#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_004 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(372,5742,19268,23160,9264) ### ### 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:=[ [0,1,2,5,95],[0,1,2,5,180],[1,2,5,180,366],[1,2,5,191,366], [0,1,2,35,125],[0,1,2,35,180],[1,2,35,180,366],[1,2,35,221,366], [0,1,2,92,95],[0,1,2,92,125],[1,2,188,191,366],[1,2,188,221,366], [0,1,4,5,95],[0,1,4,5,180],[0,1,4,180,366],[1,4,5,180,366], [1,4,5,191,366],[0,1,4,94,95],[0,1,4,94,280],[0,1,4,190,366], [1,4,190,191,366],[0,1,4,190,280],[0,1,34,35,125],[0,1,34,35,180], [0,1,34,180,366],[1,34,35,180,366],[1,34,35,221,366],[0,1,34,82,172], [0,1,34,82,268],[0,1,34,124,125],[0,1,34,124,172],[0,1,34,220,366], [1,34,220,221,366],[0,1,34,220,268],[0,1,81,82,172],[0,1,81,82,268], [0,1,81,171,172],[0,1,81,171,357],[0,1,81,267,268],[0,1,81,267,357], [0,1,91,92,95],[0,1,91,92,125],[0,1,91,94,95],[0,1,91,94,280], [0,1,91,124,125],[0,1,91,124,172],[0,1,91,171,172],[0,1,91,171,357], [0,1,91,277,280],[0,1,91,277,357],[1,187,188,191,366],[1,187,188,221,366], [0,1,187,190,366],[1,187,190,191,366],[0,1,187,190,280],[0,1,187,220,366], [1,187,220,221,366],[0,1,187,220,268],[0,1,187,267,268],[0,1,187,267,357], [0,1,187,277,280],[0,1,187,277,357],[0,2,5,26,116],[2,5,26,116,302], [0,2,5,26,212],[2,5,26,212,302],[0,2,5,95,116],[2,5,95,116,302], [2,5,95,281,302],[0,2,5,180,181],[0,2,5,181,367],[2,5,180,181,367], [2,5,180,366,367],[0,2,5,191,212],[2,5,191,212,302],[2,5,191,281,302], [0,2,5,191,367],[2,5,191,366,367],[0,2,26,29,119],[2,26,29,119,305], [0,2,26,29,215],[2,26,29,215,305],[0,2,26,116,119],[2,26,116,119,305], [2,26,116,302,305],[0,2,26,212,215],[2,26,212,215,305],[2,26,212,302,305], [0,2,29,85,175],[0,2,29,85,271],[0,2,29,119,175],[0,2,29,215,271], [0,2,35,85,175],[0,2,35,85,271],[0,2,35,125,175],[0,2,35,180,181], [0,2,35,181,367],[2,35,180,181,367],[2,35,180,366,367],[0,2,35,221,271], [0,2,35,221,367],[2,35,221,366,367],[0,2,92,95,116],[2,92,95,116,302], [2,92,95,281,302],[0,2,92,116,119],[2,92,116,119,305],[2,92,116,302,305], [0,2,92,119,175],[0,2,92,125,175],[2,92,278,281,302],[2,92,278,302,305], [0,2,188,191,212],[2,188,191,212,302],[2,188,191,281,302],[0,2,188,191,367], [2,188,191,366,367],[0,2,188,212,215],[2,188,212,215,305],[2,188,212,302,305], [0,2,188,215,271],[0,2,188,221,271],[0,2,188,221,367],[2,188,221,366,367], [2,188,278,281,302],[2,188,278,302,305],[0,3,4,5,95],[0,3,4,5,180], [0,3,4,180,366],[0,3,4,94,95],[0,3,4,94,280],[0,3,4,190,366], [0,3,4,190,280],[0,3,5,26,116],[0,3,5,26,212],[0,3,5,95,116], [0,3,5,180,181],[0,3,5,181,367],[0,3,5,191,212],[0,3,5,191,367], [0,3,24,26,116],[0,3,24,26,212],[0,3,24,114,116],[0,3,24,114,300], [0,3,24,210,212],[0,3,24,210,300],[0,3,93,94,95],[0,3,93,94,280], [0,3,93,95,116],[0,3,93,114,116],[0,3,93,114,300],[0,3,93,279,280], [0,3,93,279,300],[0,3,180,181,182],[0,3,180,182,368],[0,3,181,182,368], [0,3,181,367,368],[0,3,180,366,368],[0,3,189,190,366],[0,3,189,190,280], [0,3,189,191,212],[0,3,189,191,367],[0,3,189,210,212],[0,3,189,210,300], [0,3,189,279,280],[0,3,189,279,300],[0,3,189,366,368