# section between (2,3,4,5,6) and (1,7,... ,16), # a topological real projective 3-space with f-vector # 5*11 = 55 vertices, # 385 edges, # 384 triangles, 207 quadrilaterals, # 123 tetrahedra and 138 prisms rp3:= [ [[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],[3,7],[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],[5,7],[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]], [[1,6],[6,7],[6,8],[6,9]], [[1,6],[6,7],[6,8],[6,13]], [[1,6],[6,8],[6,9],[6,12]], [[1,6],[6,8],[6,12],[6,14]], [[1,6],[6,8],[6,13],[6,16]], [[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]], [[2,9],[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]], [[2,12],[4,12],[5,12],[6,12]], [[2,13],[3,13],[4,13],[5,13]], [[2,13],[3,13],[5,13],[6,13]], [[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]], [[4,7],[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]], [[5,7],[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]], [[6,7],[6,8],[6,9],[6,13]], [[6,7],[6,9],[6,10],[6,13]], [[6,7],[6,9],[6,10],[6,14]], [[6,7],[6,9],[6,11],[6,14]], [[6,7],[6,10],[6,12],[6,15]], [[6,7],[6,10],[6,13],[6,15]], [[6,7],[6,10],[6,14],[6,16]], [[6,7],[6,11],[6,12],[6,15]], [[6,7],[6,11],[6,12],[6,16]], [[6,7],[6,11],[6,13],[6,15]], [[6,7],[6,11],[6,14],[6,16]], [[6,8],[6,9],[6,12],[6,13]], [[6,8],[6,10],[6,11],[6,15]], [[6,8],[6,10],[6,15],[6,16]], [[6,8],[6,12],[6,13],[6,14]], [[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]], [[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]], [[1,2],[1,6],[2,7],[2,9],[6,7],[6,9]], [[1,2],[1,6],[2,7],[2,13],[6,7],[6,13]], [[1,2],[1,6],[2,8],[2,14],[6,8],[6,14]], [[1,2],[1,6],[2,8],[2,16],[6,8],[6,16]], [[1,2],[1,6],[2,9],[2,15],[6,9],[6,15]], [[1,2],[1,6],[2,13],[2,16],[6,13],[6,16]], [[1,2],[1,6],[2,14],[2,15],[6,14],[6,15]], [[1,3],[1,4],[1,6],[3,10],[4,10],[6,10]], [[1,3],[1,4],[1,6],[3,14],[4,14],[6,14]], [[1,3],[1,4],[3,10],[3,14],[4,10],[4,14]], [[1,3],[1,5],[1,6],[3,9],[5,9],[6,9]], [[1,3],[1,5],[1,6],[3,11],[5,11],[6,11]], [[1,3],[1,5],[3,9],[3,12],[5,9],[5,12]], [[1,3],[1,5],[3,11],[3,12],[5,11],[5,12]], [[1,3],[1,6],[3,9],[3,15],[6,9],[6,15]], [[1,3],[1,6],[3,10],[3,11],[6,10],[6,11]], [[1,3],[1,6],[3,14],[3,15],[6,14],[6,15]], [[1,4],[1,5],[1,6],[4,10],[5,10],[6,10]], [[1,4],[1,5],[1,6],[4,14],[5,14],[6,14]], [[1,4],[1,5],[4,10],[4,16],[5,10],[5,16]], [[1,4],[1,5],[4,14],[4,16],[5,14],[5,16]], [[1,5],[1,6],[5,9],[5,12],[6,9],[6,12]], [[1,5],[1,6],[5,10],[5,11],[6,10],[6,11]], [[1,5],[1,6],[5,12],[5,14],[6,12],[6,14]], [[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],[2,9],[2,11],[6,7],[6,9],[6,11]], [[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],[2,11],[2,13],[6,7],[6,11],[6,13]], [[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]], [[2