A(4) Root System

This model is designed to represent a 3-dimensional shadow of the convex hull of the root system of type A(4), otherwise known as the root system for SL(5,C).  The 4-dimensional solid has two types of 3-dimensional faces, namely triangular prisms and tetrahedra, this shape possessing 10 tetrahedra and 20 tiangular prisms.  Furthermore, this shape has a 2-dimensional shadow whose symmetry is the dihedral group of order 20, reflecting the fact that the Coxeter number for A(4) is 5.