# section between (2,3,4,5) and (1,6,... ,16), # a topological 3-sphere with f-vector # 4*12 = 48 vertices, # 336 edges, # 364 triangles, 159 quadrilaterals, # 129 tetrahedra and 106 prisms 3sphere:= [ [[1,2],[2,6],[2,7],[2,9]], [[1,2],[2,6],[2,7],[2,13]], [[1,2],[2,6],[2,8],[2,14]], [[1,2],[2,6],[2,8],[2,16]], [[1,2],[2,6],[2,9],[2,15]], [[1,2],[2,6],[2,13],[2,16]], [[1,2],[2,6],[2,14],[2,15]], [[1,2],[2,7],[2,9],[2,11]], [[1,2],[2,8],[2,10],[2,12]], [[1,2],[2,9],[2,11],[2,15]], [[1,2],[2,10],[2,12],[2,16]], [[1,3],[3,6],[3,9],[3,15]], [[1,3],[3,6],[3,10],[3,11]], [[1,3],[3,6],[3,14],[3,15]], [[1,3],[3,7],[3,8],[3,9]], [[1,3],[3,7],[3,8],[3,11]], [[1,3],[3,7],[3,9],[3,10]], [[1,3],[3,7],[3,10],[3,11]], [[1,3],[3,8],[3,9],[3,12]], [[1,3],[3,8],[3,11],[3,13]], [[1,3],[3,8],[3,13],[3,16]], [[1,3],[3,9],[3,10],[3,15]], [[1,3],[3,10],[3,14],[3,15]], [[1,3],[3,11],[3,12],[3,13]], [[1,3],[3,12],[3,13],[3,16]], [[1,4],[4,7],[4,8],[4,11]], [[1,4],[4,7],[4,8],[4,15]], [[1,4],[4,8],[4,11],[4,13]], [[1,4],[4,8],[4,13],[4,15]], [[1,4],[4,9],[4,11],[4,13]], [[1,4],[4,9],[4,11],[4,16]], [[1,4],[4,9],[4,13],[4,14]], [[1,4],[4,9],[4,14],[4,16]], [[1,4],[4,10],[4,12],[4,13]], [[1,4],[4,10],[4,12],[4,16]], [[1,4],[4,10],[4,13],[4,14]], [[1,4],[4,11],[4,15],[4,16]], [[1,4],[4,12],[4,13],[4,15]], [[1,4],[4,12],[4,15],[4,16]], [[1,5],[5,6],[5,9],[5,12]], [[1,5],[5,6],[5,10],[5,11]], [[1,5],[5,6],[5,12],[5,14]], [[1,5],[5,7],[5,13],[5,16]], [[1,5],[5,7],[5,15],[5,16]], [[1,5],[5,8],[5,10],[5,12]], [[1,5],[5,8],[5,12],[5,14]], [[1,5],[5,10],[5,11],[5,12]], [[1,5],[5,14],[5,15],[5,16]], [[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]], [[2,9],[3,9],[4,9],[5,9]], [[2,10],[2,12],[2,13],[2,14]], [[2,10],[2,12],[2,15],[2,16]], [[2,10],[2,13],[2,15],[2,16]], [[2,13],[3,13],[4,13],[5,13]], [[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]], [[4,6],[4,8],[4,13],[4,14]], [[4,6],[4,8],[4,13],[4,16]], [[4,6],[4,9],[4,13],[4,14]], [[4,6],[4,9],[4,13],[4,16]], [[4,6],[4,9],[4,14],[4,16]], [[4,6],[4,10],[4,11],[4,15]], [[4,6],[4,10],[4,12],[4,15]], [[4,6],[4,11],[4,12],[4,15]], [[4,7],[4,8],[4,9],[4,12]], [[4,7],[4,8],[4,9],[4,15]], [[4,7],[4,8],[4,10],[4,11]], [[4,8],[4,9],[4,10],[4,11]], [[4,8],[4,13],[4,14],[4,15]], [[4,9],[4,10],[4,11],[4,16]], [[4,10],[4,11],[4,15],[4,16]], [[4,10],[4,12],[4,13],[4,14]], [[4,10],[4,12],[4,15],[4,16]], [[4,11],[4,12],[4,14],[4,15]], [[4,12],[4,13],[4,14],[4,15]], [[5,6],[5,7],[5,12],[5,16]], [[5,6],[5,8],[5,11],[5,15]], [[5,6],[5,11],[5,