#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_012 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(756,11694,39236,47160,18864) ### ### 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:=[ [0,1,2,5,191],[0,1,2,5,372],[1,2,5,372,750],[1,2,5,383,750], [0,1,2,35,221],[0,1,2,35,372],[1,2,35,372,750],[1,2,35,413,750], [0,1,2,188,191],[0,1,2,188,221],[1,2,380,383,750],[1,2,380,413,750], [0,1,4,5,191],[0,1,4,5,372],[0,1,4,372,750],[1,4,5,372,750], [1,4,5,383,750],[0,1,4,190,191],[0,1,4,190,568],[0,1,4,382,750], [1,4,382,383,750],[0,1,4,382,568],[0,1,34,35,221],[0,1,34,35,372], [0,1,34,372,750],[1,34,35,372,750],[1,34,35,413,750],[0,1,34,178,364], [0,1,34,178,556],[0,1,34,220,221],[0,1,34,220,364],[0,1,34,412,750], [1,34,412,413,750],[0,1,34,412,556],[0,1,177,178,364],[0,1,177,178,556], [0,1,177,363,364],[0,1,177,363,741],[0,1,177,555,556],[0,1,177,555,741], [0,1,187,188,191],[0,1,187,188,221],[0,1,187,190,191],[0,1,187,190,568], [0,1,187,220,221],[0,1,187,220,364],[0,1,187,363,364],[0,1,187,363,741], [0,1,187,565,568],[0,1,187,565,741],[1,379,380,383,750],[1,379,380,413,750], [0,1,379,382,750],[1,379,382,383,750],[0,1,379,382,568],[0,1,379,412,750], [1,379,412,413,750],[0,1,379,412,556],[0,1,379,555,556],[0,1,379,555,741], [0,1,379,565,568],[0,1,379,565,741],[0,2,5,26,212],[2,5,26,212,590], [0,2,5,26,404],[2,5,26,404,590],[0,2,5,191,212],[2,5,191,212,590], [2,5,191,569,590],[0,2,5,372,373],[0,2,5,373,751],[2,5,372,373,751], [2,5,372,750,751],[0,2,5,383,404],[2,5,383,404,590],[2,5,383,569,590], [0,2,5,383,751],[2,5,383,750,751],[0,2,26,29,215],[2,26,29,215,593], [0,2,26,29,407],[2,26,29,407,593],[0,2,26,212,215],[2,26,212,215,593], [2,26,212,590,593],[0,2,26,404,407],[2,26,404,407,593],[2,26,404,590,593], [0,2,29,181,367],[0,2,29,181,559],[0,2,29,215,367],[0,2,29,407,559], [0,2,35,181,367],[0,2,35,181,559],[0,2,35,221,367],[0,2,35,372,373], [0,2,35,373,751],[2,35,372,373,751],[2,35,372,750,751],[0,2,35,413,559], [0,2,35,413,751],[2,35,413,750,751],[0,2,188,191,212],[2,188,191,212,590], [2,188,191,569,590],[0,2,188,212,215],[2,188,212,215,593],[2,188,212,590,593], [0,2,188,215,367],[0,2,188,221,367],[2,188,566,569,590],[2,188,566,590,593], [0,2,380,383,404],[2,380,383,404,590],[2,380,383,569,590],[0,2,380,383,751], [2,380,383,750,751],[0,2,380,404,407],[2,380,404,407,593],[2,380,404,590,593], [0,2,380,407,559],[0,2,380,413,559],[0,2,380,413,751],[2,380,413,750,751], [2,380,566,569,590],[2,380,566,590,593],[0,3,4,5,191],[0,3,4,5,372], [0,3,4,372,750],[0,3,4,190,191],[0,3,4,190,568],[0,3,4,382,750], [0,3,4,382,568],[0,3,5,26,212],[0,3,5,26,404],[0,3,5,191,212], [0,3,5,372,373],[0,3,5,373,751],[0,3,5,383,404],[0,3,5,383,751], [0,3,24,26,212],[0,3,24,26,404],[0,3,24,210,212],[0,3,24,210,588], [0,3,24,402,404],[0,3,24,402,588],[0,3,189,190,191],[0,3,189,190,568], [0,3,189,191,212],[0,3,189,210,212],[0,3,189,210,588],[0,3,189,567,568], [0,3,189,567,588],[0,3,372,373,374],[0,3,372,374,752],[0,3,373,374,752], [0,3,373,751,752],[0,3,372,750,752],[0,3,381,382,750],[0,3,381,382,568], [0,3,381,383,404],[0,3