# section between (1,... ,8) and (9,... ,16), # a topological 3-torus with "f-vector": # 8*8 = 64 vertices, # 488 edges, # 384 triangles, 288 quadrilaterals, # 96 tetrahedra and 192 prisms 3torus:= [ [[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]], [[1,9],[2,9],[6,9],[7,9]], [[1,9],[3,9],[5,9],[6,9]], [[1,9],[3,9],[7,9],[8,9]], [[1,9],[6,9],[7,9],[8,9]], [[1,10],[1,11],[1,12],[1,13]], [[1,10],[1,11],[1,13],[1,14]], [[1,10],[2,10],[5,10],[8,10]], [[1,10],[3,10],[4,10],[6,10]], [[1,10],[4,10],[5,10],[6,10]], [[1,11],[2,11],[4,11],[7,11]], [[1,11],[3,11],[5,11],[6,11]], [[1,11],[3,11],[7,11],[8,11]], [[1,11],[4,11],[7,11],[8,11]], [[1,12],[2,12],[3,12],[8,12]], [[1,13],[2,13],[5,13],[7,13]], [[1,13],[2,13],[6,13],[7,13]], [[1,13],[6,13],[7,13],[8,13]], [[1,14],[2,14],[5,14],[8,14]], [[1,14],[2,14],[6,14],[8,14]], [[1,14],[3,14],[4,14],[6,14]], [[1,14],[4,14],[5,14],[6,14]], [[1,15],[2,15],[4,15],[7,15]], [[1,15],[2,15],[5,15],[7,15]], [[1,15],[4,15],[7,15],[8,15]], [[1,16],[2,16],[3,16],[8,16]], [[1,16],[2,16],[6,16],[8,16]], [[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]], [[2,9],[3,9],[5,9],[6,9]], [[2,10],[2,12],[2,13],[2,14]], [[2,10],[2,12],[2,15],[2,16]], [[2,10],[2,13],[2,15],[2,16]], [[2,10],[4,10],[5,10],[6,10]], [[2,10],[4,10],[7,10],[8,10]], [[2,10],[5,10],[7,10],[8,10]], [[2,12],[3,12],[7,12],[8,12]], [[2,12],[4,12],[5,12],[6,12]], [[2,12],[4,12],[7,12],[8,12]], [[2,13],[3,13],[4,13],[5,13]], [[2,13],[3,13],[5,13],[6,13]], [[2,14],[5,14],[7,14],[8,14]], [[2,16],[3,16],[7,16],[8,16]], [[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]], [[3,11],[4,11],[5,11],[8,11]], [[3,11],[5,11],[6,11],[8,11]], [[3,12],[4,12],[6,12],[7,12]], [[3,13],[4,13],[5,13],[7,13]], [[3,14],[4,14],[6,14],[8,14]], [[3,15],[4,15],[5,15],[7,15]], [[3,15],[4,15],[5,15],[8,15]], [[3,15],[5,15],[6,15],[8,15]], [[3,16],[4,16],[6,16],[7,16]], [[3,16],[4,16],[6,16],[8,16]], [[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]], [[4,12],[5,12],[6,12],[7,12]], [[4,16],[5,16],[6,16],[7,16]], [[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]], [[6,9],[6,10],[6,13],[6,16]], [[6,9],[6,10],[6,14],[6,16]], [[6,9],[6,11],[6,12],[6,14]], [[6,9],[6,12],[6,13],[6,14]], [[6,10],[6,13],[6,15],[6,16]], [[6,11],[6,12],[6,14],[6,16]], [[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]], [[8,9],[8,10],[8,11],[8,16]], [[8,9],[8,10],[8,14],[8,16]], [[8,10],[8,11],[8,15],[8,16]], [[8,11],[8,12],[8,14],[8,15]], [[8,11],[8,12],[8,14],[8,16]], [[8,12],[8,13],[8,14],[8,15]], [[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