#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_015 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(900,13926,46724,56160,22464) ### ### 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:=[ [0,1,2,5,227],[0,1,2,5,444],[1,2,5,444,894],[1,2,5,455,894], [0,1,2,35,257],[0,1,2,35,444],[1,2,35,444,894],[1,2,35,485,894], [0,1,2,224,227],[0,1,2,224,257],[1,2,452,455,894],[1,2,452,485,894], [0,1,4,5,227],[0,1,4,5,444],[0,1,4,444,894],[1,4,5,444,894], [1,4,5,455,894],[0,1,4,226,227],[0,1,4,226,676],[0,1,4,454,894], [1,4,454,455,894],[0,1,4,454,676],[0,1,34,35,257],[0,1,34,35,444], [0,1,34,444,894],[1,34,35,444,894],[1,34,35,485,894],[0,1,34,214,436], [0,1,34,214,664],[0,1,34,256,257],[0,1,34,256,436],[0,1,34,484,894], [1,34,484,485,894],[0,1,34,484,664],[0,1,213,214,436],[0,1,213,214,664], [0,1,213,435,436],[0,1,213,435,885],[0,1,213,663,664],[0,1,213,663,885], [0,1,223,224,227],[0,1,223,224,257],[0,1,223,226,227],[0,1,223,226,676], [0,1,223,256,257],[0,1,223,256,436],[0,1,223,435,436],[0,1,223,435,885], [0,1,223,673,676],[0,1,223,673,885],[1,451,452,455,894],[1,451,452,485,894], [0,1,451,454,894],[1,451,454,455,894],[0,1,451,454,676],[0,1,451,484,894], [1,451,484,485,894],[0,1,451,484,664],[0,1,451,663,664],[0,1,451,663,885], [0,1,451,673,676],[0,1,451,673,885],[0,2,5,26,248],[2,5,26,248,698], [0,2,5,26,476],[2,5,26,476,698],[0,2,5,227,248],[2,5,227,248,698], [2,5,227,677,698],[0,2,5,444,445],[0,2,5,445,895],[2,5,444,445,895], [2,5,444,894,895],[0,2,5,455,476],[2,5,455,476,698],[2,5,455,677,698], [0,2,5,455,895],[2,5,455,894,895],[0,2,26,29,251],[2,26,29,251,701], [0,2,26,29,479],[2,26,29,479,701],[0,2,26,248,251],[2,26,248,251,701], [2,26,248,698,701],[0,2,26,476,479],[2,26,476,479,701],[2,26,476,698,701], [0,2,29,217,439],[0,2,29,217,667],[0,2,29,251,439],[0,2,29,479,667], [0,2,35,217,439],[0,2,35,217,667],[0,2,35,257,439],[0,2,35,444,445], [0,2,35,445,895],[2,35,444,445,895],[2,35,444,894,895],[0,2,35,485,667], [0,2,35,485,895],[2,35,485,894,895],[0,2,224,227,248],[2,224,227,248,698], [2,224,227,677,698],[0,2,224,248,251],[2,224,248,251,701],[2,224,248,698,701], [0,2,224,251,439],[0,2,224,257,439],[2,224,674,677,698],[2,224,674,698,701], [0,2,452,455,476],[2,452,455,476,698],[2,452,455,677,698],[0,2,452,455,895], [2,452,455,894,895],[0,2,452,476,479],[2,452,476,479,701],[2,452,476,698,701], [0,2,452,479,667],[0,2,452,485,667],[0,2,452,485,895],[2,452,485,894,895], [2,452,674,677,698],[2,452,674,698,701],[0,3,4,5,227],[0,3,4,5,444], [0,3,4,444,894],[0,3,4,226,227],[0,3,4,226,676],[0,3,4,454,894], [0,3,4,454,676],[0,3,5,26,248],[0,3,5,26,476],[0,3,5,227,248], [0,3,5,444,445],[0,3,5,445,895],[0,3,5,455,476],[0,3,5,455,895], [0,3,24,26,248],[0,3,24,26,476],[0,3,24,246,248],[0,3,24,246,696], [0,3,24,474,476],[0,3,24,474,696],[0,3,225,226,227],[0,3,225,226,676], [0,3,225,227,248],[0,3,225,246,248],[0,3,225,246,696],[0,3,225,675,676], [0,3,225,675,696],[0,3,444,445,446],[0,3,444,446,896],[0,3,445,446,896], [0,3,445,895,896],[0,3,444,894,896],[0,3,453,454,894],[0,3,453,454,676], [0,3,453,455,476],[0,3,453,455,895],[0,3,453,474,476],[0,3,453,474,696], [0,3,453,675,676],[0,3,453,675,696],[0,3,453,894,896],[0,3,453,895,896], [0,24,26,29,251],[0,24,26,29,479],[0,24,26,248,251],[0,24,26,476,479], [0,24,27,29,251],[0,24,27,29,479],[0,24,27,249,251],[0,24,27,249,699