#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### 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: ### ### ### ### hyperbolic_dodecahedral_space ### ### ### ### ### ### description: ### ### ### ### smallest known triangulation of the hyperbolic dodecahedral space ### ### with 21 vertices ### ### ### ### ### ### properties: ### ### ### ### f=(21,190,338,169), ### ### H_*=(Z,Z_5^3,0,Z), ### ### admits discrete Morse vector: (1,4,4,1), ### ### best known lower bound: (1,3,3,1) ### ### ### ### ### ### references: ### ### ### ### C. Weber and H. Seifert. ### ### Die beiden Dodekaederräume. ### ### Math. Z. 37, 237-253 (1933). ### ### ### ### A. Björner and F. H. Lutz. ### ### Simplicial manifolds, bistellar flips and a 16-vertex ### ### triangulation of the Poincaré homology 3-sphere. ### ### Exp. Math. 9, 275-289 (2000). ### ### ### ### F. H. Lutz, T. Sulanke, and E. Swartz. ### ### f-vectors of 3-manifolds. ### ### Electron. J. Comb. 16, No. 2, Research Paper R13, 33 p. (2009). ### ### ### ### B. Benedetti and F. H. Lutz. ### ### Random discrete Morse theory and a new library of triangulations. ### ### Exp. Math. 23, 66-94 (2014). ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [ 1, 2, 3, 4 ], [ 1, 2, 3, 5 ], [ 1, 2, 4, 6 ], [ 1, 2, 5, 6 ], [ 1, 3, 4, 7 ], [ 1, 3, 5, 8 ], [ 1, 3, 7, 8 ], [ 1, 4, 6, 9 ], [ 1, 4, 7, 9 ], [ 1, 5, 6, 10 ], [ 1, 5, 8, 10 ], [ 1, 6, 9, 11 ], [ 1, 6, 10, 11 ], [ 1, 7, 8, 12 ], [ 1, 7, 9, 12 ], [ 1, 8, 10, 13 ], [ 1, 8, 12, 13 ], [ 1, 9, 11, 14 ], [ 1, 9, 12, 15 ], [ 1, 9, 14, 15 ], [ 1, 10, 11, 16 ], [ 1, 10, 13, 17 ], [ 1, 10, 16, 18 ], [ 1, 10, 17, 18 ], [ 1, 11, 14, 16 ], [ 1, 12, 13, 15 ], [ 1, 13, 15, 17 ], [ 1, 14, 15, 19 ], [ 1, 14, 16, 19 ], [ 1, 15, 17, 19 ], [ 1, 16, 18, 19 ], [ 1, 17, 18, 19 ], [ 2, 3, 4, 20 ], [ 2, 3, 5, 15 ], [ 2, 3, 15, 20 ], [ 2, 4, 6, 16 ], [ 2, 4, 12, 14 ], [ 2, 4, 12, 16 ], [ 2, 4, 14, 20 ], [ 2, 5, 6, 19 ], [ 2, 5, 9, 15 ], [ 2, 5, 9, 19 ], [ 2, 6, 16, 17 ], [ 2, 6, 17, 19 ], [ 2, 8, 10, 13 ], [ 2, 8, 10, 21 ], [ 2, 8, 11, 13 ], [ 2, 8, 11, 18 ], [ 2, 8, 18, 21 ], [ 2, 9, 10, 13 ], [ 2, 9, 10, 21 ], [ 2, 9, 13, 19 ], [ 2, 9, 15, 21 ], [ 2, 