# section between (1,2,3,4,5,7) and (6,8,... ,16), # a topological octahedron space with f-vector # 6*10 = 60 vertices, # 420 edges, # 368 triangles, 264 quadrilaterals, # 96 tetrahedra and 176 prisms octahedronSpace:= [ [[1,6],[1,8],[1,9],[1,12]], [[1,6],[1,8],[1,12],[1,14]], [[1,6],[1,8],[1,13],[1,16]], [[1,9],[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]], [[1,11],[2,11],[4,11],[7,11]], [[1,13],[2,13],[5,13],[7,13]], [[1,15],[2,15],[4,15],[7,15]], [[1,15],[2,15],[5,15],[7,15]], [[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]], [[2,8],[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],[3,8],[3,10],[3,11]], [[3,6],[3,8],[3,10],[3,16]], [[3,6],[3,8],[3,14],[3,15]], [[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]], [[3,13],[4,13],[5,13],[7,13]], [[3,15],[4,15],[5,15],[7,15]], [[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]], [[4,8],[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],[5,8],[5,11],[5,15]], [[5,6],[5,11],[5,13],[5,15]], [[5,6],[5,12],[5,14],[5,16]], [[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]], [[6,7],[7,8],[7,9],[7,13]], [[6,7],[7,9],[7,10],[7,13]], [[6,7],[7,9],[7,10],[7,14]], [[6,7],[7,9],[7,11],[7,14]], [[6,7],[7,10],[7,12],[7,15]], [[6,7],[7,10],[7,13],[7,15]], [[6,7],[7,10],[7,14],[7,16]], [[6,7],[7,11],[7,12],[7,15]], [[6,7],[7,11],[7,12],[7,16]], [[6,7],[7,11],[7,13],[7,15]], [[6,7],[7,11],[7,14],[7,16]], [[7,8],[7,9],[7,13],[7,15]], [[7,8],[7,10],[7,14],[7,16]], [[7,9],[7,10],[7,12],[7,15]], [[7,9],[7,10],[7,13],[7,15]], [[7,9],[7,12],[7,15],[7,16]], [[7,11],[7,12],[7,13],[7,15]], [[7,11],[7,12],[7,13],[7,16]], [[7,11],[7,13],[7,14],[7,16]], [[1,6],[1,8],[1,9],[6,7],[7,8],[7,9]], [[1,6],[1,8],[1,13],[6,7],[7,8],[7,13]], [[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],[1,12],[5,6],[5,9],[5,12]], [[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],[1,9],[2,6],[2,9],[6,7],[7,9]], [[1,6],[1,9],[3,6],[3,9],[5,6],[5,9]], [[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],[1,13],[1,16],[2,6],[2,13],[2,16]], [[1,6],[1,13],[2,6],[2,13],[6,7],[7,13]], [[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]], [[1,8],[1,9],[1,12],[3,8],[3,9],[3,12]], [[1,8],[1,9],[3,8],[3,9],[7,8],[7,9]], [[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],[1,11],[3,8],[3,11],[7,8],[7,11]], [[1,8],[1,11],[4,8],[4,11],[7,8],[7,11]], [[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],[1,13],[1,15],[4,8],[4,13],[4,15]], [[1,8],[1,13],[1,15],[7,8],[7,13],[7,15]], [[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],[1,15],[4,8],[4,15],[7,8],[7,15]], [[1,8],[1,16],[2,8],[2,16