],[1,12],[3,9],[3,12],[8,9],[8,12]], [[1,9],[1,12],[5,9],[5,12],[6,9],[6,12]], [[1,9],[1,12],[6,9],[6,12],[8,9],[8,12]], [[1,9],[1,13],[1,14],[4,9],[4,13],[4,14]], [[1,9],[1,14],[1,16],[4,9],[4,14],[4,16]], [[1,9],[1,15],[2,9],[2,15],[6,9],[6,15]], [[1,9],[1,15],[3,9],[3,15],[6,9],[6,15]], [[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],[6,10],[6,11]], [[1,10],[1,11],[3,10],[3,11],[7,10],[7,11]], [[1,10],[1,11],[5,10],[5,11],[6,10],[6,11]], [[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],[1,12],[2,10],[2,12],[8,10],[8,12]], [[1,10],[1,12],[5,10],[5,12],[8,10],[8,12]], [[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],[1,13],[3,11],[3,13],[8,11],[8,13]], [[1,11],[1,13],[4,11],[4,13],[8,11],[8,13]], [[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],[1,14],[5,12],[5,14],[6,12],[6,14]], [[1,12],[1,14],[5,12],[5,14],[8,12],[8,14]], [[1,12],[1,14],[6,12],[6,14],[8,12],[8,14]], [[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],[1,15],[4,13],[4,15],[8,13],[8,15]], [[1,13],[1,15],[7,13],[7,15],[8,13],[8,15]], [[1,13],[1,16],[2,13],[2,16],[5,13],[5,16]], [[1,13],[1,16],[2,13],[2,16],[6,13],[6,16]], [[1,13],[1,16],[3,13],[3,16],[8,13],[8,16]], [[1,13],[1,16],[5,13],[5,16],[7,13],[7,16]], [[1,13],[1,16],[6,13],[6,16],[8,13],[8,16]], [[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],[1,15],[2,14],[2,15],[6,14],[6,15]], [[1,14],[1,15],[3,14],[3,15],[6,14],[6,15]], [[1,14],[1,16],[4,14],[4,16],[5,14],[5,16]], [[1,15],[1,16],[5,15],[5,16],[7,15],[7,16]], [[2,9],[2,10],[2,13],[8,9],[8,10],[8,13]], [[2,9],[2,10],[2,16],[4,9],[4,10],[4,16]], [[2,9],[2,10],[4,9],[4,10],[8,9],[8,10]], [[2,9],[2,11],[2,12],[6,9],[6,11],[6,12]], [[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],[2,11],[6,9],[6,11],[7,9],[7,11]], [[2,9],[2,12],[2,13],[8,9],[8,12],[8,13]], [[2,9],[2,12],[4,9],[4,12],[5,9],[5,12]], [[2,9],[2,12],[4,9],[4,12],[8,9],[8,12]], [[2,9],[2,12],[5,9],[5,12],[6,9],[6,12]], [[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]], [[2,9],[2,15],[3,9],[3,15],[6,9],[6,15]], [[2,10],[2,11],[4,10],[4,11],[6,10],[6,11]], [[2,10],[2,11],[4,10],[4,11],[7,10],[7,11]], [[2,10],[2,11],[5,10],[5,11],[6,10],[6,11]], [[2,10],[2,11],[5,10],[5,11],[7,10],[7,11]], [[2,10],[2,12],[2,13],[8,10],[8,12],[8,13]], [[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],[2,12],[4,11],[4,12],[6,11],[6,12]], [[2,11],[2,13],[5,11],[5,13],[6,11],[6,13]], [[2,11],[2,13],[5,11],[5,13],[7,11],[7,13]], [[2,11],[2,13],[6,11],[6,13],[7,11],[7,13]], [[2,11],[2,14],[2,15],[4,11],[4,14],[4,15]], [[2,11],[2,14],[2,15],[8,11],[8,14],[8,15]], [[2,11],[2,14],[2,16],[3,11],[3,14],[3,16]], [[2,11],[2,14],[2,16],[8,11],[8,14],[8,16]], [[2,11],[2,15],[2,16],[3,11],[3,15],[3,16]], [[2,11],[2,15],[2,16],[8,11],[8,15],[8,16]], [[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],[2,15],[2,16],[6,13],[6,15],[6,16]], [[2,13],[2,15],[3,13],[3,15],[6,13],[6,15]], [[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],[2,15],[6,14],[6,15],[8,14],[8,15]], [[2,14],[2,16],[3,14],[3,16],[7,14],[7,16]], [[2,14],[2,16],[7,14],[7,16],[8,14],[8,16]], [[2,15],[2,16],[6,15],[6,16],[8,15],[8,16]], [[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]], [[3,9],[3,12],[7,9],[7,12],[8,9],[8,12]], [[3,10],[3,11],[6,10],[6,11],[8,10],[8,11]], [[3,10],[3,11],[7,10],[7,11],[8,10],[8,11]], [[3,10],[3,12],[3,14],[4,10],[4,12],[4,14]], [[3,10],[3,12],[4,10],[4,12],[6,10],[6,12]], [[3,10],[3,12],[6,10],[6,12],[7,10],[7,12]], [[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]], [[3,10],[3,16],[6,10],[6,16],[7,10],[7,16]], [[3,10],[3,16],[6,10],[6,16],[8,10],[8,16]], [[3,10],[3,16],[7,10],[7,16],[8,10],[8,16]], [[3,11],[3,12],[3,16],[5,11],[5,12],[5,16]], [[3,11],[3,13],[4,11],[4,13],[8,11],[8,13]], [[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],[3,15],[5,13],[5,15],[6,13],[6,15]], [[3,13],[3,16],[4,13],[4,16],[7,13],[7,16]], [[3,13],[3,16],[4,13],[4,16],[8,13],[8,16]], [[3,14],[3,15],[4,14],[4,15],[7,14],[7,15]], [[3,14],[3,15],[4,14],[4,15],[8,14],[8,15]], [[3,14],[3,15],[5,14],[5,15],[7,14],[7,15]], [[3,14],[3,15],[6,14],[6,15],[8,14],[8,15]], [[4,9],[4,10],[4,11],[8,9],[8,10],[8,11]], [[4,9],[4,11],[5,9],[5,11],[8,9],[8,11]], [[4,9],[4,12],[5,9],[5,12],[7,9],[7,12]], [[4,9],[4,12],[7,9],[7,12],[8,9],[8,12]], [[4,9],[4,13],[4,14],[6,9],[6,13],[6,14]], [[4,9],[4,13],[4,16],[6,9],[6,13],[6,16]], [[4,9],[4,14],[4,16],[6,9],[6,14],[6,16]], [[4,9],[4,15],[5,9],[5,15],[7,9],[7,15]], [[4,9],[4,15],[5,9],[5,15],[8,9],[8,15]], [[4,9],[4,15],[7,9],[7,15],[8,9],[8,15]], [[4,10],[4,11],[4,15],[6,10],[6,11],[6,15]], [[4,10],[4,11],[7,10],[7,11],[8,10],[8,11]], [[4,10],[4,12],[4,15],[6,10],[6,12],[6,15]], [[4,11],[4,12],[4,15],[6,11],[6,12],[6,15]], [[4,13],[4,14],[4,15],[8,13],[8,14],[8,15]], [[4,13],[4,14],[6,13],[6,14],[8,13],[8,14]], [[4,13],[4,16],[5,13],[5,16],[7,13],[7,16]], [[4,13],[4,16],[6,13],[6,16],[8,13],[8,16]], [[4,14],[4,16],[5,14],[5,16],[6,14],[6,16]], [[5,9],[5,10],[5,13],[8,9],[8,10],[8,13]], [[5,9],[5,10],[5,14],[8,9],[8,10],[8,14]], [[5,9],[5,11],[5,16],[8,9],[8,11],[8,16]], [[5,9],[5,12],[5,16],[7,9],[7,