#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_013 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(804,12438,41732,50160,20064) ### ### 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:=[ [0,1,2,5,203],[0,1,2,5,396],[1,2,5,396,798],[1,2,5,407,798], [0,1,2,35,233],[0,1,2,35,396],[1,2,35,396,798],[1,2,35,437,798], [0,1,2,200,203],[0,1,2,200,233],[1,2,404,407,798],[1,2,404,437,798], [0,1,4,5,203],[0,1,4,5,396],[0,1,4,396,798],[1,4,5,396,798], [1,4,5,407,798],[0,1,4,202,203],[0,1,4,202,604],[0,1,4,406,798], [1,4,406,407,798],[0,1,4,406,604],[0,1,34,35,233],[0,1,34,35,396], [0,1,34,396,798],[1,34,35,396,798],[1,34,35,437,798],[0,1,34,190,388], [0,1,34,190,592],[0,1,34,232,233],[0,1,34,232,388],[0,1,34,436,798], [1,34,436,437,798],[0,1,34,436,592],[0,1,189,190,388],[0,1,189,190,592], [0,1,189,387,388],[0,1,189,387,789],[0,1,189,591,592],[0,1,189,591,789], [0,1,199,200,203],[0,1,199,200,233],[0,1,199,202,203],[0,1,199,202,604], [0,1,199,232,233],[0,1,199,232,388],[0,1,199,387,388],[0,1,199,387,789], [0,1,199,601,604],[0,1,199,601,789],[1,403,404,407,798],[1,403,404,437,798], [0,1,403,406,798],[1,403,406,407,798],[0,1,403,406,604],[0,1,403,436,798], [1,403,436,437,798],[0,1,403,436,592],[0,1,403,591,592],[0,1,403,591,789], [0,1,403,601,604],[0,1,403,601,789],[0,2,5,26,224],[2,5,26,224,626], [0,2,5,26,428],[2,5,26,428,626],[0,2,5,203,224],[2,5,203,224,626], [2,5,203,605,626],[0,2,5,396,397],[0,2,5,397,799],[2,5,396,397,799], [2,5,396,798,799],[0,2,5,407,428],[2,5,407,428,626],[2,5,407,605,626], [0,2,5,407,799],[2,5,407,798,799],[0,2,26,29,227],[2,26,29,227,629], [0,2,26,29,431],[2,26,29,431,629],[0,2,26,224,227],[2,26,224,227,629], [2,26,224,626,629],[0,2,26,428,431],[2,26,428,431,629],[2,26,428,626,629], [0,2,29,193,391],[0,2,29,193,595],[0,2,29,227,391],[0,2,29,431,595], [0,2,35,193,391],[0,2,35,193,595],[0,2,35,233,391],[0,2,35,396,397], [0,2,35,397,799],[2,35,396,397,799],[2,35,396,798,799],[0,2,35,437,595], [0,2,35,437,799],[2,35,437,798,799],[0,2,200,203,224],[2,200,203,224,626], [2,200,203,605,626],[0,2,200,224,227],[2,200,224,227,629],[2,200,224,626,629], [0,2,200,227,391],[0,2,200,233,391],[2,200,602,605,626],[2,200,602,626,629], [0,2,404,407,428],[2,404,407,428,626],[2,404,407,605,626],[0,2,404,407,799], [2,404,407,798,799],[0,2,404,428,431],[2,404,428,431,629],[2,404,428,626,629], [0,2,404,431,595],[0,2,404,437,595],[0,2,404,437,799],[2,404,437,798,799], [2,404,602,605,626],[2,404,602,626,629],[0,3,4,5,203],[0,3,4,5,396], [0,3,4,396,798],[0,3,4,202,203],[0,3,4,202,604],[0,3,4,406,798], [0,3,4,406,604],[0,3,5,26,224],[0,3,5,26,428],[0,3,5,203,224], [0,3,5,396,397],[0,3,5,397,799],[0,3,5,407,428],[0,3,5,407,799], [0,3,24,26,224],[0,3,24,26,428],[0,3,24,222,224],[0,3,24,222,624], [0,3,24,426,428],[0,3,24,426,624],[0,3,201,202,203],[0,3,201,202,604], [0,3,201,203,224],[0,3,201,222,224],[0,3,201,222,624],[0,3,201,603,604], [0,3,201,603,624],[0,3,396,397,398],[0,3,396,398,800],[0,3,397,398,800], [0,3,397,799,800],[0,3,396,798,800],[0,3,405,406,798],[0,3,405,