186,188,560,563,584],[186,188,560,584,587], [186,188,560,587,739],[186,188,560,593,739],[186,189,190,191,563],[0,186,189,190,562], [186,189,190,562,563],[0,186,189,191,212],[186,189,191,212,584],[186,189,191,563,584], [0,186,189,210,212],[186,189,210,212,584],[0,186,189,210,582],[186,189,210,582,584], [0,186,189,561,562],[186,189,561,562,563],[186,189,561,563,584],[0,186,189,561,582], [186,189,561,582,584],[0,186,210,212,215],[186,210,212,215,587],[186,210,212,584,587], [0,186,210,213,215],[186,210,213,215,587],[0,186,210,213,585],[186,210,213,585,587], [186,210,582,584,587],[0,186,210,582,585],[186,210,582,585,587],[0,186,213,215,367], [186,213,215,367,739],[186,213,215,587,739],[0,186,213,360,364],[186,213,360,364,736], [0,186,213,360,367],[186,213,360,367,739],[186,213,360,732,736],[186,213,360,732,739], [0,186,213,363,364],[186,213,363,364,736],[0,186,213,363,735],[186,213,363,735,736], [186,213,585,587,739],[186,213,585,732,736],[186,213,585,732,739],[0,186,213,585,735], [186,213,585,735,736],[186,219,220,221,593],[0,186,219,220,364],[186,219,220,364,736], [186,219,220,592,593],[186,219,220,592,736],[0,186,219,221,367],[186,219,221,367,739], [186,219,221,593,739],[0,186,219,360,364],[186,219,360,364,736],[0,186,219,360,367], [186,219,360,367,739],[186,219,360,732,736],[186,219,360,732,739],[186,219,591,592,593], [186,219,591,592,736],[186,219,591,593,739],[186,219,591,732,736],[186,219,591,732,739], [186,558,559,560,563],[186,558,559,560,593],[0,186,558,559,562],[186,558,559,562,563], [186,558,559,592,593],[186,558,559,592,736],[0,186,558,559,735],[186,558,559,735,736], [186,558,560,563,584],[186,558,560,584,587],[186,558,560,587,739],[186,558,560,593,739], [0,186,558,561,562],[186,558,561,562,563],[186,558,561,563,584],[0,186,558,561,582], [186,558,561,582,584],[186,558,582,584,587],[0,186,558,582,585],[186,558,582,585,587], [186,558,585,587,739],[186,558,585,732,736],[186,558,585,732,739],[0,186,558,585,735], [186,558,585,735,736],[186,558,591,592,593],[186,558,591,592,736],[186,558,591,593,739], [186,558,591,732,736],[186,558,591,732,739],[0,372,373,374,377],[372,373,374,377,563], [0,372,373,374,407],[372,373,374,407,593],[372,373,374,560,563],[372,373,374,560,593], [0,372,373,376,377],[372,373,376,377,563],[0,372,373,376,562],[372,373,376,562,563], [0,372,373,406,407],[372,373,406,407,593],[0,372,373,406,550],[372,373,406,550,736], [372,373,406,592,593],[372,373,406,592,736],[0,372,373,549,550],[372,373,549,550,736], [0,372,373,549,735],[372,373,549,735,736],[372,373,559,560,563],[372,373,559,560,593], [0,372,373,559,562],[372,373,559,562,563],[372,373,559,592,593],[372,373,559,592,736], [0,372,373,559,735],[372,373,559,735,736],[0,372,374,377,398],[372,374,377,398,584], [372,374,377,563,584],[0,372,374,398,401],[372,374,398,401,587],[372,374,398,584,587], [0,372,374,401,553],[372,374,401,553,739],[372,374,401,587,739],[0,372,374,407,553], [372,374,407,553,739],[372,374,407,593,739],[372,374,560,563,584],[372,374,560,584,587], [372,374,560,587,739],[372,374,560,593,739],[0,372,375,376,377],[372,375,376,377,563], [0,372,375,376,562],[372,375,376,562,563],[0,372,375,377,398],[372,375,377,398,584], [372,375,377,563,584],[0,372,375,396,398],[372,375,396,398,584],[0,372,375,396,582], [372,375,396,582,584],[0,372,375,561,562],[372,375,561