],[0,3,189,367,368], [0,24,26,29,119],[0,24,26,29,215],[0,24,26,116,119],[0,24,26,212,215], [0,24,27,29,119],[0,24,27,29,215],[0,24,27,117,119],[0,24,27,117,303], [0,24,27,213,215],[0,24,27,213,303],[0,24,114,116,119],[0,24,114,117,119], [0,24,114,117,303],[0,24,114,300,303],[0,24,210,212,215],[0,24,210,213,215], [0,24,210,213,303],[0,24,210,300,303],[0,27,29,85,175],[0,27,29,85,271], [0,27,29,119,175],[0,27,29,215,271],[0,27,78,82,172],[0,27,78,82,268], [0,27,78,85,175],[0,27,78,85,271],[0,27,78,168,172],[0,27,78,168,175], [0,27,78,264,268],[0,27,78,264,271],[0,27,81,82,172],[0,27,81,82,268], [0,27,81,171,172],[0,27,81,171,357],[0,27,81,267,268],[0,27,81,267,357], [0,27,117,119,175],[0,27,117,168,172],[0,27,117,168,175],[0,27,117,171,172], [0,27,117,171,357],[0,27,117,303,357],[0,27,213,215,271],[0,27,213,264,268], [0,27,213,264,271],[0,27,213,267,268],[0,27,213,267,357],[0,27,213,303,357], [0,33,34,35,125],[0,33,34,35,180],[0,33,34,180,366],[0,33,34,82,172], [0,33,34,82,268],[0,33,34,124,125],[0,33,34,124,172],[0,33,34,220,366], [0,33,34,220,268],[0,33,35,85,175],[0,33,35,85,271],[0,33,35,125,175], [0,33,35,180,181],[0,33,35,181,367],[0,33,35,221,271],[0,33,35,221,367], [0,33,78,82,172],[0,33,78,82,268],[0,33,78,85,175],[0,33,78,85,271], [0,33,78,168,172],[0,33,78,168,175],[0,33,78,264,268],[0,33,78,264,271], [0,33,123,124,125],[0,33,123,124,172],[0,33,123,125,175],[0,33,123,168,172], [0,33,123,168,175],[0,33,180,181,182],[0,33,180,182,368],[0,33,181,182,368], [0,33,181,367,368],[0,33,180,366,368],[0,33,219,220,366],[0,33,219,220,268], [0,33,219,221,271],[0,33,219,221,367],[0,33,219,264,268],[0,33,219,264,271], [0,33,219,366,368],[0,33,219,367,368],[0,90,91,92,95],[90,91,92,95,281], [0,90,91,92,125],[90,91,92,125,311],[90,91,92,278,281],[90,91,92,278,311], [0,90,91,94,95],[90,91,94,95,281],[0,90,91,94,280],[90,91,94,280,281], [0,90,91,124,125],[90,91,124,125,311],[0,90,91,124,172],[90,91,124,172,358], [90,91,124,310,311],[90,91,124,310,358],[0,90,91,171,172],[90,91,171,172,358], [0,90,91,171,357],[90,91,171,357,358],[90,91,277,278,281],[90,91,277,278,311], [0,90,91,277,280],[90,91,277,280,281],[90,91,277,310,311],[90,91,277,310,358], [0,90,91,277,357],[90,91,277,357,358],[0,90,92,95,116],[90,92,95,116,302], [90,92,95,281,302],[0,90,92,116,119],[90,92,116,119,305],[90,92,116,302,305], [0,90,92,119,175],[90,92,119,175,361],[90,92,119,305,361],[0,90,92,125,175], [90,92,125,175,361],[90,92,125,311,361],[90,92,278,281,302],[90,92,278,302,305], [90,92,278,305,361],[90,92,278,311,361],[0,90,93,94,95],[90,93,94,95,281], [0,90,93,94,280],[90,93,94,280,281],[0,90,93,95,116],[90,93,95,116,302], [90,93,95,281,302],[0,90,93,114,116],[90,93,114,116,302],[0,90,93,114,300], [90,93,114,300,302],[0,90,93,279,280],[90,93,279,280,281],[90,93,279,281,302], [0,90,93,279,300],[90,93,279,300,302],[0,90,114,116,119],[90,114,116,119,305], [90,114,116,302,305],[0,90,114,117,119],[90,114,117,119,305],[0,90,114,117,303], [90,114,117,303,305],[90,114,300,302,305],[0,90,114,300,303],[90,114,300,303,305], [0,90,117,119,175],[90,117,119,175,361],[90,117,119,305,361],