# section between (1) and (2,... ,16) (link of vertex 1),
# a topological 3-sphere with f-vector
# 1*15 = 15 vertices
# 105 edges,
# 180 triangles and
# 90 tetrahedra

3sphere:= [
  [[1,2],[1,3],[1,8],[1,12]],
  [[1,2],[1,3],[1,8],[1,16]],
  [[1,2],[1,3],[1,12],[1,16]],
  [[1,2],[1,4],[1,7],[1,11]],
  [[1,2],[1,4],[1,7],[1,15]],
  [[1,2],[1,4],[1,11],[1,15]],
  [[1,2],[1,5],[1,7],[1,13]],
  [[1,2],[1,5],[1,7],[1,15]],
  [[1,2],[1,5],[1,8],[1,10]],
  [[1,2],[1,5],[1,8],[1,14]],
  [[1,2],[1,5],[1,10],[1,16]],
  [[1,2],[1,5],[1,13],[1,16]],
  [[1,2],[1,5],[1,14],[1,15]],
  [[1,2],[1,6],[1,7],[1,9]],
  [[1,2],[1,6],[1,7],[1,13]],
  [[1,2],[1,6],[1,8],[1,14]],
  [[1,2],[1,6],[1,8],[1,16]],
  [[1,2],[1,6],[1,9],[1,15]],
  [[1,2],[1,6],[1,13],[1,16]],
  [[1,2],[1,6],[1,14],[1,15]],
  [[1,2],[1,7],[1,9],[1,11]],
  [[1,2],[1,8],[1,10],[1,12]],
  [[1,2],[1,9],[1,11],[1,15]],
  [[1,2],[1,10],[1,12],[1,16]],
  [[1,3],[1,4],[1,6],[1,10]],
  [[1,3],[1,4],[1,6],[1,14]],
  [[1,3],[1,4],[1,10],[1,14]],
  [[1,3],[1,5],[1,6],[1,9]],
  [[1,3],[1,5],[1,6],[1,11]],
  [[1,3],[1,5],[1,9],[1,12]],
  [[1,3],[1,5],[1,11],[1,12]],
  [[1,3],[1,6],[1,9],[1,15]],
  [[1,3],[1,6],[1,10],[1,11]],
  [[1,3],[1,6],[1,14],[1,15]],
  [[1,3],[1,7],[1,8],[1,9]],
  [[1,3],[1,7],[1,8],[1,11]],
  [[1,3],[1,7],[1,9],[1,10]],
  [[1,3],[1,7],[1,10],[1,11]],
  [[1,3],[1,8],[1,9],[1,12]],
  [[1,3],[1,8],[1,11],[1,13]],
  [[1,3],[1,8],[1,13],[1,16]],
  [[1,3],[1,9],[1,10],[1,15]],
  [[1,3],[1,10],[1,14],[1,15]],
  [[1,3],[1,11],[1,12],[1,13]],
  [[1,3],[1,12],[1,13],[1,16]],
  [[1,4],[1,5],[1,6],[1,10]],
  [[1,4],[1,5],[1,6],[1,14]],
  [[1,4],[1,5],[1,10],[1,16]],
  [[1,4],[1,5],[1,14],[1,16]],
  [[1,4],[1,7],[1,8],[1,11]],
  [[1,4],[1,7],[1,8],[1,15]],
  [[1,4],[1,8],[1,11],[1,13]],
  [[1,4],[1,8],[1,13],[1,15]],
  [[1,4],[1,9],[1,11],[1,13]],
  [[1,4],[1,9],[1,11],[1,16]],
  [[1,4],[1,9],[1,13],[1,14]],
  [[1,4],[1,9],[1,14],[1,16]],
  [[1,4],[1,10],[1,12],[1,13]],
  [[1,4],[1,10],[1,12],[1,16]],
  [[1,4],[1,10],[1,13],[1,14]],
  [[1,4],[1,11],[1,15],[1,16]],
  [[1,4],[1,12],[1,13],[1,15]],
  [[1,4],[1,12],[1,15],[1,16]],
  [[1,5],[1,6],[1,9],[1,12]],
  [[1,5],[1,6],[1,10],[1,11]],
  [[1,5],[1,6],[1,12],[1,14]],
  [[1,5],[1,7],[1,13],[1,16]],
  [[1,5],[1,7],[1,15],[1,16]],
  [[1,5],[1,8],[1,10],[1,12]],
  [[1,5],[1,8],[1,12],[1,14]],
  [[1,5],[1,10],[1,11],[1,12]],
  [[1,5],[1,14],[1,15],[1,16]],
  [[1,6],[1,7],[1,8],[1,9]],
  [[1,6],[1,7],[1,8],[1,13]],
  [[1,6],[1,8],[1,9],[1,12]],
  [[1,6],[1,8],[1,12],[1,14]],
  [[1,6],[1,8],[1,13],[1,16]],
  [[1,7],[1,8],[1,13],[1,15]],
  [[1,7],[1,9],[1,10],[1,14]],
  [[1,7],[1,9],[1,11],[1,14]],
  [[1,7],[1,10],[1,11],[1,14]],
  [[1,7],[1,12],[1,13],[1,15]],
  [[1,7],[1,12],[1,13],[1,16]],
  [[1,7],[1,12],[1,15],[1,16]],
  [[1,9],[1,10],[1,14],[1,15]],
  [[1,9],[1,11],[1,13],[1,14]],
  [[1,9],[1,11],[1,15],[1,16]],
  [[1,9],[1,14],[1,15],[1,16]],
  [[1,10],[1,11],[1,12],[1,13]],
  [[1,10],[1,11],[1,13],[1,14]]
];

# PL-equivalent to
#  S^3   f = (5,10,10,5)
complex:= [
[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,5],[2,3,4,5]
];