,562,563],[372,375,561,563,584], [0,372,375,561,582],[372,375,561,582,584],[0,372,396,398,401],[372,396,398,401,587], [372,396,398,584,587],[0,372,396,399,401],[372,396,399,401,587],[0,372,396,399,585], [372,396,399,585,587],[372,396,582,584,587],[0,372,396,582,585],[372,396,582,585,587], [0,372,399,401,553],[372,399,401,553,739],[372,399,401,587,739],[0,372,399,546,550], [372,399,546,550,736],[0,372,399,546,553],[372,399,546,553,739],[372,399,546,732,736], [372,399,546,732,739],[0,372,399,549,550],[372,399,549,550,736],[0,372,399,549,735], [372,399,549,735,736],[372,399,585,587,739],[372,399,585,732,736],[372,399,585,732,739], [0,372,399,585,735],[372,399,585,735,736],[0,372,405,406,407],[372,405,406,407,593], [0,372,405,406,550],[372,405,406,550,736],[372,405,406,592,593],[372,405,406,592,736], [0,372,405,407,553],[372,405,407,553,739],[372,405,407,593,739],[0,372,405,546,550], [372,405,546,550,736],[0,372,405,546,553],[372,405,546,553,739],[372,405,546,732,736], [372,405,546,732,739],[372,405,591,592,593],[372,405,591,592,736],[372,405,591,593,739], [372,405,591,732,736],[372,405,591,732,739],[372,558,559,560,563],[372,558,559,560,593], [0,372,558,559,562],[372,558,559,562,563],[372,558,559,592,593],[372,558,559,592,736], [0,372,558,559,735],[372,558,559,735,736],[372,558,560,563,584],[372,558,560,584,587], [372,558,560,587,739],[372,558,560,593,739],[0,372,558,561,562],[372,558,561,562,563], [372,558,561,563,584],[0,372,558,561,582],[372,558,561,582,584],[372,558,582,584,587], [0,372,558,582,585],[372,558,582,585,587],[372,558,585,587,739],[372,558,585,732,736], [372,558,585,732,739],[0,372,558,585,735],[372,558,585,735,736],[372,558,591,592,593], [372,558,591,592,736],[372,558,591,593,739],[372,558,591,732,736],[372,558,591,732,739], [1,2,5,41,227],[2,5,41,227,599],[1,2,5,41,413],[2,5,41,413,599], [1,2,5,191,227],[2,5,191,227,599],[2,5,191,563,599],[1,2,5,377,413], [2,5,377,413,599],[2,5,377,563,599],[1,2,35,181,367],[1,2,35,181,553], [1,2,35,221,367],[1,2,35,407,553],[1,2,38,41,227],[2,38,41,227,599], [1,2,38,41,413],[2,38,41,413,599],[1,2,38,184,370],[1,2,38,184,556], [1,2,38,224,227],[2,38,224,227,599],[1,2,38,224,370],[2,38,224,596,599], [1,2,38,410,413],[2,38,410,413,599],[1,2,38,410,556],[2,38,410,596,599], [1,2,180,181,367],[1,2,180,181,553],[1,2,180,184,370],[1,2,180,184,556], [1,2,180,366,367],[1,2,180,366,370],[1,2,180,552,553],[1,2,180,552,556], [1,2,188,191,227],[2,188,191,227,599],[2,188,191,563,599],[1,2,188,221,367], [1,2,188,224,227],[2,188,224,227,599],[1,2,188,224,370],[2,188,224,596,599], [1,2,188,366,367],[1,2,188,366,370],[2,188,560,563,599],[2,188,560,596,599], [1,2,374,377,413],[2,374,377,413,599],[2,374,377,563,599],[1,2,374,407,553], [1,2,374,410,413],[2,374,410,413,599],[1,2,374,410,556],[2,374,410,596,599], [1,2,374,552,553],[1,2,374,552,556],[2,374,560,563,599],[2,374,560,596,599], [1,4,5,41,227],[1,4,5,41,413],[1,4,5,191,227],[1,4,5,377,413], [1,4,39,41,227],[1,4,39,41,413],[1,4,39,225,227],[1,4,39,225,597], [1,4,39,411,413],[1,4,39,411,597],[1,4,190,191,227],[1,4,190,225,227], [1,4,190,225,597],[1,4,190,562,597],[1,4,376,377,413],[1,4,376,411,413], [1,4,376,411,597],[1,4,376,562,597],[1,34,35,181,367],[1,34,35,181,553], [1,34,35,221,367],[1,34,35,407,553],[1,34,175,178,364],[1,34,175,178,550], [1,34,175,181,