Primary Hypergeodesic Polytopes

Abstract

In this paper, we introduce the concept of a hypergeodesic polytope, as a four-dimensional analogue of the well-known geodesic polyhdron in 3-space. In particular, we describe twenty-eight types of primary hypergeodesic polytopes, those which are most typical, and which are most likely to be employed in structural design.

All of these primary hypergeodesic polytopes are derived from two regular 4-polytopes, the 120- and the 600-cell. They outwardly resemble 3-dimensional geodesic domes having one or two layers of framework, and possess many desirable architectural characteristics.

Cartesian coordinates of their vertices and chord factors can be determined from the figures and tables provided in the appendices to this article.