#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_015 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(896,13494,45036,54060,21624) ### ### 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:=[ [0,1,2,5,449],[0,1,2,35,479],[0,1,2,446,449],[0,1,2,446,479], [0,1,4,5,449],[0,1,4,226,670],[0,1,4,448,449],[0,1,4,448,670], [0,1,34,35,479],[0,1,34,214,436],[0,1,34,214,658],[0,1,34,256,436], [0,1,34,478,479],[0,1,34,478,658],[0,1,213,214,436],[0,1,213,214,658], [0,1,213,435,436],[0,1,213,435,879],[0,1,213,657,658],[0,1,213,657,879], [0,1,223,226,670],[0,1,223,256,436],[0,1,223,435,436],[0,1,223,435,879], [0,1,223,667,670],[0,1,223,667,879],[0,1,445,446,449],[0,1,445,446,479], [0,1,445,448,449],[0,1,445,448,670],[0,1,445,478,479],[0,1,445,478,658], [0,1,445,657,658],[0,1,445,657,879],[0,1,445,667,670],[0,1,445,667,879], [0,2,5,26,248],[2,5,26,248,692],[0,2,5,26,470],[2,5,26,470,692], [0,2,5,227,248],[2,5,227,248,692],[2,5,227,671,692],[0,2,5,449,470], [2,5,449,470,692],[2,5,449,671,692],[0,2,26,29,251],[2,26,29,251,695], [0,2,26,29,473],[2,26,29,473,695],[0,2,26,248,251],[2,26,248,251,695], [2,26,248,692,695],[0,2,26,470,473],[2,26,470,473,695],[2,26,470,692,695], [0,2,29,217,439],[0,2,29,217,661],[0,2,29,251,439],[0,2,29,473,661], [0,2,35,217,439],[0,2,35,217,661],[0,2,35,257,439],[0,2,35,479,661], [0,2,224,227,248],[2,224,227,248,692],[2,224,227,671,692],[0,2,224,248,251], [2,224,248,251,695],[2,224,248,692,695],[0,2,224,251,439],[0,2,224,257,439], [2,224,668,671,692],[2,224,668,692,695],[0,2,446,449,470],[2,446,449,470,692], [2,446,449,671,692],[0,2,446,470,473],[2,446,470,473,695],[2,446,470,692,695], [0,2,446,473,661],[0,2,446,479,661],[2,446,668,671,692],[2,446,668,692,695], [0,3,4,5,449],[0,3,4,226,670],[0,3,4,448,449],[0,3,4,448,670], [0,3,5,26,248],[0,3,5,26,470],[0,3,5,227,248],[0,3,5,449,470], [0,3,24,26,248],[0,3,24,26,470],[0,3,24,246,248],[0,3,24,246,690], [0,3,24,468,470],[0,3,24,468,690],[0,3,225,226,670],[0,3,225,227,248], [0,3,225,246,248],[0,3,225,246,690],[0,3,225,669,670],[0,3,225,669,690], [0,3,447,448,449],[0,3,447,448,670],[0,3,447,449,470],[0,3,447,468,470], [0,3,447,468,690],[0,3,447,669,670],[0,3,447,669,690],[0,24,26,29,251], [0,24,26,29,473],[0,24,26,248,251],[0,24,26,470,473],[0,24,27,29,251], [0,24,27,29,473],[0,24,27,249,251],[0,24,27,249,693],[0,24,27,471,473], [0,24,27,471,693],[0,24,246,248,251],[0,24,246,249,251],[0,24,246,249,693], [0,24,246,690,693],[0,24,468,470,473],[0,24,468,471,473],[0,24,468,471,693], [0,24,468,690,693],[0,27,29,217,439],[0,27,29,217,661],[0,27,29,251,439], [0,27,29,473,661],[0,27,210,214,436],[0,27,210,214,658],[0,27,210,217,439], [0,27,210,217,661],[0,27,210,432,436],[0,27,210,432,439],[0,27,210,654,658], [0,27,210,654,661],[0,27,213,214,436],[0,27,213,214,658],[0,27,213,435,436], [0,27,213,435,879],[0,27,213,657,658],[0,27,213,657,879],[0,27,249,251,439], [0,27,249,432,436],[0,27,249,432,439],[0,27,249,435,436],[0,27,249,435,879], [0,27,249,693,879],[0,27,471,473,661],[0,27,471,654,658],[0,27,471,654,661], [0,27,471,657,658],[0,27,471,657,879],[0,27,471,693,879],[0,33,34,35,479], [0,33,34,214,436],[0,33,34,214,658],[0,33,34,256,436],[0,33,34,478,479], [0,33,34,478,658],[0,33,35,217,439],[0,33,35,217,661],[0,33,35,257,439], [0,33,35,479,661],[0,33,210,214,436],[0,33,210,214,658],[0,33,210