#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### 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: ### ### ### ### triple_trefoil_arc (= B_17_95 = S_3_18_125_minus_star) ### ### ### ### ### ### description: ### ### ### ### non-constructible 3-ball with 17 vertices ### ### containing the triple trefoil knot as a spanning arc ### ### ### ### ### ### properties: ### ### ### ### f=(17,127,208,97), ### ### H_*=(Z,0,0,0), ### ### non-constructible, non-shellable, not collapsible, ### ### optimal discrete Morse vector: (1,2,2,0), not perfect ### ### ### ### ### ### references: ### ### ### ### B. Benedetti and F. H. Lutz. ### ### Knots in collapsible and non-collapsible balls. ### ### Electron. J. Comb. 20, No. 3, Research Paper P31, 29 p. (2013). ### ### ### ### 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, 4, 12 ], [ 1, 2, 4, 13 ], [ 1, 2, 12, 13 ], [ 1, 3, 5, 14 ], [ 1, 3, 5, 16 ], [ 1, 3, 8, 16 ], [ 1, 4, 9, 13 ], [ 1, 4, 9, 17 ], [ 1, 4, 12, 17 ], [ 1, 5, 10, 11 ], [ 1, 5, 10, 15 ], [ 1, 5, 11, 14 ], [ 1, 5, 15, 16 ], [ 1, 6, 7, 9 ], [ 1, 6, 7, 10 ], [ 1, 6, 9, 17 ], [ 1, 6, 10, 11 ], [ 1, 6, 11, 15 ], [ 1, 6, 15, 17 ], [ 1, 7, 9, 12 ], [ 1, 7, 10, 15 ], [ 1, 7, 12, 17 ], [ 1, 7, 15, 17 ], [ 1, 8, 11, 14 ], [ 1, 8, 11, 15 ], [ 1, 8, 15, 16 ], [ 1, 9, 12, 13 ], [ 2, 3, 7, 11 ], [ 2, 3, 7, 14 ], [ 2, 3, 9, 11 ], [ 2, 3, 9, 15 ], [ 2, 3, 14, 15 ], [ 2, 4, 6, 12 ], [ 2, 4, 6, 13 ], [ 2, 5, 8, 13 ], [ 2, 5, 8, 17 ], [ 2, 5, 10, 15 ], [ 2, 5, 10, 17 ], [ 2, 5, 13, 16 ], [ 2, 5, 15, 16 ], [ 2, 6, 8, 12 ], [ 2, 6, 8, 17 ], [ 2, 6, 13, 17 ], [ 2, 7, 9, 14 ], [ 2, 8, 12, 13 ], [ 2, 9, 14, 16 ], [ 2, 9, 15, 16 ], [ 2, 10, 14, 15 ], [ 2, 10, 14, 16 ], [ 2, 10, 16, 17 ], [ 2, 13, 16, 17 ], [ 3, 4, 9, 13 ], [ 3, 4, 9, 15 ], [ 3, 5, 7, 14 ], [ 3, 5, 7, 16 ], [ 3, 7, 11, 16 ], [ 3, 8, 12, 13 ], [ 3, 8, 12, 16 ], [ 3, 9, 11, 12 ], [ 3, 9, 12, 13 ], [ 3, 11, 12, 16 ], [ 4, 5, 6, 7 ], [ 4, 5, 6, 12 ], [ 4, 5, 7, 8 ], [ 4, 5, 8, 17 ], [ 4, 5, 12, 17 ], [ 4, 6, 7, 10 ], [ 4, 7, 8, 10 ], [ 4, 8, 9, 15 ], [ 4, 8, 9, 17 ], [ 4, 8, 10, 14 ], [ 4, 8, 11, 14 ], [ 4, 8, 11, 15 ], [ 4, 10, 14, 16 ], [ 4, 11, 14, 16 ], [ 5, 6, 7, 14 ], [ 5, 6, 12, 14 ], [ 5, 7, 8, 13 ], [ 5, 7, 13, 16 ], [ 5, 10, 11, 17 ], [ 5, 11, 12, 14 ], [ 5, 11, 12, 17 ], [ 6, 7, 9, 14 ], [ 6, 8, 9, 16 ], [ 6, 8, 9, 17 ], [ 6, 8, 12, 16 ], [ 6, 9, 14, 16 ], [ 6, 12, 14, 16 ], [ 6, 13, 15, 17 ], [ 7, 8, 10, 13 ], [ 7, 10, 13, 15 ], [ 7, 13, 15, 17 ], [ 7, 13, 16, 17 ], [ 8, 9, 15, 16 ], [ 8, 10, 13, 14 ], [ 10, 13, 14, 15 ], [ 11, 12, 14, 16 ] ];