Extensions of dually bipartite regular polytopes

This paper addresses the problem of finding abstract regular polytopes with preassigned facets and preassigned last entry of the Schlنfli symbol. Using C-group permutation representation (CPR) graphs we give a solution to this problem for dually bipartite regular polytopes when the last entry of the Schlنfli symbol is even. This construction is related to a previous construction by Schulte that solves the problem when the entry of the Schlنfli symbol is 6.