,217,439], [0,33,210,217,661],[0,33,210,432,436],[0,33,210,432,439],[0,33,210,654,658], [0,33,210,654,661],[0,33,255,256,436],[0,33,255,257,439],[0,33,255,432,436], [0,33,255,432,439],[0,33,477,478,479],[0,33,477,478,658],[0,33,477,479,661], [0,33,477,654,658],[0,33,477,654,661],[222,223,224,227,671],[222,223,224,257,701], [222,223,224,668,671],[222,223,224,668,701],[222,223,226,227,671],[0,222,223,226,670], [222,223,226,670,671],[222,223,256,257,701],[0,222,223,256,436],[222,223,256,436,880], [222,223,256,700,701],[222,223,256,700,880],[0,222,223,435,436],[222,223,435,436,880], [0,222,223,435,879],[222,223,435,879,880],[222,223,667,668,671],[222,223,667,668,701], [0,222,223,667,670],[222,223,667,670,671],[222,223,667,700,701],[222,223,667,700,880], [0,222,223,667,879],[222,223,667,879,880],[0,222,224,227,248],[222,224,227,248,692], [222,224,227,671,692],[0,222,224,248,251],[222,224,248,251,695],[222,224,248,692,695], [0,222,224,251,439],[222,224,251,439,883],[222,224,251,695,883],[0,222,224,257,439], [222,224,257,439,883],[222,224,257,701,883],[222,224,668,671,692],[222,224,668,692,695], [222,224,668,695,883],[222,224,668,701,883],[222,225,226,227,671],[0,222,225,226,670], [222,225,226,670,671],[0,222,225,227,248],[222,225,227,248,692],[222,225,227,671,692], [0,222,225,246,248],[222,225,246,248,692],[0,222,225,246,690],[222,225,246,690,692], [0,222,225,669,670],[222,225,669,670,671],[222,225,669,671,692],[0,222,225,669,690], [222,225,669,690,692],[0,222,246,248,251],[222,246,248,251,695],[222,246,248,692,695], [0,222,246,249,251],[222,246,249,251,695],[0,222,246,249,693],[222,246,249,693,695], [222,246,690,692,695],[0,222,246,690,693],[222,246,690,693,695],[0,222,249,251,439], [222,249,251,439,883],[222,249,251,695,883],[0,222,249,432,436],[222,249,432,436,880], [0,222,249,432,439],[222,249,432,439,883],[222,249,432,876,880],[222,249,432,876,883], [0,222,249,435,436],[222,249,435,436,880],[0,222,249,435,879],[222,249,435,879,880], [222,249,693,695,883],[222,249,693,876,880],[222,249,693,876,883],[0,222,249,693,879], [222,249,693,879,880],[222,255,256,257,701],[0,222,255,256,436],[222,255,256,436,880], [222,255,256,700,701],[222,255,256,700,880],[0,222,255,257,439],[222,255,257,439,883], [222,255,257,701,883],[0,222,255,432,436],[222,255,432,436,880],[0,222,255,432,439], [222,255,432,439,883],[222,255,432,876,880],[222,255,432,876,883],[222,255,699,700,701], [222,255,699,700,880],[222,255,699,701,883],[222,255,699,876,880],[222,255,699,876,883], [222,666,667,668,671],[222,666,667,668,701],[0,222,666,667,670],[222,666,667,670,671], [222,666,667,700,701],[222,666,667,700,880],[0,222,666,667,879],[222,666,667,879,880], [222,666,668,671,692],[222,666,668,692,695],[222,666,668,695,883],[222,666,668,701,883], [0,222,666,669,670],[222,666,669,670,671],[222,666,669,671,692],[0,222,666,669,690], [222,666,669,690,692],[222,666,690,692,695],[0,222,666,690,693],[222,666,690,693,695], [222,666,693,695,883],[222,666,693,876,880],[222,666,693,876,883],[0,222,666,693,879], [222,666,693,879,880],[222,666,699,700,701],[222,666,699,700,880],[222,666,699,701,883], [222,666,699,876,880],[222,666,699,876,883],[0,444,445,446,449],[444,445,446,449,671], [0,444,445,446,479],[444,445,446,479,701],[444,445,446,668,671],[444,445,446,668,701], [0,444,445,448,449],[444,445,448,449