Stereographic Visualization of 5-Dimensional Regular Polytopes

Abstract

Regular polytopes (RPs) are an extension of 2D (two-dimensional) regular polygons and 3D regular polyhedra in n-dimensional (n≥4) space. The high abstraction and perfect symmetry are their most prominent features. The traditional projections only show vertex and edge information. Although such projections can preserve the highest degree of symmetry of the RPs, they can not transmit their metric or topological information. Based on the generalized stereographic projection, this paper establishes visualization methods for 5D RPs, which can preserve symmetries and convey general metric and topological data. It is a general strategy that can be extended to visualize n-dimensional RPs (n>5).