[0,90,117,168,172], [90,117,168,172,358],[0,90,117,168,175],[90,117,168,175,361],[90,117,168,354,358], [90,117,168,354,361],[0,90,117,171,172],[90,117,171,172,358],[0,90,117,171,357], [90,117,171,357,358],[90,117,303,305,361],[90,117,303,354,358],[90,117,303,354,361], [0,90,117,303,357],[90,117,303,357,358],[0,90,123,124,125],[90,123,124,125,311], [0,90,123,124,172],[90,123,124,172,358],[90,123,124,310,311],[90,123,124,310,358], [0,90,123,125,175],[90,123,125,175,361],[90,123,125,311,361],[0,90,123,168,172], [90,123,168,172,358],[0,90,123,168,175],[90,123,168,175,361],[90,123,168,354,358], [90,123,168,354,361],[90,123,309,310,311],[90,123,309,310,358],[90,123,309,311,361], [90,123,309,354,358],[90,123,309,354,361],[90,276,277,278,281],[90,276,277,278,311], [0,90,276,277,280],[90,276,277,280,281],[90,276,277,310,311],[90,276,277,310,358], [0,90,276,277,357],[90,276,277,357,358],[90,276,278,281,302],[90,276,278,302,305], [90,276,278,305,361],[90,276,278,311,361],[0,90,276,279,280],[90,276,279,280,281], [90,276,279,281,302],[0,90,276,279,300],[90,276,279,300,302],[90,276,300,302,305], [0,90,276,300,303],[90,276,300,303,305],[90,276,303,305,361],[90,276,303,354,358], [90,276,303,354,361],[0,90,276,303,357],[90,276,303,357,358],[90,276,309,310,311], [90,276,309,310,358],[90,276,309,311,361],[90,276,309,354,358],[90,276,309,354,361], [186,187,188,191,281],[186,187,188,191,366],[186,187,188,221,311],[186,187,188,221,366], [186,187,188,278,281],[186,187,188,278,311],[186,187,190,191,281],[0,186,187,190,366], [186,187,190,191,366],[0,186,187,190,280],[186,187,190,280,281],[186,187,220,221,311], [0,186,187,220,366],[186,187,220,221,366],[0,186,187,220,268],[186,187,220,268,358], [186,187,220,310,311],[186,187,220,310,358],[0,186,187,267,268],[186,187,267,268,358], [0,186,187,267,357],[186,187,267,357,358],[186,187,277,278,281],[186,187,277,278,311], [0,186,187,277,280],[186,187,277,280,281],[186,187,277,310,311],[186,187,277,310,358], [0,186,187,277,357],[186,187,277,357,358],[0,186,188,191,212],[186,188,191,212,302], [186,188,191,281,302],[0,186,188,191,367],[186,188,191,366,367],[0,186,188,212,215], [186,188,212,215,305],[186,188,212,302,305],[0,186,188,215,271],[186,188,215,271,361], [186,188,215,305,361],[0,186,188,221,271],[186,188,221,271,361],[186,188,221,311,361], [0,186,188,221,367],[186,188,221,366,367],[186,188,278,281,302],[186,188,278,302,305], [186,188,278,305,361],[186,188,278,311,361],[186,189,190,191,281],[0,186,189,190,366], [186,189,190,191,366],[0,186,189,190,280],[186,189,190,280,281],[0,186,189,191,212], [186,189,191,212,302],[186,189,191,281,302],[0,186,189,191,367],[186,189,191,366,367], [0,186,189,210,212],[186,189,210,212,302],[0,186,189,210,300],[186,189,210,300,302], [0,186,189,279,280],[186,189,279,280,281],[186,189,279,281,302],[0,186,189,279,300], [186,189,279,300,302],[0,186,189,366,368],[0,186,189,367,368],[186,189,366,367,368], [0,186,210,212,215],[186,210,212,215,305],[186,210,212,302,305],[0,186,210,213,215], [186,210,213,215,305],[0,186,210,213,303],[186,210,213,303,305],[186,210,300,302,305], [0,186,210,300