Classification of non-degenerate regular polyhedral complexes of positive curvature

Abstract

In our paper [3], we classify simple regular polyhedral BP-complexes, which are polyhedral complexes satisfying certain natural conditions (B) and (P) on their vertex structures. Although 2-skeletons of higher dimensional regular polytopes are simple regular polyhedral complexes, they are not included in the above classification because they do not satisfy the condition (B), cf. [4]. It is natural to consider some suitable class of regular polyhedral complexes containing 2-skeletons of higher dimensional regular polytopes. In this paper, relaxing the condition (B), we investigate a non-degenerate regular polyhedral complex satisfying the condition (P), and give a partial answer to the classification of such polyhedral complexes.