%0 Journal Article %T Generalized CPR-graphs and applications %A Daniel Pellicer %A Asia Ivi£¿ Weiss %J Contributions to Discrete Mathematics %D 2010 %I University of Calgary %X We give conditions for oriented labeled graphs that must be satisfied in order that such are permutations representations for groups of automorphisms of chiral or orientably regular polytopes. We develop a technique for construction of highly symmetric polytopes using such graphs. In particular, we construct chiral polytopes with the automorphism group $S_n$ for each $n>5$, an infinite family of finite chiral polytopes of rank $4$, a polytope of rank $5$, as well as several infinite chiral polyhedra. %U http://cdm.math.ucalgary.ca/cdm/index.php/cdm/article/view/199