#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_014 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(852,13182,44228,53160,21264) ### ### 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:=[ [0,1,2,5,215],[0,1,2,5,420],[1,2,5,420,846],[1,2,5,431,846], [0,1,2,35,245],[0,1,2,35,420],[1,2,35,420,846],[1,2,35,461,846], [0,1,2,212,215],[0,1,2,212,245],[1,2,428,431,846],[1,2,428,461,846], [0,1,4,5,215],[0,1,4,5,420],[0,1,4,420,846],[1,4,5,420,846], [1,4,5,431,846],[0,1,4,214,215],[0,1,4,214,640],[0,1,4,430,846], [1,4,430,431,846],[0,1,4,430,640],[0,1,34,35,245],[0,1,34,35,420], [0,1,34,420,846],[1,34,35,420,846],[1,34,35,461,846],[0,1,34,202,412], [0,1,34,202,628],[0,1,34,244,245],[0,1,34,244,412],[0,1,34,460,846], [1,34,460,461,846],[0,1,34,460,628],[0,1,201,202,412],[0,1,201,202,628], [0,1,201,411,412],[0,1,201,411,837],[0,1,201,627,628],[0,1,201,627,837], [0,1,211,212,215],[0,1,211,212,245],[0,1,211,214,215],[0,1,211,214,640], [0,1,211,244,245],[0,1,211,244,412],[0,1,211,411,412],[0,1,211,411,837], [0,1,211,637,640],[0,1,211,637,837],[1,427,428,431,846],[1,427,428,461,846], [0,1,427,430,846],[1,427,430,431,846],[0,1,427,430,640],[0,1,427,460,846], [1,427,460,461,846],[0,1,427,460,628],[0,1,427,627,628],[0,1,427,627,837], [0,1,427,637,640],[0,1,427,637,837],[0,2,5,26,236],[2,5,26,236,662], [0,2,5,26,452],[2,5,26,452,662],[0,2,5,215,236],[2,5,215,236,662], [2,5,215,641,662],[0,2,5,420,421],[0,2,5,421,847],[2,5,420,421,847], [2,5,420,846,847],[0,2,5,431,452],[2,5,431,452,662],[2,5,431,641,662], [0,2,5,431,847],[2,5,431,846,847],[0,2,26,29,239],[2,26,29,239,665], [0,2,26,29,455],[2,26,29,455,665],[0,2,26,236,239],[2,26,236,239,665], [2,26,236,662,665],[0,2,26,452,455],[2,26,452,455,665],[2,26,452,662,665], [0,2,29,205,415],[0,2,29,205,631],[0,2,29,239,415],[0,2,29,455,631], [0,2,35,205,415],[0,2,35,205,631],[0,2,35,245,415],[0,2,35,420,421], [0,2,35,421,847],[2,35,420,421,847],[2,35,420,846,847],[0,2,35,461,631], [0,2,35,461,847],[2,35,461,846,847],[0,2,212,215,236],[2,212,215,236,662], [2,212,215,641,662],[0,2,212,236,239],[2,212,236,239,665],[2,212,236,662,665], [0,2,212,239,415],[0,2,212,245,415],[2,212,638,641,662],[2,212,638,662,665], [0,2,428,431,452],[2,428,431,452,662],[2,428,431,641,662],[0,2,428,431,847], [2,428,431,846,847],[0,2,428,452,455],[2,428,452,455,665],[2,428,452,662,665], [0,2,428,455,631],[0,2,428,461,631],[0,2,428,461,847],[2,428,461,846,847], [2,428,638,641,662],[2,428,638,662,665],[0,3,4,5,215],[0,3,4,5,420], [0,3,4,420,846],[0,3,4,214,215],[0,3,4,214,640],[0,3,4,430,846], [0,3,4,430,640],[0,3,5,26,236],[0,3,5,26,452],[0,3,5,215,236], [0,3,5,420,421],[0,3,5,421,847],[0,3,5,431,452],[0,3,5,431,847], [0,3,24,26,236],[0,3,24,26,452],[0,3,24,234,236],[0,3,24,234,660], [0,3,24,450,452],[0,3,24,450,660],[0,3,213,214,215],[0,3,213,214,640], [0,3,213,215,236],[0,3,213,234,236],[0,3,213,234,660],[0,3,213,639,640], [0,3,213,639,660],[0,3,420,421,422],[0,3,420,422,848],[0,3,421,422,848], [0,3,421,847,848],[0,3,420,846,848],[0,3,429,430,846],[0,3,429,430,640], [0,3,429,431,452],[0,3