# section between (1,2,3,5,6,10) and (4,7,8,9,11, ... ,16), # a topological lensspace L(5,1) with f-vector # 6*10 = 60 vertices, # 420 edges, # 380 triangles, 255 quadrilaterals, # 105 tetrahedra and 170 prisms l51:= [ [[1,4],[1,7],[1,8],[1,11]], [[1,4],[1,7],[1,8],[1,15]], [[1,4],[1,8],[1,11],[1,13]], [[1,4],[1,8],[1,13],[1,15]], [[1,4],[1,9],[1,11],[1,13]], [[1,4],[1,9],[1,11],[1,16]], [[1,4],[1,9],[1,13],[1,14]], [[1,4],[1,9],[1,14],[1,16]], [[1,4],[1,11],[1,15],[1,16]], [[1,4],[1,12],[1,13],[1,15]], [[1,4],[1,12],[1,15],[1,16]], [[1,4],[3,4],[4,6],[4,10]], [[1,4],[4,5],[4,6],[4,10]], [[1,7],[1,8],[1,13],[1,15]], [[1,7],[1,9],[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]], [[1,8],[2,8],[5,8],[8,10]], [[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],[3,9],[5,9],[6,9]], [[1,11],[3,11],[5,11],[6,11]], [[1,11],[3,11],[6,11],[10,11]], [[1,11],[5,11],[6,11],[10,11]], [[1,16],[2,16],[5,16],[10,16]], [[2,4],[2,7],[2,8],[2,12]], [[2,4],[2,7],[2,12],[2,14]], [[2,4],[2,7],[2,14],[2,15]], [[2,4],[2,8],[2,9],[2,12]], [[2,4],[2,9],[2,13],[2,16]], [[2,4],[2,11],[2,12],[2,14]], [[2,4],[2,11],[2,14],[2,15]], [[2,4],[4,5],[4,6],[4,10]], [[2,7],[2,8],[2,14],[2,16]], [[2,8],[2,9],[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],[2,11],[2,12],[2,14]], [[2,9],[2,12],[2,13],[2,14]], [[2,9],[3,9],[5,9],[6,9]], [[2,11],[5,11],[6,11],[10,11]], [[2,13],[3,13],[5,13],[6,13]], [[3,4],[3,7],[3,12],[3,14]], [[3,4],[3,7],[3,13],[3,16]], [[3,4],[3,7],[3,14],[3,15]], [[3,4],[3,8],[3,11],[3,13]], [[3,4],[3,8],[3,13],[3,16]], [[3,4],[3,8],[3,14],[3,15]], [[3,4],[3,9],[3,11],[3,13]], [[3,7],[3,8],[3,9],[3,12]], [[3,7],[3,13],[3,14],[3,16]], [[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]], [[4,5],[5,7],[5,9],[5,12]], [[4,5],[5,7],[5,9],[5,15]], [[4,5],[5,7],[5,13],[5,16]], [[4,5],[5,8],[5,9],[5,11]], [[4,5],[5,8],[5,9],[5,15]], [[4,6],[6,8],[6,13],[6,14]], [[4,6],[6,8],[6,13],[6,16]], [[4,6],[6,9],[6,13],[6,14]], [[4,6],[6,9],[6,13],[6,16]], [[4,6],[6,9],[6,14],[6,16]], [[4,6],[6,11],[6,12],[6,15]], [[4,10],[7,10],[8,10],[10,11]], [[4,10],[8,10],[9,10],[10,11]], [[4,10],[9,10],[10,11],[10,16]], [[4,10],[10,11],[10,15],[10,16]], [[4,10],[10,12],[10,13],[10,14]], [[4,10],[10,12],[10,15],[10,16]], [[5,7],[5,9],[5,12],[5,16]], [[5,7],[5,9],[5,15],[5,16]], [[5,7],[5,11],[5,13],[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],[5,11],[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],[5,14],[5,15],[5,16]], [[5,11],[5,12],[5,13],[5,15]], [[6,7],[6,8],[6,9],[6,13]], [[6,7],[6,9],[6,11],[6,14]], [[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],[6,12],[6,13],[6,14]], [[6,9],[6,11],[6,12],[6,14]], [[6,9],[6,12],[6,13],[6,14]], [[6,11],[6,12],[6,14],[6,