,381,383,751],[0,3,381,402,404],[0,3,381,402,588], [0,3,381,567,568],[0,3,381,567,588],[0,3,381,750,752],[0,3,381,751,752], [0,24,26,29,215],[0,24,26,29,407],[0,24,26,212,215],[0,24,26,404,407], [0,24,27,29,215],[0,24,27,29,407],[0,24,27,213,215],[0,24,27,213,591], [0,24,27,405,407],[0,24,27,405,591],[0,24,210,212,215],[0,24,210,213,215], [0,24,210,213,591],[0,24,210,588,591],[0,24,402,404,407],[0,24,402,405,407], [0,24,402,405,591],[0,24,402,588,591],[0,27,29,181,367],[0,27,29,181,559], [0,27,29,215,367],[0,27,29,407,559],[0,27,174,178,364],[0,27,174,178,556], [0,27,174,181,367],[0,27,174,181,559],[0,27,174,360,364],[0,27,174,360,367], [0,27,174,552,556],[0,27,174,552,559],[0,27,177,178,364],[0,27,177,178,556], [0,27,177,363,364],[0,27,177,363,741],[0,27,177,555,556],[0,27,177,555,741], [0,27,213,215,367],[0,27,213,360,364],[0,27,213,360,367],[0,27,213,363,364], [0,27,213,363,741],[0,27,213,591,741],[0,27,405,407,559],[0,27,405,552,556], [0,27,405,552,559],[0,27,405,555,556],[0,27,405,555,741],[0,27,405,591,741], [0,33,34,35,221],[0,33,34,35,372],[0,33,34,372,750],[0,33,34,178,364], [0,33,34,178,556],[0,33,34,220,221],[0,33,34,220,364],[0,33,34,412,750], [0,33,34,412,556],[0,33,35,181,367],[0,33,35,181,559],[0,33,35,221,367], [0,33,35,372,373],[0,33,35,373,751],[0,33,35,413,559],[0,33,35,413,751], [0,33,174,178,364],[0,33,174,178,556],[0,33,174,181,367],[0,33,174,181,559], [0,33,174,360,364],[0,33,174,360,367],[0,33,174,552,556],[0,33,174,552,559], [0,33,219,220,221],[0,33,219,220,364],[0,33,219,221,367],[0,33,219,360,364], [0,33,219,360,367],[0,33,372,373,374],[0,33,372,374,752],[0,33,373,374,752], [0,33,373,751,752],[0,33,372,750,752],[0,33,411,412,750],[0,33,411,412,556], [0,33,411,413,559],[0,33,411,413,751],[0,33,411,552,556],[0,33,411,552,559], [0,33,411,750,752],[0,33,411,751,752],[0,186,187,188,191],[186,187,188,191,569], [0,186,187,188,221],[186,187,188,221,599],[186,187,188,566,569],[186,187,188,566,599], [0,186,187,190,191],[186,187,190,191,569],[0,186,187,190,568],[186,187,190,568,569], [0,186,187,220,221],[186,187,220,221,599],[0,186,187,220,364],[186,187,220,364,742], [186,187,220,598,599],[186,187,220,598,742],[0,186,187,363,364],[186,187,363,364,742], [0,186,187,363,741],[186,187,363,741,742],[186,187,565,566,569],[186,187,565,566,599], [0,186,187,565,568],[186,187,565,568,569],[186,187,565,598,599],[186,187,565,598,742], [0,186,187,565,741],[186,187,565,741,742],[0,186,188,191,212],[186,188,191,212,590], [186,188,191,569,590],[0,186,188,212,215],[186,188,212,215,593],[186,188,212,590,593], [0,186,188,215,367],[186,188,215,367,745],[186,188,215,593,745],[0,186,188,221,367], [186,188,221,367,745],[186,188,221,599,745],[186,188,566,569,590],[186,188,566,590,593], [186,188,566,593,745],[186,188,566,599,745],[0,186,189,190,191],[186,189,190,191,569], [0,186,189,190,568],[186,189,190,568,569],[0,186,189,191,212],[186,189,191,212,590], [186,189,191,569,590],[0,186,189,210,212],[186,189,210,212,590],[0,186,189,210,588], [186,189,210,588,590],[0,186,189,567,568],[186,189,567,568,569],[186,189,567