#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### LIBRARY OF TRIANGULATIONS ### ### by Bruno Benedetti and Frank H. Lutz ### ### http://page.math.tu-berlin.de/~lutz/stellar/library_of_triangulations.html ### ### ### ### ### ### name of example: ### ### ### ### BH_5 ### ### ### ### ### ### description: ### ### ### ### triangulation of Bing's House with five rooms ### ### ### ### ### ### properties: ### ### ### ### f=(71,250,180), ### ### H_*=(Z,0,0), ### ### contractible, but not collapsible, ### ### optimal discrete Morse vector: (1,1,1), not perfect ### ### ### ### ### ### references: ### ### ### ### B. Benedetti, C. Lai, D. Lofano, F. H. Lutz. ### ### Random simple-homotopy theory. ### ### Arxiv:2107.09862 (2021). ### ### ### ### M. Tancer. ### ### Recognition of collapsible complexes is NP-complete. ### ### Discrete Comput. Geom. 55, 21-38 (2016). ### ### ### ### R. H. Bing. ### ### Some aspects of the topology of 3-manifolds related ### ### to the Poincaré conjecture. ### ### Lectures on Modern Mathematics, Vol. II, Wiley, NY, 1964. ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [ 1, 2, 5 ], [ 1, 2, 25 ], [ 1, 2, 27 ], [ 1, 2, 54 ], [ 1, 4, 6 ], [ 1, 4, 10 ], [ 1, 4, 36 ], [ 1, 4, 63 ], [ 1, 5, 7 ], [ 1, 6, 7 ], [ 1, 9, 11 ], [ 1, 9, 15 ], [ 1, 9, 27 ], [ 1, 9, 45 ], [ 1, 10, 12 ], [ 1, 11, 12 ], [ 1, 14, 16 ], [ 1, 14, 20 ], [ 1, 14, 36 ], [ 1, 14, 54 ], [ 1, 15, 17 ], [ 1, 16, 17 ], [ 1, 19, 21 ], [ 1, 19, 24 ], [ 1, 19, 45 ], [ 1, 19, 63 ], [ 1, 20, 22 ], [ 1, 21, 22 ], [ 1, 24, 26 ], [ 1, 25, 26 ], [ 2, 3, 5 ], [ 2, 3, 28 ], [ 2, 3, 66 ], [ 2, 5, 28 ], [ 2, 27, 28 ], [ 2, 54, 62 ], [ 2, 61, 62 ], [ 2, 65, 66 ], [ 3, 4, 6 ], [ 3, 4, 29 ], [ 3, 4, 70 ], [ 3, 5, 6 ], [ 3, 28, 29 ], [ 3, 66, 70 ], [ 4, 8, 10 ], [ 4, 8, 30 ], [ 4, 8, 37 ], [ 4, 10, 37 ], [ 4, 29, 30 ], [ 4, 36, 37 ], [ 4, 63, 71 ], [ 4, 70, 71 ], [ 5, 6, 31 ], [ 5, 7, 31 ], [ 5, 28, 31 ], [ 6, 7, 32 ], [ 6, 31, 32 ], [ 7, 31, 33 ], [ 7, 32, 33 ], [ 8, 9, 11 ], [ 8, 9, 34 ], [ 8, 9, 38 ], [ 8, 10, 11 ], [ 8, 30, 34 ], [ 8, 37, 38 ], [ 9, 13, 15 ], [ 9, 13, 39 ], [ 9, 13, 46 ], [ 9, 15, 46 ], [ 9, 27, 35 ], [ 9, 34, 35 ], [ 9, 38, 39 ], [ 9, 45, 46 ], [ 10, 11, 40 ], [ 10, 12, 40 ], [ 10, 37, 40 ], [ 11, 12, 41 ], [ 11, 40, 41 ], [ 12, 40, 42 ], [ 12, 41, 42 ], [ 13, 14, 16 ], [ 13, 14, 43 ], [ 13, 14, 47 ], [ 13, 15, 16 ], [ 13, 39, 43 ], [ 13, 46, 47 ], [ 14, 18, 20 ], [ 14, 18, 48 ], [ 14, 18, 55 ], [ 14, 20, 55 ], [ 14, 36, 44 ], [ 14, 43, 44 ], [ 14, 47, 48 ], [ 14, 54, 55 ], [ 15, 16, 49 ], [ 15, 17, 49 ], [ 15, 46, 49 ], [ 16, 17, 50 ], [ 16, 49, 50 ], [ 17, 49, 51 ], [ 17, 50, 51 ], [ 18, 19, 21 ], [ 18, 19, 52 ], [ 18, 19, 56 ], [ 18, 20, 21 ], [ 18, 48, 52 ], [ 18, 55, 56 ], [ 19, 23, 24 ], [ 19, 23, 57 ], [ 19, 23, 64 ], [ 19, 24, 64 ], [ 19, 45, 53 ], [ 19, 52, 53 ], [ 19, 56, 57 ], [ 19, 63, 64 ], [ 20, 21, 58 ], [ 20, 22, 58 ], [ 20, 55, 58 ], [ 21, 22, 59 ], [ 21, 58, 59 ], [ 22, 58, 60 ], [ 22, 59, 60 ], [ 23, 2, 25 ], [ 23, 2, 61 ], [ 23, 2, 65 ], [ 23, 24, 25 ], [ 23, 57, 61 ], [ 23, 64, 65 ], [ 24, 25, 67 ], [ 24, 26, 67 ], [ 24, 64, 67 ], [ 25, 26, 68 ], [ 25, 67, 68 ], [ 26, 67, 69 ], [ 26, 68, 69 ], [ 27, 28, 31 ], [ 27, 30, 32 ], [ 27, 30, 34 ], [ 27, 31, 33 ], [ 27, 32, 33 ], [ 27, 34, 35 ], [ 28, 29, 31 ], [ 29, 30, 32 ], [ 29, 31, 32 ], [ 36, 37, 40 ], [ 36, 39, 41 ], [ 36, 39, 43 ], [ 36, 40, 42 ], [ 36, 41, 42 ], [ 36, 43, 44 ], [ 37, 38, 40 ], [ 38, 39, 41 ], [ 38, 40, 41 ], [ 45, 46, 49 ], [ 45, 48, 50 ], [ 45, 48, 52 ], [ 45, 49, 51 ], [ 45, 50, 51 ], [ 45, 52, 53 ], [ 46, 47, 49 ], [ 47, 48, 50 ], [ 47, 49, 50 ], [ 54, 55, 58 ], [ 54, 57, 59 ], [ 54, 57, 61 ], [ 54, 58, 60 ], [ 54, 59, 60 ], [ 54, 61, 62 ], [ 55, 56, 58 ], [ 56, 57, 59 ], [ 56, 58, 59 ], [ 63, 64, 67 ], [ 63, 66, 68 ], [ 63, 66, 70 ], [ 63, 67, 69 ], [ 63, 68, 69 ], [ 63, 70, 71 ], [ 64, 65, 67 ], [ 65, 66, 68 ], [ 65, 67, 68 ] ];