13],[5,15]], [[5,6],[5,12],[5,14],[5,16]], [[5,7],[5,8],[5,10],[5,14]], [[5,7],[5,9],[5,12],[5,16]], [[5,7],[5,9],[5,15],[5,16]], [[5,7],[5,10],[5,11],[5,14]], [[5,7],[5,11],[5,13],[5,14]], [[5,8],[5,9],[5,10],[5,13]], [[5,8],[5,9],[5,10],[5,14]], [[5,8],[5,9],[5,11],[5,16]], [[5,8],[5,9],[5,13],[5,15]], [[5,8],[5,9],[5,14],[5,16]], [[5,8],[5,10],[5,12],[5,13]], [[5,8],[5,11],[5,12],[5,15]], [[5,8],[5,11],[5,12],[5,16]], [[5,8],[5,12],[5,13],[5,15]], [[5,8],[5,12],[5,14],[5,16]], [[5,9],[5,10],[5,13],[5,15]], [[5,9],[5,10],[5,14],[5,15]], [[5,9],[5,14],[5,15],[5,16]], [[5,10],[5,11],[5,12],[5,13]], [[5,10],[5,11],[5,13],[5,14]], [[5,11],[5,12],[5,13],[5,15]], [[1,2],[1,3],[2,8],[2,12],[3,8],[3,12]], [[1,2],[1,3],[2,8],[2,16],[3,8],[3,16]], [[1,2],[1,3],[2,12],[2,16],[3,12],[3,16]], [[1,2],[1,4],[2,7],[2,11],[4,7],[4,11]], [[1,2],[1,4],[2,7],[2,15],[4,7],[4,15]], [[1,2],[1,4],[2,11],[2,15],[4,11],[4,15]], [[1,2],[1,5],[2,7],[2,13],[5,7],[5,13]], [[1,2],[1,5],[2,7],[2,15],[5,7],[5,15]], [[1,2],[1,5],[2,8],[2,10],[5,8],[5,10]], [[1,2],[1,5],[2,8],[2,14],[5,8],[5,14]], [[1,2],[1,5],[2,10],[2,16],[5,10],[5,16]], [[1,2],[1,5],[2,13],[2,16],[5,13],[5,16]], [[1,2],[1,5],[2,14],[2,15],[5,14],[5,15]], [[1,3],[1,4],[3,6],[3,10],[4,6],[4,10]], [[1,3],[1,4],[3,6],[3,14],[4,6],[4,14]], [[1,3],[1,4],[3,10],[3,14],[4,10],[4,14]], [[1,3],[1,5],[3,6],[3,9],[5,6],[5,9]], [[1,3],[1,5],[3,6],[3,11],[5,6],[5,11]], [[1,3],[1,5],[3,9],[3,12],[5,9],[5,12]], [[1,3],[1,5],[3,11],[3,12],[5,11],[5,12]], [[1,4],[1,5],[4,6],[4,10],[5,6],[5,10]], [[1,4],[1,5],[4,6],[4,14],[5,6],[5,14]], [[1,4],[1,5],[4,10],[4,16],[5,10],[5,16]], [[1,4],[1,5],[4,14],[4,16],[5,14],[5,16]], [[2,6],[2,9],[2,12],[5,6],[5,9],[5,12]], [[2,6],[2,9],[2,15],[3,6],[3,9],[3,15]], [[2,6],[2,9],[3,6],[3,9],[5,6],[5,9]], [[2,6],[2,10],[2,11],[4,6],[4,10],[4,11]], [[2,6],[2,10],[2,11],[5,6],[5,10],[5,11]], [[2,6],[2,10],[4,6],[4,10],[5,6],[5,10]], [[2,6],[2,11],[2,12],[4,6],[4,11],[4,12]], [[2,6],[2,11],[2,13],[5,6],[5,11],[5,13]], [[2,6],[2,12],[4,6],[4,12],[5,6],[5,12]], [[2,6],[2,13],[2,15],[3,6],[3,13],[3,15]], [[2,6],[2,13],[3,6],[3,13],[5,6],[5,13]], [[2,7],[2,8],[2,10],[4,7],[4,8],[4,10]], [[2,7],[2,8],[2,10],[5,7],[5,8],[5,10]], [[2,7],[2,8],[2,12],[3,7],[3,8],[3,12]], [[2,7],[2,8],[2,12],[4,7],[4,8],[4,12]], [[2,7],[2,8],[2,14],[5,7],[5,8],[5,14]], [[2,7],[2,8],[2,16],[3,7],[3,8],[3,16]], [[2,7],[2,10],[2,11],[4,7],[4,10],[4,11]], [[2,7],[2,10],[2,11],[5,7],[5,10],[5,11]], [[2,7],[2,11],[2,13],[5,7],[5,11],[5,