,303],[186,210,300,303,305],[0,186,213,215,271],[186,213,215,271,361], [186,213,215,305,361],[0,186,213,264,268],[186,213,264,268,358],[0,186,213,264,271], [186,213,264,271,361],[186,213,264,354,358],[186,213,264,354,361],[0,186,213,267,268], [186,213,267,268,358],[0,186,213,267,357],[186,213,267,357,358],[186,213,303,305,361], [186,213,303,354,358],[186,213,303,354,361],[0,186,213,303,357],[186,213,303,357,358], [186,219,220,221,311],[0,186,219,220,366],[186,219,220,221,366],[0,186,219,220,268], [186,219,220,268,358],[186,219,220,310,311],[186,219,220,310,358],[0,186,219,221,271], [186,219,221,271,361],[186,219,221,311,361],[0,186,219,221,367],[186,219,221,366,367], [0,186,219,264,268],[186,219,264,268,358],[0,186,219,264,271],[186,219,264,271,361], [186,219,264,354,358],[186,219,264,354,361],[186,219,309,310,311],[186,219,309,310,358], [186,219,309,311,361],[186,219,309,354,358],[186,219,309,354,361],[0,186,219,366,368], [0,186,219,367,368],[186,219,366,367,368],[186,276,277,278,281],[186,276,277,278,311], [0,186,276,277,280],[186,276,277,280,281],[186,276,277,310,311],[186,276,277,310,358], [0,186,276,277,357],[186,276,277,357,358],[186,276,278,281,302],[186,276,278,302,305], [186,276,278,305,361],[186,276,278,311,361],[0,186,276,279,280],[186,276,279,280,281], [186,276,279,281,302],[0,186,276,279,300],[186,276,279,300,302],[186,276,300,302,305], [0,186,276,300,303],[186,276,300,303,305],[186,276,303,305,361],[186,276,303,354,358], [186,276,303,354,361],[0,186,276,303,357],[186,276,303,357,358],[186,276,309,310,311], [186,276,309,310,358],[186,276,309,311,361],[186,276,309,354,358],[186,276,309,354,361], [1,2,5,41,131],[2,5,41,131,317],[1,2,5,41,227],[2,5,41,227,317], [1,2,5,95,131],[2,5,95,131,317],[2,5,95,281,317],[1,2,5,191,227], [2,5,191,227,317],[2,5,191,281,317],[1,2,35,85,175],[1,2,35,85,271], [1,2,35,125,175],[1,2,35,221,271],[1,2,38,41,131],[2,38,41,131,317], [1,2,38,41,227],[2,38,41,227,317],[1,2,38,88,178],[1,2,38,88,274], [1,2,38,128,131],[2,38,128,131,317],[1,2,38,128,178],[2,38,128,314,317], [1,2,38,224,227],[2,38,224,227,317],[1,2,38,224,274],[2,38,224,314,317], [1,2,84,85,175],[1,2,84,85,271],[1,2,84,88,178],[1,2,84,88,274], [1,2,84,174,175],[1,2,84,174,178],[1,2,84,270,271],[1,2,84,270,274], [1,2,92,95,131],[2,92,95,131,317],[2,92,95,281,317],[1,2,92,125,175], [1,2,92,128,131],[2,92,128,131,317],[1,2,92,128,178],[2,92,128,314,317], [1,2,92,174,175],[1,2,92,174,178],[2,92,278,281,317],[2,92,278,314,317], [1,2,188,191,227],[2,188,191,227,317],[2,188,191,281,317],[1,2,188,221,271], [1,2,188,224,227],[2,188,224,227,317],[1,2,188,224,274],[2,188,224,314,317], [1,2,188,270,271],[1,2,188,270,274],[2,188,278,281,317],[2,188,278,314,317], [1,4,5,41,131],[1,4,5,41,227],[1,4,5,95,131],[1,4,5,191,227], [1,4,39,41,131],[1,4,39,41,227],[1,4,39,129,131],[1,4,39,129,315], [1,4,39,225,227],[1,4,39,225,315],[1,4,94,95,131],[1,4,94,129,131], [1,4,94,129,315],[1,4,94,280,315],[1,4,190,191,227],[1,4,190,225,227], [1,4,190,225,315],[1,4,190,280,315],[1,34,35,85,175],[1,34,35,85,271], 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