406,604], [0,3,405,407,428],[0,3,405,407,799],[0,3,405,426,428],[0,3,405,426,624], [0,3,405,603,604],[0,3,405,603,624],[0,3,405,798,800],[0,3,405,799,800], [0,24,26,29,227],[0,24,26,29,431],[0,24,26,224,227],[0,24,26,428,431], [0,24,27,29,227],[0,24,27,29,431],[0,24,27,225,227],[0,24,27,225,627], [0,24,27,429,431],[0,24,27,429,627],[0,24,222,224,227],[0,24,222,225,227], [0,24,222,225,627],[0,24,222,624,627],[0,24,426,428,431],[0,24,426,429,431], [0,24,426,429,627],[0,24,426,624,627],[0,27,29,193,391],[0,27,29,193,595], [0,27,29,227,391],[0,27,29,431,595],[0,27,186,190,388],[0,27,186,190,592], [0,27,186,193,391],[0,27,186,193,595],[0,27,186,384,388],[0,27,186,384,391], [0,27,186,588,592],[0,27,186,588,595],[0,27,189,190,388],[0,27,189,190,592], [0,27,189,387,388],[0,27,189,387,789],[0,27,189,591,592],[0,27,189,591,789], [0,27,225,227,391],[0,27,225,384,388],[0,27,225,384,391],[0,27,225,387,388], [0,27,225,387,789],[0,27,225,627,789],[0,27,429,431,595],[0,27,429,588,592], [0,27,429,588,595],[0,27,429,591,592],[0,27,429,591,789],[0,27,429,627,789], [0,33,34,35,233],[0,33,34,35,396],[0,33,34,396,798],[0,33,34,190,388], [0,33,34,190,592],[0,33,34,232,233],[0,33,34,232,388],[0,33,34,436,798], [0,33,34,436,592],[0,33,35,193,391],[0,33,35,193,595],[0,33,35,233,391], [0,33,35,396,397],[0,33,35,397,799],[0,33,35,437,595],[0,33,35,437,799], [0,33,186,190,388],[0,33,186,190,592],[0,33,186,193,391],[0,33,186,193,595], [0,33,186,384,388],[0,33,186,384,391],[0,33,186,588,592],[0,33,186,588,595], [0,33,231,232,233],[0,33,231,232,388],[0,33,231,233,391],[0,33,231,384,388], [0,33,231,384,391],[0,33,396,397,398],[0,33,396,398,800],[0,33,397,398,800], [0,33,397,799,800],[0,33,396,798,800],[0,33,435,436,798],[0,33,435,436,592], [0,33,435,437,595],[0,33,435,437,799],[0,33,435,588,592],[0,33,435,588,595], [0,33,435,798,800],[0,33,435,799,800],[0,198,199,200,203],[198,199,200,203,605], [0,198,199,200,233],[198,199,200,233,635],[198,199,200,602,605],[198,199,200,602,635], [0,198,199,202,203],[198,199,202,203,605],[0,198,199,202,604],[198,199,202,604,605], [0,198,199,232,233],[198,199,232,233,635],[0,198,199,232,388],[198,199,232,388,790], [198,199,232,634,635],[198,199,232,634,790],[0,198,199,387,388],[198,199,387,388,790], [0,198,199,387,789],[198,199,387,789,790],[198,199,601,602,605],[198,199,601,602,635], [0,198,199,601,604],[198,199,601,604,605],[198,199,601,634,635],[198,199,601,634,790], [0,198,199,601,789],[198,199,601,789,790],[0,198,200,203,224],[198,200,203,224,626], [198,200,203,605,626],[0,198,200,224,227],[198,200,224,227,629],[198,200,224,626,629], [0,198,200,227,391],[198,200,227,391,793],[198,200,227,629,793],[0,198,200,233,391], [198,200,233,391,793],[198,200,233,635,793],[198,200,602,605,626],[198,200,602,626,629], [198,200,602,629,793],[198,200,602,635,793],[0,198,201,202,203],[198,201,202,203,605], [0,198,201,202,604],[198,201,202,604,605],[0,198,201,203,224],[198,201,203,224,626], [198,201,203,605,626],[0,198,201,222,224],[198,201,222,224,626],[0,198,201,222,624], [198,201,222