#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### 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: ### ### ### ### HMT_8 ### ### ### ### ### ### description: ### ### ### ### 2-dimensional simplicial complex with torsion ### ### derived from a valid sequence for the Hadamard matrix H(8) ### ### ### ### ### ### properties: ### ### ### ### f=(39,258,220), ### ### H_*=(Z,(Z_2)^3 * (Z_4)^3 * Z_8,0), ### ### perfect discrete Morse vector: (1,7,7) ### ### ### ### ### ### references: ### ### ### ### D. Lofano and F. H. Lutz. ### ### Hadamard matrix torsion. ### ### Arxiv:2109.13052 (2021). ### ### ### ### J. J. Sylvester. ### ### Thoughts on inverse orthogonal matrices, simultaneous sign successions, ### ### and tessellated pavements in two or more colours, with applications to ### ### Newton's rule, ornamental tile-work, and the theory of numbers. ### ### The London, Edinburgh and Dublin Philosophical Magazine and Journal ### ### of Science 34, 461-475(1867). ### ### ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [ 0, 1, 4 ], [ 0, 1, 6 ], [ 0, 1, 12 ], [ 0, 1, 14 ], [ 0, 1, 20 ], [ 0, 1, 22 ], [ 0, 1, 28 ], [ 0, 1, 30 ], [ 0, 2, 3 ], [ 0, 2, 5 ], [ 0, 2, 11 ], [ 0, 2, 13 ], [ 0, 2, 19 ], [ 0, 2, 21 ], [ 0, 2, 27 ], [ 0, 2, 29 ], [ 0, 3, 6 ], [ 0, 3, 8 ], [ 0, 3, 16 ], [ 0, 3, 26 ], [ 0, 4, 5 ], [ 0, 4, 9 ], [ 0, 4, 17 ], [ 0, 4, 23 ], [ 0, 5, 8 ], [ 0, 5, 16 ], [ 0, 5, 26 ], [ 0, 6, 9 ], [ 0, 6, 17 ], [ 0, 6, 23 ], [ 0, 7, 10 ], [ 0, 7, 12 ], [ 0, 7, 14 ], [ 0, 7, 28 ], [ 0, 7, 30 ], [ 0, 8, 9 ], [ 0, 8, 19 ], [ 0, 8, 21 ], [ 0, 9, 20 ], [ 0, 9, 22 ], [ 0, 10, 11 ], [ 0, 10, 13 ], [ 0, 10, 27 ], [ 0, 10, 29 ], [ 0, 11, 14 ], [ 0, 11, 16 ], [ 0, 11, 24 ], [ 0, 12, 13 ], [ 0, 12, 17 ], [ 0, 12, 25 ], [ 0, 13, 16 ], [ 0, 13, 24 ], [ 0, 14, 17 ], [ 0, 14, 25 ], [ 0, 15, 18 ], [ 0, 15, 20 ], [ 0, 15, 22 ], [ 0, 15, 28 ], [ 0, 15, 30 ], [ 0, 16, 17 ], [ 0, 18, 19 ], [ 0, 18, 21 ], [ 0, 18, 27 ], [ 0, 18, 29 ], [ 0, 19, 22 ], [ 0, 19, 24 ], [ 0, 20, 21 ], [ 0, 20, 25 ], [ 0, 21, 24 ], [ 0, 22, 25 ], [ 0, 23, 26 ], [ 0, 23, 28 ], [ 0, 23, 30 ], [ 0, 24, 25 ], [ 0, 26, 27 ], [ 0, 26, 29 ], [ 0, 27, 30 ], [ 0, 28, 29 ], [ 1, 