#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### 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_3 ### ### ### ### ### ### description: ### ### ### ### triangulation of Bing's House with three rooms ### ### ### ### ### ### properties: ### ### ### ### f=(43,150,108), ### ### 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, 15 ], [ 1, 2, 17 ], [ 1, 2, 26 ], [ 1, 4, 6 ], [ 1, 4, 10 ], [ 1, 4, 26 ], [ 1, 4, 35 ], [ 1, 5, 7 ], [ 1, 6, 7 ], [ 1, 9, 11 ], [ 1, 9, 14 ], [ 1, 9, 17 ], [ 1, 9, 35 ], [ 1, 10, 12 ], [ 1, 11, 12 ], [ 1, 14, 16 ], [ 1, 15, 16 ], [ 2, 3, 5 ], [ 2, 3, 18 ], [ 2, 3, 38 ], [ 2, 5, 18 ], [ 2, 17, 18 ], [ 2, 26, 34 ], [ 2, 33, 34 ], [ 2, 37, 38 ], [ 3, 4, 6 ], [ 3, 4, 19 ], [ 3, 4, 42 ], [ 3, 5, 6 ], [ 3, 18, 19 ], [ 3, 38, 42 ], [ 4, 8, 10 ], [ 4, 8, 20 ], [ 4, 8, 27 ], [ 4, 10, 27 ], [ 4, 19, 20 ], [ 4, 26, 27 ], [ 4, 35, 43 ], [ 4, 42, 43 ], [ 5, 6, 21 ], [ 5, 7, 21 ], [ 5, 18, 21 ], [ 6, 7, 22 ], [ 6, 21, 22 ], [ 7, 21, 23 ], [ 7, 22, 23 ], [ 8, 9, 11 ], [ 8, 9, 24 ], [ 8, 9, 28 ], [ 8, 10, 11 ], [ 8, 20, 24 ], [ 8, 27, 28 ], [ 9, 13, 14 ], [ 9, 13, 29 ], [ 9, 13, 36 ], [ 9, 14, 36 ], [ 9, 17, 25 ], [ 9, 24, 25 ], [ 9, 28, 29 ], [ 9, 35, 36 ], [ 10, 11, 30 ], [ 10, 12, 30 ], [ 10, 27, 30 ], [ 11, 12, 31 ], [ 11, 30, 31 ], [ 12, 30, 32 ], [ 12, 31, 32 ], [ 13, 2, 15 ], [ 13, 2, 33 ], [ 13, 2, 37 ], [ 13, 14, 15 ], [ 13, 29, 33 ], [ 13, 36, 37 ], [ 14, 15, 39 ], [ 14, 16, 39 ], [ 14, 36, 39 ], [ 15, 16, 40 ], [ 15, 39, 40 ], [ 16, 39, 41 ], [ 16, 40, 41 ], [ 17, 18, 21 ], [ 17, 20, 22 ], [ 17, 20, 24 ], [ 17, 21, 23 ], [ 17, 22, 23 ], [ 17, 24, 25 ], [ 18, 19, 21 ], [ 19, 20, 22 ], [ 19, 21, 22 ], [ 26, 27, 30 ], [ 26, 29, 31 ], [ 26, 29, 33 ], [ 26, 30, 32 ], [ 26, 31, 32 ], [ 26, 33, 34 ], [ 27, 28, 30 ], [ 28, 29, 31 ], [ 28, 30, 31 ], [ 35, 36, 39 ], [ 35, 38, 40 ], [ 35, 38, 42 ], [ 35, 39, 41 ], [ 35, 40, 41 ], [ 35, 42, 43 ], [ 36, 37, 39 ], [ 37, 38, 40 ], [ 37, 39, 40 ] ];