,624,626],[0,198,201,603,604],[198,201,603,604,605],[198,201,603,605,626], [0,198,201,603,624],[198,201,603,624,626],[0,198,222,224,227],[198,222,224,227,629], [198,222,224,626,629],[0,198,222,225,227],[198,222,225,227,629],[0,198,222,225,627], [198,222,225,627,629],[198,222,624,626,629],[0,198,222,624,627],[198,222,624,627,629], [0,198,225,227,391],[198,225,227,391,793],[198,225,227,629,793],[0,198,225,384,388], [198,225,384,388,790],[0,198,225,384,391],[198,225,384,391,793],[198,225,384,786,790], [198,225,384,786,793],[0,198,225,387,388],[198,225,387,388,790],[0,198,225,387,789], [198,225,387,789,790],[198,225,627,629,793],[198,225,627,786,790],[198,225,627,786,793], [0,198,225,627,789],[198,225,627,789,790],[0,198,231,232,233],[198,231,232,233,635], [0,198,231,232,388],[198,231,232,388,790],[198,231,232,634,635],[198,231,232,634,790], [0,198,231,233,391],[198,231,233,391,793],[198,231,233,635,793],[0,198,231,384,388], [198,231,384,388,790],[0,198,231,384,391],[198,231,384,391,793],[198,231,384,786,790], [198,231,384,786,793],[198,231,633,634,635],[198,231,633,634,790],[198,231,633,635,793], [198,231,633,786,790],[198,231,633,786,793],[198,600,601,602,605],[198,600,601,602,635], [0,198,600,601,604],[198,600,601,604,605],[198,600,601,634,635],[198,600,601,634,790], [0,198,600,601,789],[198,600,601,789,790],[198,600,602,605,626],[198,600,602,626,629], [198,600,602,629,793],[198,600,602,635,793],[0,198,600,603,604],[198,600,603,604,605], [198,600,603,605,626],[0,198,600,603,624],[198,600,603,624,626],[198,600,624,626,629], [0,198,600,624,627],[198,600,624,627,629],[198,600,627,629,793],[198,600,627,786,790], [198,600,627,786,793],[0,198,600,627,789],[198,600,627,789,790],[198,600,633,634,635], [198,600,633,634,790],[198,600,633,635,793],[198,600,633,786,790],[198,600,633,786,793], [402,403,404,407,605],[402,403,404,407,798],[402,403,404,437,635],[402,403,404,437,798], [402,403,404,602,605],[402,403,404,602,635],[402,403,406,407,605],[0,402,403,406,798], [402,403,406,407,798],[0,402,403,406,604],[402,403,406,604,605],[402,403,436,437,635], [0,402,403,436,798],[402,403,436,437,798],[0,402,403,436,592],[402,403,436,592,790], [402,403,436,634,635],[402,403,436,634,790],[0,402,403,591,592],[402,403,591,592,790], [0,402,403,591,789],[402,403,591,789,790],[402,403,601,602,605],[402,403,601,602,635], [0,402,403,601,604],[402,403,601,604,605],[402,403,601,634,635],[402,403,601,634,790], [0,402,403,601,789],[402,403,601,789,790],[0,402,404,407,428],[402,404,407,428,626], [402,404,407,605,626],[0,402,404,407,799],[402,404,407,798,799],[0,402,404,428,431], [402,404,428,431,629],[402,404,428,626,629],[0,402,404,431,595],[402,404,431,595,793], [402,404,431,629,793],[0,402,404,437,595],[402,404,437,595,793],[402,404,437,635,793], [0,402,404,437,799],[402,404,437,798,799],[402,404,602,605,626],[402,404,602,626,629], [402,404,602,629,793],[402,404,602,635,793],[402,405,406,407,605],[0,402,405,406,798], [402,405,406,407,798],[0,402,405,406,604],[402,405,406,604,605],[0,402,405,407,428], [402