11, 12, 16 ], [ 2, 11, 12, 18 ], [ 2, 11, 13, 19 ], [ 2, 11, 16, 17 ], [ 2, 11, 17, 19 ], [ 2, 12, 14, 18 ], [ 2, 14, 18, 21 ], [ 2, 14, 20, 21 ], [ 2, 15, 20, 21 ], [ 3, 4, 7, 11 ], [ 3, 4, 11, 20 ], [ 3, 5, 8, 17 ], [ 3, 5, 14, 15 ], [ 3, 5, 14, 17 ], [ 3, 6, 7, 11 ], [ 3, 6, 7, 16 ], [ 3, 6, 11, 20 ], [ 3, 6, 12, 18 ], [ 3, 6, 12, 20 ], [ 3, 6, 16, 18 ], [ 3, 7, 8, 19 ], [ 3, 7, 16, 19 ], [ 3, 8, 9, 17 ], [ 3, 8, 9, 19 ], [ 3, 9, 13, 17 ], [ 3, 9, 13, 19 ], [ 3, 10, 12, 14 ], [ 3, 10, 12, 20 ], [ 3, 10, 14, 15 ], [ 3, 10, 15, 20 ], [ 3, 12, 14, 18 ], [ 3, 13, 14, 17 ], [ 3, 13, 14, 21 ], [ 3, 13, 19, 21 ], [ 3, 14, 18, 21 ], [ 3, 16, 18, 19 ], [ 3, 18, 19, 21 ], [ 4, 5, 10, 19 ], [ 4, 5, 10, 21 ], [ 4, 5, 11, 20 ], [ 4, 5, 11, 21 ], [ 4, 5, 19, 20 ], [ 4, 6, 8, 9 ], [ 4, 6, 8, 13 ], [ 4, 6, 13, 16 ], [ 4, 7, 9, 18 ], [ 4, 7, 11, 18 ], [ 4, 8, 9, 18 ], [ 4, 8, 11, 13 ], [ 4, 8, 11, 18 ], [ 4, 10, 12, 14 ], [ 4, 10, 12, 21 ], [ 4, 10, 14, 19 ], [ 4, 11, 13, 21 ], [ 4, 12, 16, 21 ], [ 4, 13, 16, 21 ], [ 4, 14, 19, 20 ], [ 5, 6, 10, 19 ], [ 5, 8, 10, 21 ], [ 5, 8, 17, 21 ], [ 5, 9, 11, 14 ], [ 5, 9, 11, 20 ], [ 5, 9, 14, 15 ], [ 5, 9, 19, 20 ], [ 5, 11, 14, 17 ], [ 5, 11, 17, 21 ], [ 6, 7, 11, 15 ], [ 6, 7, 15, 17 ], [ 6, 7, 16, 17 ], [ 6, 8, 9, 20 ], [ 6, 8, 12, 13 ], [ 6, 8, 12, 20 ], [ 6, 9, 11, 20 ], [ 6, 10, 11, 15 ], [ 6, 10, 15, 19 ], [ 6, 12, 13, 18 ], [ 6, 13, 16, 18 ], [ 6, 15, 17, 19 ], [ 7, 8, 12, 20 ], [ 7, 8, 19, 20 ], [ 7, 9, 10, 12 ], [ 7, 9, 10, 18 ], [ 7, 10, 12, 20 ], [ 7, 10, 18, 20 ], [ 7, 11, 15, 18 ], [ 7, 13, 14, 17 ], [ 7, 13, 14, 20 ], [ 7, 13, 15, 17 ], [ 7, 13, 15, 18 ], [ 7, 13, 18, 20 ], [ 7, 14, 16, 17 ], [ 7, 14, 16, 19 ], [ 7, 14, 19, 20 ], [ 8, 9, 17, 18 ], [ 8, 9, 19, 20 ], [ 8, 17, 18, 21 ], [ 9, 10, 12, 21 ], [ 9, 10, 13, 17 ], [ 9, 10, 17, 18 ], [ 9, 12, 15, 21 ], [ 10, 11, 15, 16 ], [ 10, 14, 15, 19 ], [ 10, 15, 16, 20 ], [ 10, 16, 18, 20 ], [ 11, 12, 15, 16 ], [ 11, 12, 15, 18 ], [ 11, 13, 19, 21 ], [ 11, 14, 16, 17 ], [ 11, 17, 19, 21 ], [ 12, 13, 15, 18 ], [ 12, 15, 16, 21 ], [ 13, 14, 20, 21 ], [ 13, 16, 18, 20 ], [ 13, 16, 20, 21 ], [ 15, 16, 20, 21 ], [ 17, 18, 19, 21 ] ];