# section between (1,2,3,4,5,9) and (6,7,8,10,... ,16), # a prism space P(3) with f-vector # 6*10 = 60 vertices, # 420 edges, # 348 triangles, 279 quadrilaterals, # 81 tetrahedra and 186 prisms 3sphere:= [ [[1,6],[1,7],[1,8],[1,13]], [[1,6],[1,8],[1,12],[1,14]], [[1,6],[1,8],[1,13],[1,16]], [[1,6],[3,6],[5,6],[6,9]], [[1,7],[1,8],[1,13],[1,15]], [[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]], [[1,10],[1,11],[1,12],[1,13]], [[1,10],[1,11],[1,13],[1,14]], [[1,12],[3,12],[5,12],[9,12]], [[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],[2,13],[2,15],[2,16]], [[2,6],[3,6],[5,6],[6,9]], [[2,7],[2,8],[2,14],[2,16]], [[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]], [[2,10],[2,12],[2,13],[2,14]], [[2,10],[2,12],[2,15],[2,16]], [[2,10],[2,13],[2,15],[2,16]], [[2,12],[4,12],[5,12],[9,12]], [[2,13],[3,13],[4,13],[5,13]], [[2,13],[3,13],[4,13],[9,13]], [[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],[3,10],[3,11]], [[3,7],[3,8],[3,10],[3,16]], [[3,7],[3,13],[3,14],[3,16]], [[3,11],[3,12],[3,13],[3,16]], [[3,11],[3,13],[3,14],[3,16]], [[3,11],[4,11],[5,11],[9,11]], [[4,6],[4,8],[4,13],[4,14]], [[4,6],[4,8],[4,13],[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],[4,10],[4,11]], [[4,8],[4,13],[4,14],[4,15]], [[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],[5,10],[5,11],[5,14]], [[5,7],[5,11],[5,13],[5,14]], [[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]], [[5,10],[5,11],[5,12],[5,13]], [[5,10],[5,11],[5,13],[5,14]], [[5,11],[5,12],[5,13],[5,15]], [[6,9],[7,9],[8,9],[9,13]], [[6,9],[7,9],[9,10],[9,13]], [[6,9],[7,9],[9,10],[9,14]], [[6,9],[7,9],[9,11],[9,14]], [[6,9],[8,9],[9,12],[9,13]], [[6,9],[9,10],[9,13],[9,16]], [[6,9],[9,10],[9,14],[9,16]], [[6,9],[9,11],[9,12],[9,14]], [[6,9],[9,12],[9,13],[9,14]], [[7,9],[8,9],[9,13],[9,15]], [[7,9],[9,10],[9,12],[9,15]], [[7,9],[9,10],[9,13],[9,15]], [[7,9],[9,12],[9,15],[9,16]], [[8,9],[9,10],[9,11],[9,16]], [[8,9],[9,10],[9,14],[9,16]], [[1,6],[1,7],[1,8],[6,9],[7,9],[8,9]], [[1,6],[1,7],[1,13],[2,6],[2,7],[2,13]], [[1,6],[1,7],[2,6],[2,7],[6,9],[7,9]], [[1,6],[1,8],[1,12],[6,9],[8,9],[9,12]], [[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],[1,10],[1,11],[3,6],[3,10],[3,11]], [[1,6],[1,10],[1,11],[5,6],[5,10],[5,11]], [[1,6],[1,10],[3,6],[3,10],[4,6],[4,10]], [[1,6],[1,10],[4,6],[4,10],[5,6],[5,10]], [[1,6],[1,11],[3,6],[3,11],[5,6],[5,11]], [[1,6],[1,12],[1,14],[5,6],[5,12],[5,14]], [[1,6],[1,12],[5,6],[5,12],[6,9],[9,12]], [[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]], [[1,6],[1,14],[3,6],[3,14],[4,6],[4,14]], [[1,6],[1,14],[4,6],[4,14],[5,6],[5,14]], [[1,6],[1,15],[2,6],[2,15],[6,9],[9,15]], [[1,6],[1,15],[3,6],[3,15],[6,9],[9,15]], [[1,7],[1,8],[1,11],[3,7],[3,8],[3,11]], [[1,7],[1,8],[1,11],[4,7],[4,8],[4,11]], [[1,7],[1,8],[1,15],[4,7],[4,8],[4,15]], [[1,7],[1,8],[3,7],[3,8],[7,9],[8,9]], [[1,7],[1,10],[1,11],[3,7],[3,10],[3,11]], [[1,7],[1,10],[1,14],[7,9],[9,10],[9,14]], [[1,7],[1,10],[3,7],[3,10],[7,9],[9,10]], [[1,7],[1,11],[1,14],[7,9],[9,11],[9,14]], [[1,7],[1,11],[2,7],[2