,405,407,428,626],[402,405,407,605,626],[0,402,405,407,799],[402,405,407,798,799], [0,402,405,426,428],[402,405,426,428,626],[0,402,405,426,624],[402,405,426,624,626], [0,402,405,603,604],[402,405,603,604,605],[402,405,603,605,626],[0,402,405,603,624], [402,405,603,624,626],[0,402,405,798,800],[0,402,405,799,800],[402,405,798,799,800], [0,402,426,428,431],[402,426,428,431,629],[402,426,428,626,629],[0,402,426,429,431], [402,426,429,431,629],[0,402,426,429,627],[402,426,429,627,629],[402,426,624,626,629], [0,402,426,624,627],[402,426,624,627,629],[0,402,429,431,595],[402,429,431,595,793], [402,429,431,629,793],[0,402,429,588,592],[402,429,588,592,790],[0,402,429,588,595], [402,429,588,595,793],[402,429,588,786,790],[402,429,588,786,793],[0,402,429,591,592], [402,429,591,592,790],[0,402,429,591,789],[402,429,591,789,790],[402,429,627,629,793], [402,429,627,786,790],[402,429,627,786,793],[0,402,429,627,789],[402,429,627,789,790], [402,435,436,437,635],[0,402,435,436,798],[402,435,436,437,798],[0,402,435,436,592], [402,435,436,592,790],[402,435,436,634,635],[402,435,436,634,790],[0,402,435,437,595], [402,435,437,595,793],[402,435,437,635,793],[0,402,435,437,799],[402,435,437,798,799], [0,402,435,588,592],[402,435,588,592,790],[0,402,435,588,595],[402,435,588,595,793], [402,435,588,786,790],[402,435,588,786,793],[402,435,633,634,635],[402,435,633,634,790], [402,435,633,635,793],[402,435,633,786,790],[402,435,633,786,793],[0,402,435,798,800], [0,402,435,799,800],[402,435,798,799,800],[402,600,601,602,605],[402,600,601,602,635], [0,402,600,601,604],[402,600,601,604,605],[402,600,601,634,635],[402,600,601,634,790], [0,402,600,601,789],[402,600,601,789,790],[402,600,602,605,626],[402,600,602,626,629], [402,600,602,629,793],[402,600,602,635,793],[0,402,600,603,604],[402,600,603,604,605], [402,600,603,605,626],[0,402,600,603,624],[402,600,603,624,626],[402,600,624,626,629], [0,402,600,624,627],[402,600,624,627,629],[402,600,627,629,793],[402,600,627,786,790], [402,600,627,786,793],[0,402,600,627,789],[402,600,627,789,790],[402,600,633,634,635], [402,600,633,634,790],[402,600,633,635,793],[402,600,633,786,790],[402,600,633,786,793], [1,2,5,41,239],[2,5,41,239,641],[1,2,5,41,443],[2,5,41,443,641], [1,2,5,203,239],[2,5,203,239,641],[2,5,203,605,641],[1,2,5,407,443], [2,5,407,443,641],[2,5,407,605,641],[1,2,35,193,391],[1,2,35,193,595], [1,2,35,233,391],[1,2,35,437,595],[1,2,38,41,239],[2,38,41,239,641], [1,2,38,41,443],[2,38,41,443,641],[1,2,38,196,394],[1,2,38,196,598], [1,2,38,236,239],[2,38,236,239,641],[1,2,38,236,394],[2,38,236,638,641], [1,2,38,440,443],[2,38,440,443,641],[1,2,38,440,598],[2,38,440,638,641], [1,2,192,193,391],[1,2,192,193,595],[1,2,192,196,394],[1,2,192,196,598], [1,2,192,390,391],[1,2,192,390,394],[1,2,192,594,595],[1,2,192,594,598], [1,2,200,203,239],[2,200,203,239,641],[2,200,203,605,641],[1,2,200,233,391], [1,2,200,236,239],[2,200,236,239,641],[1,2,200,236,394],[2,200,236,638,641], [1,2,200,390,391],[1,2,200,390,394],[2,200,602,605,641],[2,200,602,638,641], [1,2,404,407,443],[2,404,407,443,641],[2,404,407,605,641],[1,2,404,437,595], [1,2,404,440,443],[2,404,440,443,641],[1,2,404,440,598],[2,404,440,638,641], [1,2,404,594,595],[1,2,404,594,598],[2,404,602,605,641],[2,404,602,638,641], [1,4,5,41,239],[1,4,5,41,443],[1,4,5,203,239],[1,4,5,407,443], [1,4,39,41,239],[1,4,39,41,443],[1,4,39,237,239],[1,4,39,237,639], [1,4,39,441,443],[1,4,39,441,639],[1,4,202,203,239],[1,4,202,237,239], [1,4,202,237,639],[1,4,202,604,639],[1,4,406,407,443],[1,4,406,441,443], [1,4,406,441,639],[1,4,406,604,639],[1,34,35,193,391],[1,34,35,193,595], [1,34,35,233,391],[1,34,35,437,595],[1,34,187,190,388],[1,34,187,190,592], [1,34,187,193,391],[1,34,187,193,595],[1,34,187,385,388],[1,34,187,385,391], [1,34,187,589,592],[1,34,187,589,595],[1,34,232,233,391],[1,34,232,385,388], [1,34,232,385,391],[1,34,436,437,595],[1,34,436,589,592],[1,34,436,589,595], [1,36,38,41,239],[1,36,38,41,443],[1,36,38,196,394],[1,36,38,196,598], [1,36,38,236,239],[1,36,38,236,394],[1,36,38,440,443],[1,36,38,440,598], [1,36,39,41,239],[1,36,39,41,443],[1,36,39,237,239],[1,36,39,237,639], [1,36,39,441,443],[1,36,39,441,639],[1,36,187,190,388],[1,36,187,190,592], [1,36,187,193,391],[1,36,187,193,595],[1,36,187,385,388],[1,36,187,385,391], [1,36,187,589,592],[1,36,187,589,595],[1,36,189,190,388],[1,36,189,190,592], [1,36,189,387,388],[1,36,189,387,789],[1,36,189,591,592],[1,36,189,591,789], [1,36,192,193,391],[1,36,192,193,595],[1,36,192,196,394],[1,36,192,196,598], [1,36,192,390,391],[1,36,192,390,394],[1,36,192,594,595],[1,36,192,594,598], [1,36,234,236,239],[1,36,234,236,394],[1,36,234,237,239],[1,36,234,237,639], [1,36,234,385,388],[1,36,234,385,391],[1,36,234,387,388],[1,36,234,387,789], [1,36,234,390,391],[1,36,234,390,394],[1,36,234,636,639],[1,36,234,636,789], [1,36,438,440,443],[1,36,438,440,598],[1,36,438,441,443],[1,36,438,441,639], [1,36,438,589,592],[1,36,438,589,595],[1,36,438,591,592],[1,36,438,591,789], [1,36,438,594,595],[1,36,438,594,598],[1,36,438,636,639],[1,36,438,636,789], [1,199,200,203,239],[199,200,203,239,641],[199,200,203,605,641],[1,199,200,233,391], [199,200,233,391,793],[199,200,233,635,793],[1,199,200,236,239],[199,200,236,239,641], [1,199,200,236,394],[199,200,236,394,796],[199,200,236,638,641],[199,200,236,638,796], [1,199,200,390,391],[199,200,390,391,793],[1,199,200,390,394],[199,200,390,394,796], [199,200,390,792,793],[199,200,390,792,796],[199,200,602,605,641],[199,200,602,635,793], [199,200,602,638,641],[199,200,602,638,796],[199,200,602,792,793],[199,200,602,792,796], [1,199,202,203,239],[199,202,203,239,641],[199,202,203,605,641],[1,199,202,237,239], [199,202,237,239,641],[1,199,202,237,639],[199,202,237,639,641],[199,202,604,605,641], [1,199,202,604,639],[199,202,604,639,641],[1,199,232,233,391],[199,232,233,391,793], [199,232,233,635,793],[1,199,232,385,388],[199,232,385,388,790],[1,199,232,385,391], [199,232,385,391,793],[199,232,385,787,790],[199,232,385,787,793],[199,232,634,635,793], 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