367],[1,34,175,181,553],[1,34,175,361,364],[1,34,175,361,367], [1,34,175,547,550],[1,34,175,547,553],[1,34,220,221,367],[1,34,220,361,364], [1,34,220,361,367],[1,34,406,407,553],[1,34,406,547,550],[1,34,406,547,553], [1,36,38,41,227],[1,36,38,41,413],[1,36,38,184,370],[1,36,38,184,556], [1,36,38,224,227],[1,36,38,224,370],[1,36,38,410,413],[1,36,38,410,556], [1,36,39,41,227],[1,36,39,41,413],[1,36,39,225,227],[1,36,39,225,597], [1,36,39,411,413],[1,36,39,411,597],[1,36,175,178,364],[1,36,175,178,550], [1,36,175,181,367],[1,36,175,181,553],[1,36,175,361,364],[1,36,175,361,367], [1,36,175,547,550],[1,36,175,547,553],[1,36,177,178,364],[1,36,177,178,550], [1,36,177,363,364],[1,36,177,363,735],[1,36,177,549,550],[1,36,177,549,735], [1,36,180,181,367],[1,36,180,181,553],[1,36,180,184,370],[1,36,180,184,556], [1,36,180,366,367],[1,36,180,366,370],[1,36,180,552,553],[1,36,180,552,556], [1,36,222,224,227],[1,36,222,224,370],[1,36,222,225,227],[1,36,222,225,597], [1,36,222,361,364],[1,36,222,361,367],[1,36,222,363,364],[1,36,222,363,735], [1,36,222,366,367],[1,36,222,366,370],[1,36,222,594,597],[1,36,222,594,735], [1,36,408,410,413],[1,36,408,410,556],[1,36,408,411,413],[1,36,408,411,597], [1,36,408,547,550],[1,36,408,547,553],[1,36,408,549,550],[1,36,408,549,735], [1,36,408,552,553],[1,36,408,552,556],[1,36,408,594,597],[1,36,408,594,735], [1,187,188,191,227],[187,188,191,227,599],[187,188,191,563,599],[1,187,188,221,367], [187,188,221,367,739],[187,188,221,593,739],[1,187,188,224,227],[187,188,224,227,599], [1,187,188,224,370],[187,188,224,370,742],[187,188,224,596,599],[187,188,224,596,742], [1,187,188,366,367],[187,188,366,367,739],[1,187,188,366,370],[187,188,366,370,742], [187,188,366,738,739],[187,188,366,738,742],[187,188,560,563,599],[187,188,560,593,739], [187,188,560,596,599],[187,188,560,596,742],[187,188,560,738,739],[187,188,560,738,742], [1,187,190,191,227],[187,190,191,227,599],[187,190,191,563,599],[1,187,190,225,227], [187,190,225,227,599],[1,187,190,225,597],[187,190,225,597,599],[187,190,562,563,599], [1,187,190,562,597],[187,190,562,597,599],[1,187,220,221,367],[187,220,221,367,739], [187,220,221,593,739],[1,187,220,361,364],[187,220,361,364,736],[1,187,220,361,367], 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[55,58,63,65,251],[55,58,63,65,437],[55,58,63,249,251],[55,58,63,249,621], [55,58,63,435,437],[55,58,63,435,621],[55,58,244,245,251],[55,58,244,249,251], [55,58,244,249,621],[55,58,244,616,621],[55,58,430,431,437],[55,58,430,435,437], [55,58,430,435,621],[55,58,430,616,621],[55,60,62,65,251],[55,60,62,65,437], [55,60,62,248,251],[55,60,62,434,437],[55,60,63,65,251],[55,60,63,65,437], [55,60,63,249,251],[55,60,63,249,621],[55,60,63,435,437],[55,60,63,435,621], [55,60,246,248,251],[55,60,246,249,251],[55,60,246,249,621],[55,60,246,618,621], [55,60,432,434,437],[55,60,432,435,437],[55,60,432,435,621],[55,60,432,618,621], [55,241,242,245,251],[241,242,245,251,623],[241,242,245,617,623],[55,241,242,248,251], [241,242,248,251,623],[241,242,248,620,623],[241,242,614,617,623],[241,242,614,620,623], [55,241,244,245,251],[241,244,245,251,623],[241,244,245,617,623],[55,241,244,249,251], [241,244,249,251,623],[55,241,244,249,621],[241,244,249,621,623],[241,244,616,617,623], 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