,569,590], [0,186,189,567,588],[186,189,567,588,590],[0,186,210,212,215],[186,210,212,215,593], [186,210,212,590,593],[0,186,210,213,215],[186,210,213,215,593],[0,186,210,213,591], [186,210,213,591,593],[186,210,588,590,593],[0,186,210,588,591],[186,210,588,591,593], [0,186,213,215,367],[186,213,215,367,745],[186,213,215,593,745],[0,186,213,360,364], [186,213,360,364,742],[0,186,213,360,367],[186,213,360,367,745],[186,213,360,738,742], [186,213,360,738,745],[0,186,213,363,364],[186,213,363,364,742],[0,186,213,363,741], [186,213,363,741,742],[186,213,591,593,745],[186,213,591,738,742],[186,213,591,738,745], [0,186,213,591,741],[186,213,591,741,742],[0,186,219,220,221],[186,219,220,221,599], [0,186,219,220,364],[186,219,220,364,742],[186,219,220,598,599],[186,219,220,598,742], [0,186,219,221,367],[186,219,221,367,745],[186,219,221,599,745],[0,186,219,360,364], [186,219,360,364,742],[0,186,219,360,367],[186,219,360,367,745],[186,219,360,738,742], [186,219,360,738,745],[186,219,597,598,599],[186,219,597,598,742],[186,219,597,599,745], [186,219,597,738,742],[186,219,597,738,745],[186,564,565,566,569],[186,564,565,566,599], [0,186,564,565,568],[186,564,565,568,569],[186,564,565,598,599],[186,564,565,598,742], [0,186,564,565,741],[186,564,565,741,742],[186,564,566,569,590],[186,564,566,590,593], [186,564,566,593,745],[186,564,566,599,745],[0,186,564,567,568],[186,564,567,568,569], [186,564,567,569,590],[0,186,564,567,588],[186,564,567,588,590],[186,564,588,590,593], [0,186,564,588,591],[186,564,588,591,593],[186,564,591,593,745],[186,564,591,738,742], [186,564,591,738,745],[0,186,564,591,741],[186,564,591,741,742],[186,564,597,598,599], [186,564,597,598,742],[186,564,597,599,745],[186,564,597,738,742],[186,564,597,738,745], [378,379,380,383,569],[378,379,380,383,750],[378,379,380,413,599],[378,379,380,413,750], [378,379,380,566,569],[378,379,380,566,599],[378,379,382,383,569],[0,378,379,382,750], [378,379,382,383,750],[0,378,379,382,568],[378,379,382,568,569],[378,379,412,413,599], [0,378,379,412,750],[378,379,412,413,750],[0,378,379,412,556],[378,379,412,556,742], [378,379,412,598,599],[378,379,412,598,742],[0,378,379,555,556],[378,379,555,556,742], [0,378,379,555,741],[378,379,555,741,742],[378,379,565,566,569],[378,379,565,566,599], [0,378,379,565,568],[378,379,565,568,569],[378,379,565,598,599],[378,379,565,598,742], [0,378,379,565,741],[378,379,565,741,742],[0,378,380,383,404],[378,380,383,404,590], [378,380,383,569,590],[0,378,380,383,751],[378,380,383,750,751],[0,378,380,404,407], [378,380,404,407,593],[378,380,404,590,593],[0,378,380,407,559],[378,380,407,559,745], [378,380,407,593,745],[0,378,380,413,559],[378,380,413,559,745],[378,380,413,599,745], [0,378,380,413,751],[378,380,413,750,751],[378,380,566,569,590],[378,380,566,590,593], [378,380,566,593,745],[378,380,566,599,745],[378,381,382,383,569],[0,378,381,382,750], [378,381,382,383,750],[0,378,381,382,568],[378,381,382,568,569],[0,378,381,383,404], [378,381,383,404,590],[378,381,383,569,590],[0,378,381,383,751],[378,381,383,750,751], [0,378,381,402