Twisted honeycombs \(\{\) 3,5,3\(\}\) , and their groups (Q1059279)

A honeycomb of type \(\{\) 3,5,3\(\}\) is finite when it has Petrie polygons of length 4,6,7 or 9. In these cases its group of automorphisms is isomorphic to PSL(2,9), PSL(2,11)\(\times {\mathfrak C}_ 2\), PSL(2,29) or PSL(2,19). Its edges and faces are incident in a manner indicated by the vertices of a bipartite graph of girth 8 (in the first case) or 10, whose group is PGL(2,9), PGL(2,11)\(\times {\mathfrak C}_ 2\), PSL(2,29)\(\times {\mathfrak C}_ 2\) or PGL(2,19), respectively.