,11],[4,7],[4,11]], [[1,7],[1,11],[2,7],[2,11],[7,9],[9,11]], [[1,7],[1,13],[1,16],[5,7],[5,13],[5,16]], [[1,7],[1,13],[2,7],[2,13],[5,7],[5,13]], [[1,7],[1,15],[1,16],[5,7],[5,15],[5,16]], [[1,7],[1,15],[2,7],[2,15],[4,7],[4,15]], [[1,7],[1,15],[2,7],[2,15],[5,7],[5,15]], [[1,8],[1,10],[1,12],[2,8],[2,10],[2,12]], [[1,8],[1,10],[1,12],[5,8],[5,10],[5,12]], [[1,8],[1,10],[2,8],[2,10],[5,8],[5,10]], [[1,8],[1,11],[1,13],[3,8],[3,11],[3,13]], [[1,8],[1,11],[1,13],[4,8],[4,11],[4,13]], [[1,8],[1,12],[1,14],[5,8],[5,12],[5,14]], [[1,8],[1,12],[2,8],[2,12],[3,8],[3,12]], [[1,8],[1,12],[3,8],[3,12],[8,9],[9,12]], [[1,8],[1,13],[1,15],[4,8],[4,13],[4,15]], [[1,8],[1,13],[1,16],[3,8],[3,13],[3,16]], [[1,8],[1,14],[2,8],[2,14],[5,8],[5,14]], [[1,8],[1,16],[2,8],[2,16],[3,8],[3,16]], [[1,10],[1,11],[1,12],[5,10],[5,11],[5,12]], [[1,10],[1,12],[1,13],[4,10],[4,12],[4,13]], [[1,10],[1,12],[1,16],[2,10],[2,12],[2,16]], [[1,10],[1,12],[1,16],[4,10],[4,12],[4,16]], [[1,10],[1,13],[1,14],[4,10],[4,13],[4,14]], [[1,10],[1,14],[1,15],[3,10],[3,14],[3,15]], [[1,10],[1,14],[1,15],[9,10],[9,14],[9,15]], [[1,10],[1,14],[3,10],[3,14],[4,10],[4,14]], [[1,10],[1,15],[3,10],[3,15],[9,10],[9,15]], [[1,10],[1,16],[2,10],[2,16],[5,10],[5,16]], [[1,10],[1,16],[4,10],[4,16],[5,10],[5,16]], [[1,11],[1,12],[1,13],[3,11],[3,12],[3,13]], [[1,11],[1,12],[3,11],[3,12],[5,11],[5,12]], [[1,11],[1,13],[1,14],[9,11],[9,13],[9,14]], [[1,11],[1,13],[4,11],[4,13],[9,11],[9,13]], [[1,11],[1,15],[1,16],[4,11],[4,15],[4,16]], [[1,11],[1,15],[1,16],[9,11],[9,15],[9,16]], [[1,11],[1,15],[2,11],[2,15],[4,11],[4,15]], [[1,11],[1,15],[2,11],[2,15],[9,11],[9,15]], [[1,11],[1,16],[4,11],[4,16],[9,11],[9,16]], [[1,12],[1,13],[1,15],[4,12],[4,13],[4,15]], [[1,12],[1,13],[1,16],[3,12],[3,13],[3,16]], [[1,12],[1,15],[1,16],[4,12],[4,15],[4,16]], [[1,12],[1,16],[2,12],[2,16],[3,12],[3,16]], [[1,13],[1,14],[4,13],[4,14],[9,13],[9,14]], [[1,13],[1,16],[2,13],[2,16],[5,13],[5,16]], [[1,14],[1,15],[1,16],[5,14],[5,15],[5,16]], [[1,14],[1,15],[1,16],[9,14],[9,15],[9,16]], [[1,14],[1,15],[2,14],[2,15],[5,14],[5,15]], [[1,14],[1,16],[4,14],[4,16],[5,14],[5,16]], [[1,14],[1,16],[4,14],[4,16],[9,14],[9,16]], [[2,6],[2,7],[2,11],[6,9],[7,9],[9,11]], [[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],[2,12],[6,9],[9,11],[9,12]], [[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],[2,12],[5,6],[5,12],[6,9],[9,12]], [[2,6],[2,13],[2,15],[3,6],[3,13],[3,15]], [[2,6],[2,13],[3,6],[3,13],[5,6],[5,13]], [[2,6],[2,15],[3,6],[3,15],[6,9],[9,15]], [[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],[2,10],[2,13],[8,9],[9,10],[9,13]], [[2,8],[2,10],[4,8],[4,10],[8,9],[9,10]], [[2,8],[2,12],[2,13],[8,9],[9,12],[9,13]], [[2,8],[2,12],[4,8],[4,12],[8,9],[9,12]], [[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],[2,13],[2,16],[9,10],[9,13],[9,16]], [[2,10],[2,16],[4,10],[4,16],[5,10],[5,16]], [[2,10],[2,16],[4,10],[4,16],[9,10],[9,16]], [[2,11],[2,12],[2,14],[4,11],[4,12],[4,14]], [[2,11],[2,12],[2,14],[9,11],[9,12],[9,14]], [[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