####################################################################################
####################################################################################
####################################################################################
###                                                                              ###
###                                                                              ###
###  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:                                                            ###
###                                                                              ###
###    poincare                                                                  ###
###                                                                              ###
###                                                                              ###
###  description:                                                                ###
###                                                                              ###
###    smallest known triangulation of the Poincaré homology 3-sphere            ###
###    with 16 vertices and 90 facets                                            ###
###                                                                              ###
###                                                                              ###
###  properties:                                                                 ###
###                                                                              ###
###    f=(16,106,180,90),                                                        ###
###    H_*=(Z,0,0,Z),                                                            ###
###    pi_1= binary icosahedral group,                                           ###
###    optimal discrete Morse vector: (1,2,2,1), not perfect                     ###
###                                                                              ###
###                                                                              ###
###  references:                                                                 ###
###                                                                              ###
###    H. Poincaré.                                                              ###
###    Cinquième complément à l'analysis situs.                                  ###
###    Rend. Circ. Mat. Palermo 18, 45-110 (1904).                               ###
###                                                                              ###
###    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).                                             ###
###                                                                              ###
###    A. Björner and F. H. Lutz.                                                ###
###    A 16-vertex triangulation of the Poincaré homology 3-sphere               ###
###    and non-PL spheres with few vertices.                                     ###
###    Electronic Geometry Models No. 2003.04.001 (2003).                        ###
###    http://www.eg-models.de/2003.04.001.                                      ###
###                                                                              ###
###    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, 9 ], [ 1, 2, 4, 15 ], [ 1, 2, 6, 14 ], [ 1, 2, 6, 15 ], 
  [ 1, 2, 9, 14 ], [ 1, 3, 4, 12 ], [ 1, 3, 4, 15 ], [ 1, 3, 7, 10 ], 
  [ 1, 3, 7, 12 ], [ 1, 3, 10, 15 ], [ 1, 4, 9, 12 ], [ 1, 5, 6, 13 ], 
  [ 1, 5, 6, 14 ], [ 1, 5, 8, 11 ], [ 1, 5, 8, 13 ], [ 1, 5, 11, 14 ], 
  [ 1, 6, 13, 15 ], [ 1, 7, 8, 10 ], [ 1, 7, 8, 11 ], [ 1, 7, 11, 12 ], 
  [ 1, 8, 10, 13 ], [ 1, 9, 11, 12 ], [ 1, 9, 11, 14 ], [ 1, 10, 13, 15 ], 
  [ 2, 3, 5, 10 ], [ 2, 3, 5, 11 ], [ 2, 3, 7, 10 ], [ 2, 3, 7, 13 ], 
  [ 2, 3, 11, 13 ], [ 2, 4, 9, 13 ], [ 2, 4, 11, 13 ], [ 2, 4, 11, 15 ], 
  [ 2, 5, 8, 11 ], [ 2, 5, 8, 12 ], [ 2, 5, 10, 12 ], [ 2, 6, 10, 12 ], 
  [ 2, 6, 10, 14 ], [ 2, 6, 12, 15 ], [ 2, 7, 9, 13 ], [ 2, 7, 9, 14 ], 
  [ 2, 7, 10, 14 ], [ 2, 8, 11, 15 ], [ 2, 8, 12, 15 ], [ 3, 4, 5, 14 ], 
  [ 3, 4, 5, 15 ], [ 3, 4, 12, 14 ], [ 3, 5, 10, 15 ], [ 3, 5, 11, 14 ], 
  [ 3, 7, 12, 13 ], [ 3, 11, 13, 14 ], [ 3, 12, 13, 14 ], [ 4, 5, 6, 7 ], 
  [ 4, 5, 6, 14 ], [ 4, 5, 7, 15 ], [ 4, 6, 7, 11 ], [ 4, 6, 10, 11 ], 
  [ 4, 6, 10, 14 ], [ 4, 7, 11, 15 ], [ 4, 8, 9, 12 ], [ 4, 8, 9, 13 ], 
  [ 4, 8, 10, 13 ], [ 4, 8, 10, 14 ], [ 4, 8, 12, 14 ], [ 4, 10, 11, 13 ], 
  [ 5, 6, 7, 13 ], [ 5, 7, 9, 13 ], [ 5, 7, 9, 15 ], [ 5, 8, 9, 12 ], 
  [ 5, 8, 9, 13 ], [ 5, 9, 10, 12 ], [ 5, 9, 10, 15 ], [ 6, 7, 11, 12 ], 
  [ 6, 7, 12, 13 ], [ 6, 10, 11, 12 ], [ 6, 12, 13, 15 ], [ 7, 8, 10, 14 ], 
  [ 7, 8, 11, 15 ], [ 7, 8, 14, 15 ], [ 7, 9, 14, 15 ], [ 8, 12, 14, 15 ], 
  [ 9, 10, 11, 12 ], [ 9, 10, 11, 16 ], [ 9, 10, 15, 16 ], [ 9, 11, 14, 16 ], 
  [ 9, 14, 15, 16 ], [ 10, 11, 13, 16 ], [ 10, 13, 15, 16 ], [ 11, 13, 14, 16 ], 
  [ 12, 13, 14, 15 ], [ 13, 14, 15, 16 ] ];