Binary Icosahedral Group and 600-Cell

Abstract

In this article, we have an explicit description of the binary isosahedral group as a 600-cell. We introduce a method to construct binary polyhedral groups as a subset of quaternions H via spin map of SO(3). In addition, we show that the binary icosahedral group in H is the set of vertices of a 600-cell by applying the Coxeter–Dynkin diagram of H4.

Keywords

• binary polyhedral group
• icosahedron
• dodecahedron
• 600-cell