13]], [[2,7],[2,12],[2,14],[3,7],[3,12],[3,14]], [[2,7],[2,12],[2,14],[4,7],[4,12],[4,14]], [[2,7],[2,14],[2,15],[4,7],[4,14],[4,15]], [[2,7],[2,14],[2,15],[5,7],[5,14],[5,15]], [[2,7],[2,14],[2,16],[3,7],[3,14],[3,16]], [[2,8],[2,9],[2,10],[4,8],[4,9],[4,10]], [[2,8],[2,9],[2,12],[4,8],[4,9],[4,12]], [[2,9],[2,10],[2,16],[4,9],[4,10],[4,16]], [[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],[2,12],[4,9],[4,12],[5,9],[5,12]], [[2,9],[2,13],[2,14],[3,9],[3,13],[3,14]], [[2,9],[2,13],[2,16],[4,9],[4,13],[4,16]], [[2,9],[2,13],[3,9],[3,13],[4,9],[4,13]], [[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]], [[2,10],[2,16],[4,10],[4,16],[5,10],[5,16]], [[2,11],[2,12],[2,14],[4,11],[4,12],[4,14]], [[2,11],[2,14],[2,15],[4,11],[4,14],[4,15]], [[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]], [[2,13],[2,16],[4,13],[4,16],[5,13],[5,16]], [[3,6],[3,7],[3,12],[4,6],[4,7],[4,12]], [[3,6],[3,7],[3,16],[4,6],[4,7],[4,16]], [[3,6],[3,8],[3,11],[5,6],[5,8],[5,11]], [[3,6],[3,8],[3,14],[4,6],[4,8],[4,14]], [[3,6],[3,8],[3,15],[5,6],[5,8],[5,15]], [[3,6],[3,8],[3,16],[4,6],[4,8],[4,16]], [[3,6],[3,10],[3,12],[4,6],[4,10],[4,12]], [[3,6],[3,13],[3,15],[5,6],[5,13],[5,15]], [[3,7],[3,12],[3,14],[4,7],[4,12],[4,14]], [[3,7],[3,13],[3,14],[5,7],[5,13],[5,14]], [[3,7],[3,13],[3,16],[4,7],[4,13],[4,16]], [[3,7],[3,13],[4,7],[4,13],[5,7],[5,13]], [[3,7],[3,14],[3,15],[4,7],[4,14],[4,15]], [[3,7],[3,14],[3,15],[5,7],[5,14],[5,15]], [[3,7],[3,15],[4,7],[4,15],[5,7],[5,15]], [[3,8],[3,11],[3,13],[4,8],[4,11],[4,13]], [[3,8],[3,11],[4,8],[4,11],[5,8],[5,11]], [[3,8],[3,13],[3,16],[4,8],[4,13],[4,16]], [[3,8],[3,14],[3,15],[4,8],[4,14],[4,15]], [[3,8],[3,15],[4,8],[4,15],[5,8],[5,15]], [[3,9],[3,11],[3,13],[4,9],[4,11],[4,13]], [[3,9],[3,11],[3,16],[5,9],[5,11],[5,16]], [[3,9],[3,11],[4,9],[4,11],[5,9],[5,11]], [[3,9],[3,12],[3,16],[5,9],[5,12],[5,16]], [[3,10],[3,12],[3,14],[4,10],[4,12],[4,14]], [[3,10],[3,13],[3,14],[5,10],[5,13],[5,14]], [[3,10],[3,13],[3,15],[5,10],[5,13],[5,15]], [[3,10],[3,14],[3,15],[5,10],[5,14],[5,15]], [[3,11],[3,12],[3,16],[5,11],[5,12],[5,16]], [[4,6],[4,7],[4,12],[5,6],[5,7],[5,12]], [[4,6],[4,7],[4,16],[5,6],[5,7],[5,16]], [[4,6],[4,14],[4,16],[5,6],[5,14],[5,16]], [[4,7],[4,9],[4,12],[5,7],[5,9],[5,12]], [[4,7],[4,9],[4,15],[5,7],[5,9],[5,15]], [[4,7],[4,13],[4,16],[5,7],[5,13],[5,16]], [[4,8],[4,9],[4,11],[5,8],[5,9],[5,11]], [[4,8],[4,9],[4,15],[5,8],[5,9],[5,15]], ]; # 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] ];