], [0,24,27,477,479],[0,24,27,477,699],[0,24,246,248,251],[0,24,246,249,251], [0,24,246,249,699],[0,24,246,696,699],[0,24,474,476,479],[0,24,474,477,479], [0,24,474,477,699],[0,24,474,696,699],[0,27,29,217,439],[0,27,29,217,667], [0,27,29,251,439],[0,27,29,479,667],[0,27,210,214,436],[0,27,210,214,664], [0,27,210,217,439],[0,27,210,217,667],[0,27,210,432,436],[0,27,210,432,439], [0,27,210,660,664],[0,27,210,660,667],[0,27,213,214,436],[0,27,213,214,664], [0,27,213,435,436],[0,27,213,435,885],[0,27,213,663,664],[0,27,213,663,885], [0,27,249,251,439],[0,27,249,432,436],[0,27,249,432,439],[0,27,249,435,436], [0,27,249,435,885],[0,27,249,699,885],[0,27,477,479,667],[0,27,477,660,664], [0,27,477,660,667],[0,27,477,663,664],[0,27,477,663,885],[0,27,477,699,885], [0,33,34,35,257],[0,33,34,35,444],[0,33,34,444,894],[0,33,34,214,436], [0,33,34,214,664],[0,33,34,256,257],[0,33,34,256,436],[0,33,34,484,894], [0,33,34,484,664],[0,33,35,217,439],[0,33,35,217,667],[0,33,35,257,439], [0,33,35,444,445],[0,33,35,445,895],[0,33,35,485,667],[0,33,35,485,895], [0,33,210,214,436],[0,33,210,214,664],[0,33,210,217,439],[0,33,210,217,667], [0,33,210,432,436],[0,33,210,432,439],[0,33,210,660,664],[0,33,210,660,667], [0,33,255,256,257],[0,33,255,256,436],[0,33,255,257,439],[0,33,255,432,436], [0,33,255,432,439],[0,33,444,445,446],[0,33,444,446,896],[0,33,445,446,896], [0,33,445,895,896],[0,33,444,894,896],[0,33,483,484,894],[0,33,483,484,664], [0,33,483,485,667],[0,33,483,485,895],[0,33,483,660,664],[0,33,483,660,667], [0,33,483,894,896],[0,33,483,895,896],[0,222,223,224,227],[222,223,224,227,677], [0,222,223,224,257],[222,223,224,257,707],[222,223,224,674,677],[222,223,224,674,707], [0,222,223,226,227],[222,223,226,227,677],[0,222,223,226,676],[222,223,226,676,677], [0,222,223,256,257],[222,223,256,257,707],[0,222,223,256,436],[222,223,256,436,886], [222,223,256,706,707],[222,223,256,706,886],[0,222,223,435,436],[222,223,435,436,886], [0,222,223,435,885],[222,223,435,885,886],[222,223,673,674,677],[222,223,673,674,707], [0,222,223,673,676],[222,223,673,676,677],[222,223,673,706,707],[222,223,673,706,886], [0,222,223,673,885],[222,223,673,885,886],[0,222,224,227,248],[222,224,227,248,698], [222,224,227,677,698],[0,222,224,248,251],[222,224,248,251,701],[222,224,248,698,701], [0,222,224,251,439],[222,224,251,439,889],[222,224,251,701,889],[0,222,224,257,439], [222,224,257,439,889],[222,224,257,707,889],[222,224,674,677,698],[222,224,674,698,701], [222,224,674,701,889],[222,224,674,707,889],[0,222,225,226,227],[222,225,226,227,677], [0,222,225,226,676],[222,225,226,676,677],[0,222,225,227,248],[222,225,227,248,698], [222,225,227,677,698],[0,222,225,246,248],[222,225,246,248,698],[0,222,225,246,696], [222,225,246,696,698],[0,222,225,675,676],[222,225,675,676,677],[222,225,675,677,698], [0,222,225,675,696],[222,225,675,696,698],[0,222,246,248,251],[222,246,248,251,701], [222,246,248,698,701],[0,222,246,249,251],[222,246,249,251,701],[0,222,246,249,699], [222,246,249,699,701],[222,246,696,698,701],[0,222,246,696,699],[222,246,696,699,701], [0,222,249,251,439],[222,249,251,439,889],[222,249,251,701,889],[0,222,249,432,436], [222,249,432,436,886],[0,222,249,432,439],[222,249,432,439,889],[222,249,432,882,886], [222,249,432,882,889],[0,222,249,435,436],[222,249,435,436,886],[0,222,249,435,885