16]], [[7,10],[8,10],[10,14],[10,16]], [[7,10],[9,10],[10,12],[10,15]], [[7,10],[9,10],[10,13],[10,15]], [[8,10],[9,10],[10,11],[10,16]], [[8,10],[9,10],[10,14],[10,16]], [[8,10],[10,11],[10,15],[10,16]], [[1,4],[1,7],[1,11],[2,4],[2,7],[2,11]], [[1,4],[1,7],[1,15],[2,4],[2,7],[2,15]], [[1,4],[1,11],[1,15],[2,4],[2,11],[2,15]], [[1,4],[1,12],[1,13],[4,10],[10,12],[10,13]], [[1,4],[1,12],[1,16],[4,10],[10,12],[10,16]], [[1,4],[1,13],[1,14],[4,10],[10,13],[10,14]], [[1,4],[1,14],[1,16],[4,5],[5,14],[5,16]], [[1,4],[1,14],[3,4],[3,14],[4,6],[6,14]], [[1,4],[1,14],[3,4],[3,14],[4,10],[10,14]], [[1,4],[1,14],[4,5],[4,6],[5,14],[6,14]], [[1,4],[1,16],[4,5],[4,10],[5,16],[10,16]], [[1,7],[1,8],[1,9],[3,7],[3,8],[3,9]], [[1,7],[1,8],[1,9],[6,7],[6,8],[6,9]], [[1,7],[1,8],[1,11],[3,7],[3,8],[3,11]], [[1,7],[1,8],[1,13],[6,7],[6,8],[6,13]], [[1,7],[1,9],[1,11],[2,7],[2,9],[2,11]], [[1,7],[1,9],[1,14],[7,10],[9,10],[10,14]], [[1,7],[1,9],[2,7],[2,9],[6,7],[6,9]], [[1,7],[1,9],[3,7],[3,9],[7,10],[9,10]], [[1,7],[1,11],[1,14],[7,10],[10,11],[10,14]], [[1,7],[1,11],[3,7],[3,11],[7,10],[10,11]], [[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],[1,13],[2,7],[2,13],[6,7],[6,13]], [[1,7],[1,15],[1,16],[5,7],[5,15],[5,16]], [[1,7],[1,15],[2,7],[2,15],[5,7],[5,15]], [[1,8],[1,9],[1,12],[3,8],[3,9],[3,12]], [[1,8],[1,9],[1,12],[6,8],[6,9],[6,12]], [[1,8],[1,11],[1,13],[3,8],[3,11],[3,13]], [[1,8],[1,12],[1,14],[5,8],[5,12],[5,14]], [[1,8],[1,12],[1,14],[6,8],[6,12],[6,14]], [[1,8],[1,12],[2,8],[2,12],[3,8],[3,12]], [[1,8],[1,12],[2,8],[2,12],[8,10],[10,12]], [[1,8],[1,12],[5,8],[5,12],[8,10],[10,12]], [[1,8],[1,13],[1,16],[3,8],[3,13],[3,16]], [[1,8],[1,13],[1,16],[6,8],[6,13],[6,16]], [[1,8],[1,14],[2,8],[2,14],[5,8],[5,14]], [[1,8],[1,14],[2,8],[2,14],[6,8],[6,14]], [[1,8],[1,16],[2,8],[2,16],[3,8],[3,16]], [[1,8],[1,16],[2,8],[2,16],[6,8],[6,16]], [[1,9],[1,11],[1,15],[2,9],[2,11],[2,15]], [[1,9],[1,12],[3,9],[3,12],[5,9],[5,12]], [[1,9],[1,12],[5,9],[5,12],[6,9],[6,12]], [[1,9],[1,14],[1,15],[9,10],[10,14],[10,15]], [[1,9],[1,15],[2,9],[2,15],[6,9],[6,15]], [[1,9],[1,15],[3,9],[3,15],[6,9],[6,15]], [[1,9],[1,15],[3,9],[3,15],[9,10],[10,15]], [[1,11],[1,12],[1,13],[3,11],[3,12],[3,13]], [[1,11],[1,12],[1,13],[10,11],[10,12],[10,13]], [[1,11],[1,12],[3,11],[3,12],[5,11],[5,12]], [[1,11],[1,12],[5,11],[5,12],[10,11],[10,12]], [[1,11],[1,13],[1,14],[10,11],[10,13],[10,14]], [[1,12],[1,13],[1,16],[3,12],[3,13],[3,16]], [[1,12],[1,14],[5,12],[5,14],[6,12],[6,14]], [[1,12],[1,16],[2,12],[2,16],[3,12],[3,16]], [[1,12],[1,16],[2,12],[2,16],[10,12],[10,16]], [[1,13],[1,16],[2,13],[2,16],[5,13],[5,16]], [[1,13],[1,16],[2,13],[2,16],[6,13],[6,16]], [[1,14],[