# section between (1,2,3) and (4,... ,16),
# a topological 3-sphere with f-vector
# 3*13 = 39 vertices,
# 273 edges,
# 336 triangles, 99 quadrilaterals,
# 135 tetrahedra and 66 prisms

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

# 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]
];