], [222,249,435,885,886],[222,249,699,701,889],[222,249,699,882,886],[222,249,699,882,889], [0,222,249,699,885],[222,249,699,885,886],[0,222,255,256,257],[222,255,256,257,707], [0,222,255,256,436],[222,255,256,436,886],[222,255,256,706,707],[222,255,256,706,886], [0,222,255,257,439],[222,255,257,439,889],[222,255,257,707,889],[0,222,255,432,436], [222,255,432,436,886],[0,222,255,432,439],[222,255,432,439,889],[222,255,432,882,886], [222,255,432,882,889],[222,255,705,706,707],[222,255,705,706,886],[222,255,705,707,889], [222,255,705,882,886],[222,255,705,882,889],[222,672,673,674,677],[222,672,673,674,707], [0,222,672,673,676],[222,672,673,676,677],[222,672,673,706,707],[222,672,673,706,886], [0,222,672,673,885],[222,672,673,885,886],[222,672,674,677,698],[222,672,674,698,701], [222,672,674,701,889],[222,672,674,707,889],[0,222,672,675,676],[222,672,675,676,677], [222,672,675,677,698],[0,222,672,675,696],[222,672,675,696,698],[222,672,696,698,701], [0,222,672,696,699],[222,672,696,699,701],[222,672,699,701,889],[222,672,699,882,886], [222,672,699,882,889],[0,222,672,699,885],[222,672,699,885,886],[222,672,705,706,707], [222,672,705,706,886],[222,672,705,707,889],[222,672,705,882,886],[222,672,705,882,889], [450,451,452,455,677],[450,451,452,455,894],[450,451,452,485,707],[450,451,452,485,894], [450,451,452,674,677],[450,451,452,674,707],[450,451,454,455,677],[0,450,451,454,894], [450,451,454,455,894],[0,450,451,454,676],[450,451,454,676,677],[450,451,484,485,707], [0,450,451,484,894],[450,451,484,485,894],[0,450,451,484,664],[450,451,484,664,886], [450,451,484,706,707],[450,451,484,706,886],[0,450,451,663,664],[450,451,663,664,886], [0,450,451,663,885],[450,451,663,885,886],[450,451,673,674,677],[450,451,673,674,707], [0,450,451,673,676],[450,451,673,676,677],[450,451,673,706,707],[450,451,673,706,886], [0,450,451,673,885],[450,451,673,885,886],[0,450,452,455,476],[450,452,455,476,698], [450,452,455,677,698],[0,450,452,455,895],[450,452,455,894,895],[0,450,452,476,479], [450,452,476,479,701],[450,452,476,698,701],[0,450,452,479,667],[450,452,479,667,889], [450,452,479,701,889],[0,450,452,485,667],[450,452,485,667,889],[450,452,485,707,889], [0,450,452,485,895],[450,452,485,894,895],[450,452,674,677,698],[450,452,674,698,701], [450,452,674,701,889],[450,452,674,707,889],[450,453,454,455,677],[0,450,453,454,894], [450,453,454,455,894],[0,450,453,454,676],[450,453,454,676,677],[0,450,453,455,476], [450,453,455,476,698],[450,453,455,677,698],[0,450,453,455,895],[450,453,455,894,895], [0,450,453,474,476],[450,453,474,476,698],[0,450,453,474,696],[450,453,474,696,698], [0,450,453,675,676],[450,453,675,676,677],[450,453,675,677,698],[0,450,453,675,696], [450,453,675,696,698],[0,450,453,894,896],[0,450,453,895,896],[450,453,894,895,896], [0,450,474,476,479],[450,474,476,479,701],[450,474,476,698,701],[0,450,474,477,479], [450,474,477,479,701],[0,450,474,477,699],[450,474,477,699,701],[450,474,696,698,701], [0,450,474,696,699],[450,474,696,699,701],[0,450,477,479,667],[450,477,479,667,889], [450,477,479,701,889],[0,450,477,660,664],[450,477,660,664,886],[0,450,477,660,667], [450,477,660,667,889],[450,477,660,882,886],[450,477,660,882,889],[0,450,477,663,664], [450,477,663,664,886],[0,450,477,663,885],[450,477,663,885,886],[450,477,699,701,889], [450,477,699,882,886],