12],[7,16]], [[5,9],[5,13],[5,15],[8,9],[8,13],[8,15]], [[5,9],[5,14],[5,16],[8,9],[8,14],[8,16]], [[5,9],[5,15],[5,16],[7,9],[7,15],[7,16]], [[5,10],[5,11],[5,14],[7,10],[7,11],[7,14]], [[5,10],[5,12],[5,13],[8,10],[8,12],[8,13]], [[5,10],[5,14],[7,10],[7,14],[8,10],[8,14]], [[5,11],[5,12],[5,15],[8,11],[8,12],[8,15]], [[5,11],[5,12],[5,16],[8,11],[8,12],[8,16]], [[5,11],[5,13],[5,14],[7,11],[7,13],[7,14]], [[5,11],[5,13],[5,15],[6,11],[6,13],[6,15]], [[5,11],[5,15],[6,11],[6,15],[8,11],[8,15]], [[5,12],[5,13],[5,15],[8,12],[8,13],[8,15]], [[5,12],[5,14],[5,16],[6,12],[6,14],[6,16]], [[5,12],[5,14],[5,16],[8,12],[8,14],[8,16]], [[5,12],[5,16],[6,12],[6,16],[7,12],[7,16]], [[6,9],[6,10],[6,13],[7,9],[7,10],[7,13]], [[6,9],[6,10],[6,14],[7,9],[7,10],[7,14]], [[6,9],[6,11],[6,14],[7,9],[7,11],[7,14]], [[6,9],[6,12],[6,13],[8,9],[8,12],[8,13]], [[6,9],[6,13],[7,9],[7,13],[8,9],[8,13]], [[6,10],[6,11],[6,15],[8,10],[8,11],[8,15]], [[6,10],[6,12],[6,15],[7,10],[7,12],[7,15]], [[6,10],[6,13],[6,15],[7,10],[7,13],[7,15]], [[6,10],[6,14],[6,16],[7,10],[7,14],[7,16]], [[6,10],[6,15],[6,16],[8,10],[8,15],[8,16]], [[6,11],[6,12],[6,15],[7,11],[7,12],[7,15]], [[6,11],[6,12],[6,16],[7,11],[7,12],[7,16]], [[6,11],[6,13],[6,15],[7,11],[7,13],[7,15]], [[6,11],[6,14],[6,16],[7,11],[7,14],[7,16]], [[6,12],[6,13],[6,14],[8,12],[8,13],[8,14]], [[7,9],[7,13],[7,15],[8,9],[8,13],[8,15]], [[7,10],[7,14],[7,16],[8,10],[8,14],[8,16]] ]; # PL-equivalent to ## T^3 f = (15,105,180,90) complex:= [ [1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,8], [1,3,7,9],[1,3,8,9],[1,4,6,10],[1,4,7,11],[1,4,10,11],[1,5,6,12], [1,5,8,13],[1,5,12,13],[1,6,10,14],[1,6,12,14],[1,7,9,11],[1,8,9,13], [1,9,11,15],[1,9,13,15],[1,10,11,14],[1,11,14,15],[1,12,13,14], [1,13,14,15],[2,3,4,12],[2,3,5,14],[2,3,10,12],[2,3,10,14],[2,4,6,13], [2,4,8,12],[2,4,8,13],[2,5,6,15],[2,5,9,14],[2,5,9,15],[2,6,11,13], [2,6,11,15],[2,7,8,10],[2,7,8,11],[2,7,9,10],[2,7,9,11],[2,8,10,12], [2,8,11,13],[2,9,10,14],[2,9,11,15],[3,4,7,12],[3,5,8,14],[3,6,7,9], [3,6,7,13],[3,6,8,9],[3,6,8,15],[3,6,11,13],[3,6,11,15],[3,7,12,13], [3,8,14,15],[3,10,11,12],[3,10,11,14],[3,11,12,13],[3,11,14,15], [4,5,7,11],[4,5,7,14],[4,5,9,14],[4,5,9,15],[4,5,10,11],[4,5,10,15], [4,6,10,13],[4,7,12,14],[4,8,9,12],[4,8,9,13],[4,9,12,14],[4,9,13,15], [4,10,13,15],[5,6,12,15],[5,7,8,11],[5,7,8,14],[5,8,11,13], [5,10,11,12],[5,10,12,15],[5,11,12,13],[6,7,9,10],[6,7,10,13], [6,8,9,12],[6,8,12,15],[6,9,10,14],[6,9,12,14],[7,8,10,15],[7,8,14,15], [7,10,13,15],[7,12,13,14],[7,13,14,15],[8,10,12,15] ];