],[2,14],[3,11],[3,14],[9,11],[9,14]], [[2,11],[2,15],[2,16],[3,11],[3,15],[3,16]], [[2,11],[2,15],[3,11],[3,15],[9,11],[9,15]], [[2,12],[2,13],[2,14],[9,12],[9,13],[9,14]], [[2,12],[2,15],[2,16],[3,12],[3,15],[3,16]], [[2,13],[2,14],[3,13],[3,14],[9,13],[9,14]], [[2,13],[2,16],[4,13],[4,16],[5,13],[5,16]], [[2,13],[2,16],[4,13],[4,16],[9,13],[9,16]], [[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],[3,8],[3,12],[7,9],[8,9],[9,12]], [[3,7],[3,10],[3,12],[7,9],[9,10],[9,12]], [[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]], [[3,10],[3,12],[3,14],[4,10],[4,12],[4,14]], [[3,10],[3,12],[3,15],[9,10],[9,12],[9,15]], [[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]], [[3,11],[3,13],[3,14],[9,11],[9,13],[9,14]], [[3,11],[3,13],[4,11],[4,13],[9,11],[9,13]], [[3,11],[3,15],[3,16],[9,11],[9,15],[9,16]], [[3,11],[3,16],[5,11],[5,16],[9,11],[9,16]], [[3,12],[3,15],[3,16],[9,12],[9,15],[9,16]], [[3,12],[3,16],[5,12],[5,16],[9,12],[9,16]], [[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],[4,13],[4,14],[6,9],[9,13],[9,14]], [[4,6],[4,13],[4,16],[6,9],[9,13],[9,16]], [[4,6],[4,14],[4,16],[5,6],[5,14],[5,16]], [[4,6],[4,14],[4,16],[6,9],[9,14],[9,16]], [[4,7],[4,8],[4,12],[7,9],[8,9],[9,12]], [[4,7],[4,8],[4,15],[7,9],[8,9],[9,15]], [[4,7],[4,12],[5,7],[5,12],[7,9],[9,12]], [[4,7],[4,13],[4,16],[5,7],[5,13],[5,16]], [[4,7],[4,15],[5,7],[5,15],[7,9],[9,15]], [[4,8],[4,10],[4,11],[8,9],[9,10],[9,11]], [[4,8],[4,11],[5,8],[5,11],[8,9],[9,11]], [[4,8],[4,15],[5,8],[5,15],[8,9],[9,15]], [[4,10],[4,11],[4,16],[9,10],[9,11],[9,16]], [[5,7],[5,12],[5,16],[7,9],[9,12],[9,16]], [[5,7],[5,15],[5,16],[7,9],[9,15],[9,16]], [[5,8],[5,10],[5,13],[8,9],[9,10],[9,13]], [[5,8],[5,10],[5,14],[8,9],[9,10],[9,14]], [[5,8],[5,11],[5,16],[8,9],[9,11],[9,16]], [[5,8],[5,13],[5,15],[8,9],[9,13],[9,15]], [[5,8],[5,14],[5,16],[8,9],[9,14],[9,16]], [[5,10],[5,13],[5,15],[9,10],[9,13],[9,15]], [[5,10],[5,14],[5,15],[9,10],[9,14],[9,15]], [[5,14],[5,15],[5,16],[9,14],[9,15],[9,16]], ]; # PL-equivalent to # P_3 f = (15,97,164,82) complex:=[ [1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,7], [1,4,6,8],[1,4,7,9],[1,4,8,9],[1,5,6,10],[1,5,7,11],[1,5,10,11], [1,6,8,10],[1,7,9,12],[1,7,11,12],[1,8,9,13],[1,8,10,13],[1,9,12,13], [1,10,11,13],[1,11,12,13],[2,3,4,11],[2,3,5,9],[2,3,9,11],[2,4,6,13], [2,4,11,13],[2,5,6,14],[2,5,9,14],[2,6,13,14],[2,9,10,11],[2,9,10,14], [2,10,11,13],[2,10,13,14],[3,4,7,10],[3,4,10,14],[3,4,11,14], [3,5,7,13],[3,5,9,13],[3,6,8,10],[3,6,8,11],[3,6,9,11],[3,6,9,12], [3,6,10,12],[3,7,10,15],[3,7,13,15],[3,8,10,14],[3,8,11,14], [3,9,12,13],[3,10,12,15],[3,12,13,15],[4,5,8,9],[4,5,8,15],[4,5,9,14], [4,5,12,14],[4,5,12,15],[4,6,8,15],[4,6,13,15],[4,7,9,10],[4,9,10,14], [4,11,12,13],[4,11,12,14],[4,12,13,15],[5,6,10,12],[5,6,12,14], [5,7,8,11],[5,7,8,13],[5,8,9,13],[5,8,11,15],[5,10,11,15],[5,10,12,15], [6,7,9,12],[6,7,9,15],[6,7,12,14],[6,7,13,14],[6,7,13,15],[6,8,11,15], [6,9,11,15],[7,8,11,14],[7,8,13,14],[7,9,10,15],[7,11,12,14], [8,10,13,14],[9,10,11,15] ];