,429,431,847],[0,3,429,450,452],[0,3,429,450,660], [0,3,429,639,640],[0,3,429,639,660],[0,3,429,846,848],[0,3,429,847,848], [0,24,26,29,239],[0,24,26,29,455],[0,24,26,236,239],[0,24,26,452,455], [0,24,27,29,239],[0,24,27,29,455],[0,24,27,237,239],[0,24,27,237,663], [0,24,27,453,455],[0,24,27,453,663],[0,24,234,236,239],[0,24,234,237,239], [0,24,234,237,663],[0,24,234,660,663],[0,24,450,452,455],[0,24,450,453,455], [0,24,450,453,663],[0,24,450,660,663],[0,27,29,205,415],[0,27,29,205,631], [0,27,29,239,415],[0,27,29,455,631],[0,27,198,202,412],[0,27,198,202,628], [0,27,198,205,415],[0,27,198,205,631],[0,27,198,408,412],[0,27,198,408,415], [0,27,198,624,628],[0,27,198,624,631],[0,27,201,202,412],[0,27,201,202,628], [0,27,201,411,412],[0,27,201,411,837],[0,27,201,627,628],[0,27,201,627,837], [0,27,237,239,415],[0,27,237,408,412],[0,27,237,408,415],[0,27,237,411,412], [0,27,237,411,837],[0,27,237,663,837],[0,27,453,455,631],[0,27,453,624,628], [0,27,453,624,631],[0,27,453,627,628],[0,27,453,627,837],[0,27,453,663,837], [0,33,34,35,245],[0,33,34,35,420],[0,33,34,420,846],[0,33,34,202,412], [0,33,34,202,628],[0,33,34,244,245],[0,33,34,244,412],[0,33,34,460,846], [0,33,34,460,628],[0,33,35,205,415],[0,33,35,205,631],[0,33,35,245,415], [0,33,35,420,421],[0,33,35,421,847],[0,33,35,461,631],[0,33,35,461,847], [0,33,198,202,412],[0,33,198,202,628],[0,33,198,205,415],[0,33,198,205,631], [0,33,198,408,412],[0,33,198,408,415],[0,33,198,624,628],[0,33,198,624,631], [0,33,243,244,245],[0,33,243,244,412],[0,33,243,245,415],[0,33,243,408,412], [0,33,243,408,415],[0,33,420,421,422],[0,33,420,422,848],[0,33,421,422,848], [0,33,421,847,848],[0,33,420,846,848],[0,33,459,460,846],[0,33,459,460,628], [0,33,459,461,631],[0,33,459,461,847],[0,33,459,624,628],[0,33,459,624,631], [0,33,459,846,848],[0,33,459,847,848],[0,210,211,212,215],[210,211,212,215,641], [0,210,211,212,245],[210,211,212,245,671],[210,211,212,638,641],[210,211,212,638,671], [0,210,211,214,215],[210,211,214,215,641],[0,210,211,214,640],[210,211,214,640,641], [0,210,211,244,245],[210,211,244,245,671],[0,210,211,244,412],[210,211,244,412,838], [210,211,244,670,671],[210,211,244,670,838],[0,210,211,411,412],[210,211,411,412,838], [0,210,211,411,837],[210,211,411,837,838],[210,211,637,638,641],[210,211,637,638,671], [0,210,211,637,640],[210,211,637,640,641],[210,211,637,670,671],[210,211,637,670,838], [0,210,211,637,837],[210,211,637,837,838],[0,210,212,215,236],[210,212,215,236,662], [210,212,215,641,662],[0,210,212,236,239],[210,212,236,239,665],[210,212,236,662,665], [0,210,212,239,415],[210,212,239,415,841],[210,212,239,665,841],[0,210,212,245,415], [210,212,245,415,841],[210,212,245,671,841],[210,212,638,641,662],[210,212,638,662,665], [210,212,638,665,841],[210,212,638,671,841],[0,210,213,214,215],[210,213,214,215,641], [0,210,213,214,640],[210,213,214,640,641],[0,210,213,215,236],[210,213,215,236,662], [210,213,215,641,662],[0,210,213,234,236],[210,213,234,236,662],[0,210,213,234,660], [210,213,234,660,662],[0,210,213,639,640],[210,213,639,640,641],[210,213,639