[450,477,699,882,889],[0,450,477,699,885],[450,477,699,885,886], [450,483,484,485,707],[0,450,483,484,894],[450,483,484,485,894],[0,450,483,484,664], [450,483,484,664,886],[450,483,484,706,707],[450,483,484,706,886],[0,450,483,485,667], [450,483,485,667,889],[450,483,485,707,889],[0,450,483,485,895],[450,483,485,894,895], [0,450,483,660,664],[450,483,660,664,886],[0,450,483,660,667],[450,483,660,667,889], [450,483,660,882,886],[450,483,660,882,889],[450,483,705,706,707],[450,483,705,706,886], [450,483,705,707,889],[450,483,705,882,886],[450,483,705,882,889],[0,450,483,894,896], [0,450,483,895,896],[450,483,894,895,896],[450,672,673,674,677],[450,672,673,674,707], [0,450,672,673,676],[450,672,673,676,677],[450,672,673,706,707],[450,672,673,706,886], [0,450,672,673,885],[450,672,673,885,886],[450,672,674,677,698],[450,672,674,698,701], [450,672,674,701,889],[450,672,674,707,889],[0,450,672,675,676],[450,672,675,676,677], [450,672,675,677,698],[0,450,672,675,696],[450,672,675,696,698],[450,672,696,698,701], [0,450,672,696,699],[450,672,696,699,701],[450,672,699,701,889],[450,672,699,882,886], [450,672,699,882,889],[0,450,672,699,885],[450,672,699,885,886],[450,672,705,706,707], [450,672,705,706,886],[450,672,705,707,889],[450,672,705,882,886],[450,672,705,882,889], [1,2,5,41,263],[2,5,41,263,713],[1,2,5,41,491],[2,5,41,491,713], [1,2,5,227,263],[2,5,227,263,713],[2,5,227,677,713],[1,2,5,455,491], [2,5,455,491,713],[2,5,455,677,713],[1,2,35,217,439],[1,2,35,217,667], [1,2,35,257,439],[1,2,35,485,667],[1,2,38,41,263],[2,38,41,263,713], [1,2,38,41,491],[2,38,41,491,713],[1,2,38,220,442],[1,2,38,220,670], [1,2,38,260,263],[2,38,260,263,713],[1,2,38,260,442],[2,38,260,710,713], [1,2,38,488,491],[2,38,488,491,713],[1,2,38,488,670],[2,38,488,710,713], [1,2,216,217,439],[1,2,216,217,667],[1,2,216,220,442],[1,2,216,220,670], [1,2,216,438,439],[1,2,216,438,442],[1,2,216,666,667],[1,2,216,666,670], [1,2,224,227,263],[2,224,227,263,713],[2,224,227,677,713],[1,2,224,257,439], [1,2,224,260,263],[2,224,260,263,713],[1,2,224,260,442],[2,224,260,710,713], [1,2,224,438,439],[1,2,224,438,442],[2,224,674,677,713],[2,224,674,710,713], [1,2,452,455,491],[2,452,455,491,713],[2,452,455,677,713],[1,2,452,485,667], [1,2,452,488,491],[2,452,488,491,713],[1,2,452,488,670],[2,452,488,710,713], [1,2,452,666,667],[1,2,452,666,670],[2,452,674,677,713],[2,452,674,710,713], [1,4,5,41,263],[1,4,5,41,491],[1,4,5,227,263],[1,4,5,455,491], [1,4,39,41,263],[1,4,39,41,491],[1,4,39,261,263],[1,4,39,261,711], [1,4,39,489,491],[1,4,39,489,711],[1,4,226,227,263],[1,4,226,261,263], [1,4,226,261,711],[1,4,226,676,711],[1,4,454,455,491],[1,4,454,489,491], [1,4,454,489,711],[1,4,454,676,711],[1,34,35,217,439],[1,34,35,217,667], [1,34,35,257,439],[1,34,35,485,667],[1,34,211,214,436],[1,34,211,214,664], [1,34,211,217,439],[1,34,211,217,667],[1,34,211,433,436],[1,34,211,433,439], [1,34,211,661,664],[1,34,211,661,667],[1,34,256,257,439],[1,34,256,433,436], [1,34,256,433,439],[1,34,484,485,667],[1,34,484,661,664],[1,34,484,661,667], [1,36,38,41,263],[1,36,38,41,491],[1,36,38,220,442],[1,36,38,220,670], [1,36,38,260,263],[1,36,38,260,442],[1,36,38,488,491],[1,36,38,488,670], 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[207,657,879,880,891],[657,879,880,891,892],[207,657,879,881,891],[657,879,881,891,892] ];