4D-polytopes and their dual polytopes of the coxeter group W(A _4) represented by quaternions

摘要

Four-dimensional A _4 polytopes and their dual polytopes have been constructed as the orbits of the CoxeterWeyl group W(A _4) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(A _4) orbit into three dimensions is made using the subgroup W(A _3). A generalization of the Catalan solids for 3D-polyhedra has been developed and dual polytopes of the uniform A _4 polytopes have been constructed.