,671],[0,444,445,448,670],[444,445,448,670,671], [0,444,445,478,479],[444,445,478,479,701],[0,444,445,478,658],[444,445,478,658,880], [444,445,478,700,701],[444,445,478,700,880],[0,444,445,657,658],[444,445,657,658,880], [0,444,445,657,879],[444,445,657,879,880],[444,445,667,668,671],[444,445,667,668,701], [0,444,445,667,670],[444,445,667,670,671],[444,445,667,700,701],[444,445,667,700,880], [0,444,445,667,879],[444,445,667,879,880],[0,444,446,449,470],[444,446,449,470,692], [444,446,449,671,692],[0,444,446,470,473],[444,446,470,473,695],[444,446,470,692,695], [0,444,446,473,661],[444,446,473,661,883],[444,446,473,695,883],[0,444,446,479,661], [444,446,479,661,883],[444,446,479,701,883],[444,446,668,671,692],[444,446,668,692,695], [444,446,668,695,883],[444,446,668,701,883],[0,444,447,448,449],[444,447,448,449,671], [0,444,447,448,670],[444,447,448,670,671],[0,444,447,449,470],[444,447,449,470,692], [444,447,449,671,692],[0,444,447,468,470],[444,447,468,470,692],[0,444,447,468,690], [444,447,468,690,692],[0,444,447,669,670],[444,447,669,670,671],[444,447,669,671,692], [0,444,447,669,690],[444,447,669,690,692],[0,444,468,470,473],[444,468,470,473,695], [444,468,470,692,695],[0,444,468,471,473],[444,468,471,473,695],[0,444,468,471,693], [444,468,471,693,695],[444,468,690,692,695],[0,444,468,690,693],[444,468,690,693,695], [0,444,471,473,661],[444,471,473,661,883],[444,471,473,695,883],[0,444,471,654,658], [444,471,654,658,880],[0,444,471,654,661],[444,471,654,661,883],[444,471,654,876,880], [444,471,654,876,883],[0,444,471,657,658],[444,471,657,658,880],[0,444,471,657,879], [444,471,657,879,880],[444,471,693,695,883],[444,471,693,876,880],[444,471,693,876,883], [0,444,471,693,879],[444,471,693,879,880],[0,444,477,478,479],[444,477,478,479,701], [0,444,477,478,658],[444,477,478,658,880],[444,477,478,700,701],[444,477,478,700,880], [0,444,477,479,661],[444,477,479,661,883],[444,477,479,701,883],[0,444,477,654,658], [444,477,654,658,880],[0,444,477,654,661],[444,477,654,661,883],[444,477,654,876,880], [444,477,654,876,883],[444,477,699,700,701],[444,477,699,700,880],[444,477,699,701,883], [444,477,699,876,880],[444,477,699,876,883],[444,666,667,668,671],[444,666,667,668,701], [0,444,666,667,670],[444,666,667,670,671],[444,666,667,700,701],[444,666,667,700,880], [0,444,666,667,879],[444,666,667,879,880],[444,666,668,671,692],[444,666,668,692,695], [444,666,668,695,883],[444,666,668,701,883],[0,444,666,669,670],[444,666,669,670,671], [444,666,669,671,692],[0,444,666,669,690],[444,666,669,690,692],[444,666,690,692,695], [0,444,666,690,693],[444,666,690,693,695],[444,666,693,695,883],[444,666,693,876,880], [444,666,693,876,883],[0,444,666,693,879],[444,666,693,879,880],[444,666,699,700,701], [444,666,699,700,880],[444,666,699,701,883],[444,666,699,876,880],[444,666,699,876,883], [1,2,5,41,263],[2,5,41,263,707],[1,2,5,41,485],[2,5,41,485,707], [1,2,5,227,263],[2,5,227,263,707],[2,5,227,671,707],[1,2,5,449,485], [2,5,449,485,707],[2,5,449,671,707],[1,2,35,217,439],[1,2,35,217,661], [1,2,35,257,439],[1,2,35,479,661],[1,2,38,41,263],[2,38,41,263,707], [1,2,38,41,485],[2,38,41,485,707],[1,2,38,220,442],[1,2,38,220,664], [1,2,38,260,263],[2,38,260,263,707],[1,2,38,260,442],[2,38,260,704,707], [1,2,38,482,485],[2,38,482,485,707],[1,2,38,482,664],[2,38,482,704,707], [1,