,641,662], [0,210,213,639,660],[210,213,639,660,662],[0,210,234,236,239],[210,234,236,239,665], [210,234,236,662,665],[0,210,234,237,239],[210,234,237,239,665],[0,210,234,237,663], [210,234,237,663,665],[210,234,660,662,665],[0,210,234,660,663],[210,234,660,663,665], [0,210,237,239,415],[210,237,239,415,841],[210,237,239,665,841],[0,210,237,408,412], [210,237,408,412,838],[0,210,237,408,415],[210,237,408,415,841],[210,237,408,834,838], [210,237,408,834,841],[0,210,237,411,412],[210,237,411,412,838],[0,210,237,411,837], [210,237,411,837,838],[210,237,663,665,841],[210,237,663,834,838],[210,237,663,834,841], [0,210,237,663,837],[210,237,663,837,838],[0,210,243,244,245],[210,243,244,245,671], [0,210,243,244,412],[210,243,244,412,838],[210,243,244,670,671],[210,243,244,670,838], [0,210,243,245,415],[210,243,245,415,841],[210,243,245,671,841],[0,210,243,408,412], [210,243,408,412,838],[0,210,243,408,415],[210,243,408,415,841],[210,243,408,834,838], [210,243,408,834,841],[210,243,669,670,671],[210,243,669,670,838],[210,243,669,671,841], [210,243,669,834,838],[210,243,669,834,841],[210,636,637,638,641],[210,636,637,638,671], [0,210,636,637,640],[210,636,637,640,641],[210,636,637,670,671],[210,636,637,670,838], [0,210,636,637,837],[210,636,637,837,838],[210,636,638,641,662],[210,636,638,662,665], [210,636,638,665,841],[210,636,638,671,841],[0,210,636,639,640],[210,636,639,640,641], [210,636,639,641,662],[0,210,636,639,660],[210,636,639,660,662],[210,636,660,662,665], [0,210,636,660,663],[210,636,660,663,665],[210,636,663,665,841],[210,636,663,834,838], [210,636,663,834,841],[0,210,636,663,837],[210,636,663,837,838],[210,636,669,670,671], [210,636,669,670,838],[210,636,669,671,841],[210,636,669,834,838],[210,636,669,834,841], [426,427,428,431,641],[426,427,428,431,846],[426,427,428,461,671],[426,427,428,461,846], [426,427,428,638,641],[426,427,428,638,671],[426,427,430,431,641],[0,426,427,430,846], [426,427,430,431,846],[0,426,427,430,640],[426,427,430,640,641],[426,427,460,461,671], [0,426,427,460,846],[426,427,460,461,846],[0,426,427,460,628],[426,427,460,628,838], [426,427,460,670,671],[426,427,460,670,838],[0,426,427,627,628],[426,427,627,628,838], [0,426,427,627,837],[426,427,627,837,838],[426,427,637,638,641],[426,427,637,638,671], [0,426,427,637,640],[426,427,637,640,641],[426,427,637,670,671],[426,427,637,670,838], [0,426,427,637,837],[426,427,637,837,838],[0,426,428,431,452],[426,428,431,452,662], [426,428,431,641,662],[0,426,428,431,847],[426,428,431,846,847],[0,426,428,452,455], [426,428,452,455,665],[426,428,452,662,665],[0,426,428,455,631],[426,428,455,631,841], [426,428,455,665,841],[0,426,428,461,631],[426,428,461,631,841],[426,428,461,671,841], [0,426,428,461,847],[426,428,461,846,847],[426,428,638,641,662],[426,428,638,662,665], [426,428,638,665,841],[426,428,638,671,841],[426,429,430,431,641],[0,426,429,430,846], [426,429,430,431,846],[0,426,429,430,640],[426,429,430,640,641],[0,426,429,431,452], [426,429,431,452,662],[426,429,431,641,662],[0,426,429,431,847],[426,429,431,846,847], [0,426,429,450