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],[1,15],[3,14],[3,15],[10,14],[10,15]], [[2,4],[2,7],[2,8],[4,10],[7,10],[8,10]], [[2,4],[2,7],[2,11],[4,10],[7,10],[10,11]], [[2,4],[2,8],[2,9],[4,10],[8,10],[9,10]], [[2,4],[2,9],[2,12],[4,5],[5,9],[5,12]], [[2,4],[2,9],[2,13],[3,4],[3,9],[3,13]], [[2,4],[2,9],[2,16],[4,10],[9,10],[10,16]], [[2,4],[2,9],[3,4],[3,9],[4,5],[5,9]], [[2,4],[2,11],[2,12],[4,6],[6,11],[6,12]], [[2,4],[2,11],[4,6],[4,10],[6,11],[10,11]], [[2,4],[2,12],[4,5],[4,6],[5,12],[6,12]], [[2,4],[2,13],[2,16],[4,5],[5,13],[5,16]], [[2,4],[2,13],[3,4],[3,13],[4,5],[5,13]], [[2,4],[2,16],[4,5],[4,10],[5,16],[10,16]], [[2,7],[2,8],[2,12],[3,7],[3,8],[3,12]], [[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],[2,8],[5,7],[5,8],[7,10],[8,10]], [[2,7],[2,9],[2,11],[6,7],[6,9],[6,11]], [[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],[2,11],[5,7],[5,11],[7,10],[10,11]], [[2,7],[2,12],[2,14],[3,7],[3,12],[3,14]], [[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],[2,13],[8,10],[9,10],[10,13]], [[2,8],[2,12],[2,13],[8,10],[10,12],[10,13]], [[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],[2,11],[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],[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],[9,10],[10,13],[10,16]], [[2,9],[2,15],[3,9],[3,15],[6,9],[6,15]], [[2,11],[2,13],[5,11],[5,13],[6,11],[6,13]], [[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],[2,13],[2,14],[10,12],[10,13],[10,14]], [[2,12],[2,14],[3,12],[3,14],[10,12],[10,14]], [[2,12],[2,15],[2,16],[3,12],[3,15],[3,16]], [[2,12],[2,15],[2,16],[10,12],[10,15],[10,16]], [[2,12],[2,15],[3,12],[3,15],[10,12],[10,15]], [[2,13],[2,14],[3,13],[3,14],[10,13],[10,14]], [[2,13],[2,15],[2,16],[6,13],[6,15],[6,16]], [[2,13],[2,15],[2,16],[10,13],[10,15],[10,16]], [[2,13],[2,15],[3,13],[3,15],[6,13],[6,15]], [[2,13],[2,15],[3,13],[3,15],[10,13],[10,15]], [[3,4],[3,7],[3,12],[4,6],[6,7],[6,12]], [[3,4],[3,7],[3,13],[4,5],[5,7],[5,13]], [[3,4],[3,7],[3,15],[4,5],[5,7],[5,15]], [[3,4],[3,7],[3,16],[4,6],[6,7],[6,16]], [[3,4],[3,8],[3,11],[4,5],[5,8],[5,11]], [[3,4],[3,8],[3,14],[4,6],[6,8],[6,14]], [[3,4],[3,8],[3,15],[4,5],[5,8],[5,15]], [[3,4],[3,8],[3,16],[4,6],[6,8],[6,16]], [[3,4],[3,9],[3,11],[4,5],[5,9],[5,11]], [[3,4],[3,12],[3,14],[4,10],[10,12],[10,14]], [[3,4],[3,12],[4,6],[4,10],[6,12],[10,12]], [[3,7],[3,8],[3,11],[7,10],[8,10],[10,11]], [[3,7],[3,8],[3,16],[7,10],[8,10],[10,16]], [[3,7],[3,9],[3,12],[7,10],[9,10],[10,12]], [[3,7],[3,12],[6,7],[6,12],[7,10],[10,12]], [[3,7],[3,13],[3,14],[5,7],[5,13],[5,14]], [[3,7],[3,14],[3,15],[5,7],[5,14],[5,15]], [[3,7],[3,16],[6,7],[6,16],[7,10],[10,16]], [[3,8],[3,11],[5,8],[5,11],[6,8],[6,11]], [[3,8],[3,11],[6,8],[6,11],[8,10