,404],[378,381,402,404,590],[0,378,381,402,588],[378,381,402,588,590], [0,378,381,567,568],[378,381,567,568,569],[378,381,567,569,590],[0,378,381,567,588], [378,381,567,588,590],[0,378,381,750,752],[0,378,381,751,752],[378,381,750,751,752], [0,378,402,404,407],[378,402,404,407,593],[378,402,404,590,593],[0,378,402,405,407], [378,402,405,407,593],[0,378,402,405,591],[378,402,405,591,593],[378,402,588,590,593], [0,378,402,588,591],[378,402,588,591,593],[0,378,405,407,559],[378,405,407,559,745], [378,405,407,593,745],[0,378,405,552,556],[378,405,552,556,742],[0,378,405,552,559], [378,405,552,559,745],[378,405,552,738,742],[378,405,552,738,745],[0,378,405,555,556], [378,405,555,556,742],[0,378,405,555,741],[378,405,555,741,742],[378,405,591,593,745], [378,405,591,738,742],[378,405,591,738,745],[0,378,405,591,741],[378,405,591,741,742], [378,411,412,413,599],[0,378,411,412,750],[378,411,412,413,750],[0,378,411,412,556], [378,411,412,556,742],[378,411,412,598,599],[378,411,412,598,742],[0,378,411,413,559], [378,411,413,559,745],[378,411,413,599,745],[0,378,411,413,751],[378,411,413,750,751], [0,378,411,552,556],[378,411,552,556,742],[0,378,411,552,559],[378,411,552,559,745], [378,411,552,738,742],[378,411,552,738,745],[378,411,597,598,599],[378,411,597,598,742], [378,411,597,599,745],[378,411,597,738,742],[378,411,597,738,745],[0,378,411,750,752], [0,378,411,751,752],[378,411,750,751,752],[378,564,565,566,569],[378,564,565,566,599], [0,378,564,565,568],[378,564,565,568,569],[378,564,565,598,599],[378,564,565,598,742], [0,378,564,565,741],[378,564,565,741,742],[378,564,566,569,590],[378,564,566,590,593], [378,564,566,593,745],[378,564,566,599,745],[0,378,564,567,568],[378,564,567,568,569], [378,564,567,569,590],[0,378,564,567,588],[378,564,567,588,590],[378,564,588,590,593], [0,378,564,588,591],[378,564,588,591,593],[378,564,591,593,745],[378,564,591,738,742], [378,564,591,738,745],[0,378,564,591,741],[378,564,591,741,742],[378,564,597,598,599], [378,564,597,598,742],[378,564,597,599,745],[378,564,597,738,742],[378,564,597,738,745], [1,2,5,41,227],[2,5,41,227,605],[1,2,5,41,419],[2,5,41,419,605], [1,2,5,191,227],[2,5,191,227,605],[2,5,191,569,605],[1,2,5,383,419], [2,5,383,419,605],[2,5,383,569,605],[1,2,35,181,367],[1,2,35,181,559], [1,2,35,221,367],[1,2,35,413,559],[1,2,38,41,227],[2,38,41,227,605], [1,2,38,41,419],[2,38,41,419,605],[1,2,38,184,370],[1,2,38,184,562], [1,2,38,224,227],[2,38,224,227,605],[1,2,38,224,370],[2,38,224,602,605], [1,2,38,416,419],[2,38,416,419,605],[1,2,38,416,562],[2,38,416,602,605], [1,2,180,181,367],[1,2,180,181,559],[1,2,180,184,370],[1,2,180,184,562], [1,2,180,366,367],[1,2,180,366,370],[1,2,180,558,559],[1,2,180,558,562], [1,2,188,191,227],[2,188,191,227,605],[2,188,191,569,605],[1,2,188,221,367], [1,2,188,224,227],[2,188,224,227,605],[1,2,188,224,370],[2,188,224,602,605], [1,2,188,366,367],[1,2,188,366,370],[2,188,566,569,605],[2,188,566,602,605], [1,2,380,383,419],[2,380,383,419,605],[2,380,383,569,605],[1,2,380,413,559], 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