2, 31 ], [ 1, 2, 32 ], [ 1, 2, 33 ], [ 1, 2, 34 ], [ 1, 2, 35 ], [ 1, 2, 36 ], [ 1, 2, 37 ], [ 1, 2, 38 ], [ 1, 4, 38 ], [ 1, 6, 37 ], [ 1, 12, 36 ], [ 1, 14, 35 ], [ 1, 20, 34 ], [ 1, 22, 33 ], [ 1, 28, 32 ], [ 1, 30, 31 ], [ 2, 3, 32 ], [ 2, 5, 31 ], [ 2, 11, 33 ], [ 2, 13, 34 ], [ 2, 19, 35 ], [ 2, 21, 36 ], [ 2, 27, 38 ], [ 2, 29, 37 ], [ 3, 4, 5 ], [ 3, 4, 32 ], [ 3, 4, 34 ], [ 3, 4, 36 ], [ 3, 4, 38 ], [ 3, 5, 6 ], [ 3, 8, 34 ], [ 3, 16, 36 ], [ 3, 26, 38 ], [ 4, 9, 32 ], [ 4, 17, 34 ], [ 4, 23, 36 ], [ 5, 6, 31 ], [ 5, 6, 33 ], [ 5, 6, 35 ], [ 5, 6, 37 ], [ 5, 8, 33 ], [ 5, 16, 35 ], [ 5, 26, 37 ], [ 6, 9, 31 ], [ 6, 17, 33 ], [ 6, 23, 35 ], [ 7, 8, 9 ], [ 7, 8, 33 ], [ 7, 8, 34 ], [ 7, 8, 37 ], [ 7, 8, 38 ], [ 7, 9, 10 ], [ 7, 12, 33 ], [ 7, 14, 34 ], [ 7, 28, 38 ], [ 7, 30, 37 ], [ 8, 19, 37 ], [ 8, 21, 38 ], [ 9, 10, 31 ], [ 9, 10, 32 ], [ 9, 10, 35 ], [ 9, 10, 36 ], [ 9, 20, 35 ], [ 9, 22, 36 ], [ 10, 11, 32 ], [ 10, 13, 31 ], [ 10, 27, 35 ], [ 10, 29, 36 ], [ 11, 12, 13 ], [ 11, 12, 32 ], [ 11, 12, 33 ], [ 11, 12, 36 ], [ 11, 12, 37 ], [ 11, 13, 14 ], [ 11, 16, 37 ], [ 11, 24, 36 ], [ 12, 17, 32 ], [ 12, 25, 37 ], [ 13, 14, 31 ], [ 13, 14, 34 ], [ 13, 14, 35 ], [ 13, 14, 38 ], [ 13, 16, 38 ], [ 13, 24, 35 ], [ 14, 17, 31 ], [ 14, 25, 38 ], [ 15, 16, 17 ], [ 15, 16, 35 ], [ 15, 16, 36 ], [ 15, 16, 37 ], [ 15, 16, 38 ], [ 15, 17, 18 ], [ 15, 20, 37 ], [ 15, 22, 38 ], [ 15, 28, 35 ], [ 15, 30, 36 ], [ 17, 18, 31 ], [ 17, 18, 32 ], [ 17, 18, 33 ], [ 17, 18, 34 ], [ 18, 19, 32 ], [ 18, 21, 31 ], [ 18, 27, 33 ], [ 18, 29, 34 ], [ 19, 20, 21 ], [ 19, 20, 32 ], [ 19, 20, 34 ], [ 19, 20, 35 ], [ 19, 20, 37 ], [ 19, 21, 22 ], [ 19, 24, 34 ], [ 20, 25, 32 ], [ 21, 22, 31 ], [ 21, 22, 33 ], [ 21, 22, 36 ], [ 21, 22, 38 ], [ 21, 24, 33 ], [ 22, 25, 31 ], [ 23, 24, 25 ], [ 23, 24, 33 ], [ 23, 24, 34 ], [ 23, 24, 35 ], [ 23, 24, 36 ], [ 23, 25, 26 ], [ 23, 28, 33 ], [ 23, 30, 34 ], [ 25, 26, 31 ], [ 25, 26, 32 ], [ 25, 26, 37 ], [ 25, 26, 38 ], [ 26, 27, 32 ], [ 26, 29, 31 ], [ 27, 28, 29 ], [ 27, 28, 32 ], [ 27, 28, 33 ], [ 27, 28, 35 ], [ 27, 28, 38 ], [ 27, 29, 30 ], [ 29, 30, 31 ], [ 29, 30, 34 ], [ 29, 30, 36 ], [ 29, 30, 37 ] ];