],[10,11]], [[3,8],[3,14],[3,15],[6,8],[6,14],[6,15]], [[3,8],[3,15],[5,8],[5,15],[6,8],[6,15]], [[3,8],[3,16],[6,8],[6,16],[8,10],[10,16]], [[3,9],[3,11],[3,16],[5,9],[5,11],[5,16]], [[3,9],[3,12],[3,15],[9,10],[10,12],[10,15]], [[3,9],[3,12],[3,16],[5,9],[5,12],[5,16]], [[3,11],[3,12],[3,16],[5,11],[5,12],[5,16]], [[3,13],[3,14],[5,13],[5,14],[10,13],[10,14]], [[3,13],[3,15],[5,13],[5,15],[6,13],[6,15]], [[3,13],[3,15],[5,13],[5,15],[10,13],[10,15]], [[3,14],[3,15],[5,14],[5,15],[10,14],[10,15]], [[4,5],[4,6],[5,7],[5,12],[6,7],[6,12]], [[4,5],[4,6],[5,7],[5,16],[6,7],[6,16]], [[4,5],[4,6],[5,14],[5,16],[6,14],[6,16]], [[4,6],[4,10],[6,11],[6,15],[10,11],[10,15]], [[4,6],[4,10],[6,12],[6,15],[10,12],[10,15]], [[5,7],[5,8],[5,14],[7,10],[8,10],[10,14]], [[5,7],[5,11],[5,14],[7,10],[10,11],[10,14]], [[5,7],[5,12],[5,16],[6,7],[6,12],[6,16]], [[5,8],[5,9],[5,13],[8,10],[9,10],[10,13]], [[5,8],[5,9],[5,14],[8,10],[9,10],[10,14]], [[5,8],[5,11],[5,15],[6,8],[6,11],[6,15]], [[5,8],[5,12],[5,13],[8,10],[10,12],[10,13]], [[5,9],[5,13],[5,15],[9,10],[10,13],[10,15]], [[5,9],[5,14],[5,15],[9,10],[10,14],[10,15]], [[5,11],[5,12],[5,13],[10,11],[10,12],[10,13]], [[5,11],[5,13],[5,14],[10,11],[10,13],[10,14]], [[5,11],[5,13],[5,15],[6,11],[6,13],[6,15]], [[5,12],[5,14],[5,16],[6,12],[6,14],[6,16]], [[6,7],[6,9],[6,13],[7,10],[9,10],[10,13]], [[6,7],[6,9],[6,14],[7,10],[9,10],[10,14]], [[6,7],[6,12],[6,15],[7,10],[10,12],[10,15]], [[6,7],[6,13],[6,15],[7,10],[10,13],[10,15]], [[6,7],[6,14],[6,16],[7,10],[10,14],[10,16]], [[6,8],[6,11],[6,15],[8,10],[10,11],[10,15]], [[6,8],[6,15],[6,16],[8,10],[10,15],[10,16]], [[6,9],[6,13],[6,16],[9,10],[10,13],[10,16]], [[6,9],[6,14],[6,16],[9,10],[10,14],[10,16]], [[6,13],[6,15],[6,16],[10,13],[10,15],[10,16]], ]; # PL-equivalent to # L(5,1) 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],[1,5,10,12], [1,5,11,12],[1,6,8,10],[1,7,9,11],[1,8,9,13],[1,8,10,13],[1,9,11,14], [1,9,13,14],[1,10,12,13],[1,11,12,14],[1,12,13,14],[2,3,4,10], [2,3,5,9],[2,3,9,12],[2,3,10,11],[2,3,11,12],[2,4,6,13],[2,4,10,13], [2,5,6,15],[2,5,9,15],[2,6,13,15],[2,8,10,13],[2,8,10,14],[2,8,13,15], [2,8,14,15],[2,9,12,15],[2,10,11,14],[2,11,12,14],[2,12,14,15], [3,4,7,15],[3,4,10,15],[3,5,7,14],[3,5,9,14],[3,6,8,12],[3,6,8,14], [3,6,9,12],[3,6,9,14],[3,7,14,15],[3,8,11,12],[3,8,11,15],[3,8,14,15], [3,10,11,15],[4,5,8,9],[4,5,8,12],[4,5,9,15],[4,5,10,12],[4,5,10,15], [4,6,8,12],[4,6,12,13],[4,7,9,15],[4,10,12,13],[5,6,10,15],[5,7,11,13], [5,7,13,14],[5,8,9,13],[5,8,11,12],[5,8,11,13],[5,9,13,14],[6,7,9,11], [6,7,9,12],[6,7,11,13],[6,7,12,13],[6,8,10,14],[6,9,11,14], [6,10,11,14],[6,10,11,15],[6,11,13,15],[7,9,12,15],[7,12,13,14], [7,12,14,15],[8,11,13,15] ];