],[3,8],[3,16]], [[1,9],[1,10],[1,14],[7,9],[7,10],[7,14]], [[1,9],[1,10],[1,15],[3,9],[3,10],[3,15]], [[1,9],[1,10],[3,9],[3,10],[7,9],[7,10]], [[1,9],[1,11],[1,13],[4,9],[4,11],[4,13]], [[1,9],[1,11],[1,14],[7,9],[7,11],[7,14]], [[1,9],[1,11],[1,15],[2,9],[2,11],[2,15]], [[1,9],[1,11],[1,16],[4,9],[4,11],[4,16]], [[1,9],[1,11],[2,9],[2,11],[7,9],[7,11]], [[1,9],[1,12],[3,9],[3,12],[5,9],[5,12]], [[1,9],[1,13],[1,14],[4,9],[4,13],[4,14]], [[1,9],[1,14],[1,16],[4,9],[4,14],[4,16]], [[1,10],[1,11],[1,12],[5,10],[5,11],[5,12]], [[1,10],[1,11],[1,14],[7,10],[7,11],[7,14]], [[1,10],[1,11],[3,10],[3,11],[7,10],[7,11]], [[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],[3,10],[3,14],[4,10],[4,14]], [[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],[1,15],[1,16],[4,11],[4,15],[4,16]], [[1,11],[1,15],[2,11],[2,15],[4,11],[4,15]], [[1,12],[1,13],[1,15],[4,12],[4,13],[4,15]], [[1,12],[1,13],[1,15],[7,12],[7,13],[7,15]], [[1,12],[1,13],[1,16],[3,12],[3,13],[3,16]], [[1,12],[1,13],[1,16],[7,12],[7,13],[7,16]], [[1,12],[1,15],[1,16],[4,12],[4,15],[4,16]], [[1,12],[1,15],[1,16],[7,12],[7,15],[7,16]], [[1,12],[1,16],[2,12],[2,16],[3,12],[3,16]], [[1,13],[1,16],[2,13],[2,16],[5,13],[5,16]], [[1,13],[1,16],[5,13],[5,16],[7,13],[7,16]], [[1,14],[1,15],[1,16],[5,14],[5,15],[5,16]], [[1,14],[1,15],[2,14],[2,15],[5,14],[5,15]], [[1,14],[1,16],[4,14],[4,16],[5,14],[5,16]], [[1,15],[1,16],[5,15],[5,16],[7,15],[7,16]], [[2,6],[2,9],[2,11],[6,7],[7,9],[7,11]], [[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],[2,11],[2,13],[6,7],[7,11],[7,13]], [[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]], [[2,8],[2,9],[2,10],[4,8],[4,9],[4,10]], [[2,8],[2,9],[2,12],[4,8],[4,9],[4,12]], [[2,8],[2,10],[4,8],[4,10],[7,8],[7,10]], [[2,8],[2,10],[5,8],[5,10],[7,8],[7,10]], [[2,8],[2,12],[3,8],[3,12],[7,8],[7,12]], [[2,8],[2,12],[4,8],[4,12],[7,8],[7,12]], [[2,8],[2,14],[2,16],[7,8],[7,14],[7,16]], [[2,8],[2,14],[5,8],[5,14],[7,8],[7,14]], [[2,8],[2,16],[3,8],[3,16],[7,8],[7,16]], [[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],[2,11],[4,10],[4,11],[7,10],[7,11]], [[2,10],[2,11],[5,10],[5,11],[7,10],[7,11]], [[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],[2,13],[5,11],[5,13],[7,11],[7,13]], [[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],[2,14],[3,12],[3,14],[7,12],[7,14]], [[2,12],[2,14],[4,12],[4,14],[7,12],[7,14]], [[2,12],[2,15],[2,16],[3,12],[3,15],[3,16]], [[2,13],[2,16],[4,13],[4,16],[5,13],[5,16]], [[2,14],[2,15],[4,14],[4,15],[7,14],[7,15]], [[2,14],[2,15],[5,14],[5,15],[7,14],[7,15]], [[2,14],[2,16],[3,14],[3,16],[7,14],[7,16]], [[