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###                                                                              ###
###                                                                              ###
###  LIBRARY OF TRIANGULATIONS                                                   ###
###  by Bruno Benedetti and Frank H. Lutz                                        ###
###  http://page.math.tu-berlin.de/~lutz/stellar/library_of_triangulations.html  ###
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###                                                                              ###
###  name of example:                                                            ###
###                                                                              ###
###    trefoil (= S_3_13_56)                                                     ###
###                                                                              ###
###                                                                              ###
###  description:                                                                ###
###                                                                              ###
###    non-constructible 3-sphere with 13 vertices                               ###
###    containing the trefoil knot                                               ###
###                                                                              ###
###                                                                              ###
###  properties:                                                                 ###
###                                                                              ###
###    f=(13,69,112,56),                                                         ###
###    H_*=(Z,0,0,Z),                                                            ###
###    non-constructible, non-shellable,                                         ###
###    perfect discrete Morse vector: (1,0,0,1)                                  ###
###                                                                              ###
###                                                                              ###
###  references:                                                                 ###
###                                                                              ###
###    F. H. Lutz.                                                               ###
###    Small examples of nonconstructible simplicial balls and spheres.          ###
###    SIAM J. Discrete Math. 18, 103-109 (2004).                                ###
###                                                                              ###
###    B. Benedetti and F. H. Lutz.                                              ###
###    Random discrete Morse theory and a new library of triangulations.         ###
###    Exp. Math. 23, 66-94 (2014).                                              ###
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facets:=[ [ 1, 2, 6, 9 ], [ 1, 2, 6, 12 ], [ 1, 2, 9, 12 ], [ 1, 3, 5, 8 ], 
  [ 1, 3, 5, 11 ], [ 1, 3, 8, 11 ], [ 1, 5, 8, 10 ], [ 1, 5, 10, 11 ], 
  [ 1, 6, 7, 9 ], [ 1, 6, 7, 12 ], [ 1, 7, 8, 10 ], [ 1, 7, 8, 11 ], 
  [ 1, 7, 9, 13 ], [ 1, 7, 10, 12 ], [ 1, 7, 11, 13 ], [ 1, 9, 10, 12 ], 
  [ 1, 9, 10, 13 ], [ 1, 10, 11, 13 ], [ 2, 3, 4, 7 ], [ 2, 3, 4, 10 ], 
  [ 2, 3, 7, 10 ], [ 2, 4, 5, 7 ], [ 2, 4, 5, 10 ], [ 2, 5, 7, 13 ], 
  [ 2, 5, 8, 10 ], [ 2, 5, 8, 13 ], [ 2, 6, 9, 11 ], [ 2, 6, 11, 13 ], 
  [ 2, 6, 12, 13 ], [ 2, 7, 8, 10 ], [ 2, 7, 8, 11 ], [ 2, 7, 11, 13 ], 
  [ 2, 8, 9, 11 ], [ 2, 8, 9, 12 ], [ 2, 8, 12, 13 ], [ 3, 4, 6, 7 ], 
  [ 3, 4, 6, 10 ], [ 3, 5, 8, 13 ], [ 3, 5, 9, 11 ], [ 3, 5, 9, 13 ], 
  [ 3, 6, 7, 12 ], [ 3, 6, 10, 13 ], [ 3, 6, 12, 13 ], [ 3, 7, 10, 12 ], 
  [ 3, 8, 9, 11 ], [ 3, 8, 9, 12 ], [ 3, 8, 12, 13 ], [ 3, 9, 10, 12 ], 
  [ 3, 9, 10, 13 ], [ 4, 5, 6, 7 ], [ 4, 5, 6, 10 ], [ 5, 6, 7, 9 ], 
  [ 5, 6, 9, 11 ], [ 5, 6, 10, 11 ], [ 5, 7, 9, 13 ], [ 6, 10, 11, 13 ] ];