,8],[2,14],[2,15],[6,8],[6,14],[6,15]], [[2,8],[2,15],[2,16],[6,8],[6,15],[6,16]], [[2,9],[2,10],[2,16],[4,9],[4,10],[4,16]], [[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],[2,12],[4,9],[4,12],[5,9],[5,12]], [[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],[5,10],[5,11],[6,10],[6,11]], [[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],[2,12],[4,11],[4,12],[6,11],[6,12]], [[2,11],[2,13],[5,11],[5,13],[6,11],[6,13]], [[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],[2,15],[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]], [[3,7],[3,10],[3,12],[6,7],[6,10],[6,12]], [[3,7],[3,10],[3,16],[6,7],[6,10],[6,16]], [[3,7],[3,12],[3,14],[4,7],[4,12],[4,14]], [[3,7],[3,12],[4,7],[4,12],[6,7],[6,12]], [[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]], [[3,7],[3,16],[4,7],[4,16],[6,7],[6,16]], [[3,8],[3,10],[3,11],[6,8],[6,10],[6,11]], [[3,8],[3,10],[3,16],[6,8],[6,10],[6,16]], [[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],[3,11],[5,8],[5,11],[6,8],[6,11]], [[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],[3,14],[3,15],[6,8],[6,14],[6,15]], [[3,8],[3,14],[4,8],[4,14],[6,8],[6,14]], [[3,8],[3,15],[4,8],[4,15],[5,8],[5,15]], [[3,8],[3,15],[5,8],[5,15],[6,8],[6,15]], [[3,8],[3,16],[4,8],[4,16],[6,8],[6,16]], [[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],[3,12],[4,10],[4,12],[6,10],[6,12]], [[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]], [[3,11],[3,12],[3,16],[5,11],[5,12],[5,16]], [[3,13],[3,15],[5,13],[5,15],[6,13],[6,15]], [[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],[4,12],[5,7],[5,12],[6,7],[6,12]], [[4,7],[4,13],[4,16],[5,7],[5,13],[5,16]], [[4,7],[4,16],[5,7],[5,16],[6,7],[6,16]], [[4,8],[4,9],[4,11],[5,8],[5,9],[5,11]], [[4,8],[4,9],[4,15],[5,8],[5,9],[5,15]], [[4,8],[4,13],[4,14],[6,8],[6,13],[6,14]], [[4,8],[4,13],[4,16],[6,8],[6,13],[6,16]], [[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]], [[4,10],[4,11],[4,15],[6,10],[6,11],[6,15]], [[4,10],[4,12],[4,15],[6,10],[6,12],[6,15]], [[4,11],[4,12],[4,15],[6,11],[6,12],[6,15]], [[4,14],[4,16],[5,14],[5,16],[6,14],[6,16]], [[5,7],[5,12],[5,16],[6,7],[6,12],[6,16]], [[5,8],[5,11],[5,15],[6,8],[6,11],[6,15]], [[5,11],[5,13],[5,15],[6,11],[6,13],[6,15]], [[5,12],[5,14],[5,16],[6,12],[6,14],[6,16]], ]; # PL-equivalent to # RP^3 f = (11,51,80,40) 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], [1,4,6,7],[1,5,6,7],[2,3,4,8],[2,3,5,9],[2,3,8,9],[2,4,6,10], [2,4,8,10],[2,5,6,11],[2,5,9,11],[2,6,10,11],[2,7,8,9],[2,7,8,10], [2,7,9,11],[2,7,10,11],[3,4,7,11],[3,4,8,11],[3,5,7,10],[3,5,9,10], [3,6,8,9],[3,6,8,11],[3,6,9,10],[3,6,10,11],[3,7,10,11],[4,5,8,10], [4,5,8,11],[4,5,9,10],[4,5,9,11],[4,6,7,9],[4,6,9,10],[4,7,9,11], [5,6,7,8],[5,6,8,11],[5,7,8,10],[6,7,8,9] ];