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],[3,10],[3,12],[6,7],[7,10],[7,12]], [[3,6],[3,10],[3,16],[6,7],[7,10],[7,16]], [[3,6],[3,12],[4,6],[4,12],[6,7],[7,12]], [[3,6],[3,13],[3,15],[5,6],[5,13],[5,15]], [[3,6],[3,16],[4,6],[4,16],[6,7],[7,16]], [[3,8],[3,9],[3,12],[7,8],[7,9],[7,12]], [[3,8],[3,10],[3,11],[7,8],[7,10],[7,11]], [[3,8],[3,10],[3,16],[7,8],[7,10],[7,16]], [[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],[3,10],[3,12],[7,9],[7,10],[7,12]], [[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]], [[3,12],[3,14],[4,12],[4,14],[7,12],[7,14]], [[3,13],[3,14],[3,16],[7,13],[7,14],[7,16]], [[3,13],[3,14],[5,13],[5,14],[7,13],[7,14]], [[3,13],[3,16],[4,13],[4,16],[7,13],[7,16]], [[3,14],[3,15],[4,14],[4,15],[7,14],[7,15]], [[3,14],[3,15],[5,14],[5,15],[7,14],[7,15]], [[4,6],[4,12],[5,6],[5,12],[6,7],[7,12]], [[4,6],[4,14],[4,16],[5,6],[5,14],[5,16]], [[4,6],[4,16],[5,6],[5,16],[6,7],[7,16]], [[4,8],[4,9],[4,11],[5,8],[5,9],[5,11]], [[4,8],[4,9],[4,12],[7,8],[7,9],[7,12]], [[4,8],[4,9],[4,15],[5,8],[5,9],[5,15]], [[4,8],[4,9],[4,15],[7,8],[7,9],[7,15]], [[4,8],[4,10],[4,11],[7,8],[7,10],[7,11]], [[4,9],[4,12],[5,9],[5,12],[7,9],[7,12]], [[4,9],[4,15],[5,9],[5,15],[7,9],[7,15]], [[4,13],[4,16],[5,13],[5,16],[7,13],[7,16]], [[5,6],[5,12],[5,16],[6,7],[7,12],[7,16]], [[5,8],[5,10],[5,14],[7,8],[7,10],[7,14]], [[5,9],[5,12],[5,16],[7,9],[7,12],[7,16]], [[5,9],[5,15],[5,16],[7,9],[7,15],[7,16]], [[5,10],[5,11],[5,14],[7,10],[7,11],[7,14]], [[5,11],[5,13],[5,14],[7,11],[7,13],[7,14]], ]; # PL-equivalent to # octahedron_space f = (15,102,174,87) 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],[1,4,7,8],[1,5,6,9],[1,5,7,10],[1,5,9,10],[1,6,8,11], [1,6,9,11],[1,7,8,12],[1,7,10,13],[1,7,12,13],[1,8,11,12],[1,9,10,13], [1,9,11,14],[1,9,13,14],[1,11,12,14],[1,12,13,14],[2,3,4,15],[2,3,5,8], [2,3,8,15],[2,4,6,12],[2,4,12,15],[2,5,6,13],[2,5,8,11],[2,5,11,13], [2,6,12,13],[2,7,10,13],[2,7,10,14],[2,7,12,13],[2,7,12,15], [2,7,14,15],[2,8,10,11],[2,8,10,14],[2,8,14,15],[2,10,11,13], [3,4,7,11],[3,4,11,13],[3,4,13,15],[3,5,7,14],[3,5,8,12],[3,5,12,14], [3,6,7,11],[3,6,7,14],[3,6,10,11],[3,6,10,12],[3,6,12,14],[3,8,9,12], [3,8,9,13],[3,8,13,15],[3,9,10,12],[3,9,10,13],[3,10,11,13], [4,5,10,14],[4,5,10,15],[4,5,11,13],[4,5,11,14],[4,5,13,15],[4,6,8,10], [4,6,10,12],[4,7,8,9],[4,7,9,11],[4,8,9,14],[4,8,10,14],[4,9,11,14], [4,10,12,15],[5,6,9,15],[5,6,13,15],[5,7,10,14],[5,8,11,12], [5,9,10,15],[5,11,12,14],[6,7,9,11],[6,7,9,15],[6,7,14,15],[6,8,10,11], [6,12,13,14],[6,13,14,15],[7,8,9,12],[7,9,12,15],[8,9,13,14], [8,13,14,15],[9,10,12,15] ];