,452],[426,429,450,452,662],[0,426,429,450,660],[426,429,450,660,662], [0,426,429,639,640],[426,429,639,640,641],[426,429,639,641,662],[0,426,429,639,660], [426,429,639,660,662],[0,426,429,846,848],[0,426,429,847,848],[426,429,846,847,848], [0,426,450,452,455],[426,450,452,455,665],[426,450,452,662,665],[0,426,450,453,455], [426,450,453,455,665],[0,426,450,453,663],[426,450,453,663,665],[426,450,660,662,665], [0,426,450,660,663],[426,450,660,663,665],[0,426,453,455,631],[426,453,455,631,841], [426,453,455,665,841],[0,426,453,624,628],[426,453,624,628,838],[0,426,453,624,631], [426,453,624,631,841],[426,453,624,834,838],[426,453,624,834,841],[0,426,453,627,628], [426,453,627,628,838],[0,426,453,627,837],[426,453,627,837,838],[426,453,663,665,841], [426,453,663,834,838],[426,453,663,834,841],[0,426,453,663,837],[426,453,663,837,838], [426,459,460,461,671],[0,426,459,460,846],[426,459,460,461,846],[0,426,459,460,628], [426,459,460,628,838],[426,459,460,670,671],[426,459,460,670,838],[0,426,459,461,631], [426,459,461,631,841],[426,459,461,671,841],[0,426,459,461,847],[426,459,461,846,847], [0,426,459,624,628],[426,459,624,628,838],[0,426,459,624,631],[426,459,624,631,841], [426,459,624,834,838],[426,459,624,834,841],[426,459,669,670,671],[426,459,669,670,838], [426,459,669,671,841],[426,459,669,834,838],[426,459,669,834,841],[0,426,459,846,848], [0,426,459,847,848],[426,459,846,847,848],[426,636,637,638,641],[426,636,637,638,671], [0,426,636,637,640],[426,636,637,640,641],[426,636,637,670,671],[426,636,637,670,838], [0,426,636,637,837],[426,636,637,837,838],[426,636,638,641,662],[426,636,638,662,665], [426,636,638,665,841],[426,636,638,671,841],[0,426,636,639,640],[426,636,639,640,641], [426,636,639,641,662],[0,426,636,639,660],[426,636,639,660,662],[426,636,660,662,665], [0,426,636,660,663],[426,636,660,663,665],[426,636,663,665,841],[426,636,663,834,838], [426,636,663,834,841],[0,426,636,663,837],[426,636,663,837,838],[426,636,669,670,671], [426,636,669,670,838],[426,636,669,671,841],[426,636,669,834,838],[426,636,669,834,841], [1,2,5,41,251],[2,5,41,251,677],[1,2,5,41,467],[2,5,41,467,677], [1,2,5,215,251],[2,5,215,251,677],[2,5,215,641,677],[1,2,5,431,467], [2,5,431,467,677],[2,5,431,641,677],[1,2,35,205,415],[1,2,35,205,631], [1,2,35,245,415],[1,2,35,461,631],[1,2,38,41,251],[2,38,41,251,677], [1,2,38,41,467],[2,38,41,467,677],[1,2,38,208,418],[1,2,38,208,634], [1,2,38,248,251],[2,38,248,251,677],[1,2,38,248,418],[2,38,248,674,677], [1,2,38,464,467],[2,38,464,467,677],[1,2,38,464,634],[2,38,464,674,677], [1,2,204,205,415],[1,2,204,205,631],[1,2,204,208,418],[1,2,204,208,634], [1,2,204,414,415],[1,2,204,414,418],[1,2,204,630,631],[1,2,204,630,634], [1,2,212,215,251],[2,212,215,251,677],[2,212,215,641,677],[1,2,212,245,415], [1,2,212,248,251],[2,212,248,251,677],[1,2,212,248,418],[2,212,248,674,677], [1,2,212,414,415],[1,2,212,414,418],[2,212,638,641,677],[2,212,638,674,677], [1,2,428,431,467],[2,428,431,467,677],[2,428,431,641,677],[1,2,428,461,631], 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