2,216,217,439],[1,2,216,217,661],[1,2,216,220,442],[1,2,216,220,664], [1,2,216,438,439],[1,2,216,438,442],[1,2,216,660,661],[1,2,216,660,664], [1,2,224,227,263],[2,224,227,263,707],[2,224,227,671,707],[1,2,224,257,439], [1,2,224,260,263],[2,224,260,263,707],[1,2,224,260,442],[2,224,260,704,707], [1,2,224,438,439],[1,2,224,438,442],[2,224,668,671,707],[2,224,668,704,707], [1,2,446,449,485],[2,446,449,485,707],[2,446,449,671,707],[1,2,446,479,661], [1,2,446,482,485],[2,446,482,485,707],[1,2,446,482,664],[2,446,482,704,707], [1,2,446,660,661],[1,2,446,660,664],[2,446,668,671,707],[2,446,668,704,707], [1,4,5,41,263],[1,4,5,41,485],[1,4,5,227,263],[1,4,5,449,485], [1,4,39,41,263],[1,4,39,41,485],[1,4,39,261,263],[1,4,39,261,705], [1,4,39,483,485],[1,4,39,483,705],[1,4,226,227,263],[1,4,226,261,263], [1,4,226,261,705],[1,4,226,670,705],[1,4,448,449,485],[1,4,448,483,485], [1,4,448,483,705],[1,4,448,670,705],[1,34,35,217,439],[1,34,35,217,661], [1,34,35,257,439],[1,34,35,479,661],[1,34,211,214,436],[1,34,211,214,658], [1,34,211,217,439],[1,34,211,217,661],[1,34,211,433,436],[1,34,211,433,439], [1,34,211,655,658],[1,34,211,655,661],[1,34,256,257,439],[1,34,256,433,436], [1,34,256,433,439],[1,34,478,479,661],[1,34,478,655,658],[1,34,478,655,661], [1,36,38,41,263],[1,36,38,41,485],[1,36,38,220,442],[1,36,38,220,664], [1,36,38,260,263],[1,36,38,260,442],[1,36,38,482,485],[1,36,38,482,664], [1,36,39,41,263],[1,36,39,41,485],[1,36,39,261,263],[1,36,39,261,705], [1,36,39,483,485],[1,36,39,483,705],[1,36,211,214,436],[1,36,211,214,658], [1,36,211,217,439],[1,36,211,217,661],[1,36,211,433,436],[1,36,211,433,439], [1,36,211,655,658],[1,36,211,655,661],[1,36,213,214,436],[1,36,213,214,658], [1,36,213,435,436],[1,36,213,435,879],[1,36,213,657,658],[1,36,213,657,879], [1,36,216,217,439],[1,36,216,217,661],[1,36,216,220,442],[1,36,216,220,664], [1,36,216,438,439],[1,36,216,438,442],[1,36,216,660,661],[1,36,216,660,664], [1,36,258,260,263],[1,36,258,260,442],[1,36,258,261,263],[1,36,258,261,705], [1,36,258,433,436],[1,36,258,433,439],[1,36,258,435,436],[1,36,258,435,879], [1,36,258,438,439],[1,36,258,438,442],[1,36,258,702,705],[1,36,258,702,879], [1,36,480,482,485],[1,36,480,482,664],[1,36,480,483,485],[1,36,480,483,705], [1,36,480,655,658],[1,36,480,655,661],[1,36,480,657,658],[1,36,480,657,879], [1,36,480,660,661],[1,36,480,660,664],[1,36,480,702,705],[1,36,480,702,879], [1,223,224,227,263],[223,224,227,263,707],[223,224,227,671,707],[1,223,224,257,439], [223,224,257,439,883],[223,224,257,701,883],[1,223,224,260,263],[223,224,260,263,707], [1,223,224,260,442],[223,224,260,442,886],[223,224,260,704,707],[223,224,260,704,886], [1,223,224,438,439],[223,224,438,439,883],[1,223,224,438,442],[223,224,438,442,886], [223,224,438,882,883],[223,224,438,882,886],[223,224,668,671,707],[223,224,668,701,883], [223,224,668,704,707],[223,224,668,704,886],[223,224,668,882,883],[223,224,668,882,886], [1,223,226,227,263],[223,226,227,263,707],[223,226,227,671,707],[1,223,226,261,263], [223,226,261,263,707],[1,223,226,261,705],[223,226,261,705,707],[223,226,670,671,707], [1,223,226,670,705],[223,226,670,705,707],[1,223,256,257,439],[223,256,257,439,883], [223,256,257,701,883],[1,223,256,433,436],[223,256,433,436,880],[1,223,256,433,439], 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