Abstract. A polytope is perfect if its shape cannot be changed without changing the action of its symmetry group on its face-lattice. Perfect polytopes are completely known only in dimensions 2 and 3, while exploring their various possible classes in dimension $4$ is still in progress. Here a new class is constructed which is closely related to regular 4-polytopes. In addition, there are some interesting coincidences between the $f$-vectors of some of them, which are briefly discussed at the end of the paper.

AMS Subject Classification (1991): 20F55, 52B05, 52B15

Received May 28, 2002, and in revised form March 24, 2003. (Registered under 2939/2009.)