# section between (1,2) and (3,... ,16),
# a topological 3-sphere with f-vector
# 2*14 = 28 vertices,
# 196 edges,
# 288 triangles, 36 quadrilaterals,
# 132 tetrahedra and 24 prisms

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

# 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]
];