Catalan solids are the duals of the Archimedean solids, the vertices of which can be
obtained from the Coxeter–Dynkin diagrams A 3⁠, B 3⁠, and H 3 whose simple roots can be …

Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter–Weyl
groups W (An) and W (Dn) are constructed. The face-centred cubic (fcc) and body-centred …

We note that all regular and semiregular polytopes in arbitrary dimensions can be obtained
from the Coxeter-Dynkin diagrams. The vertices of a regular or semiregular polytope are the …

Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as
those of E 8, have been used extensively in the literature. The present paper analyses such …

E 8 is prominent in mathematics and theoretical physics, and is generally viewed as an
exceptional symmetry in an eight-dimensional (8D) space very different from the space we …

Four-dimensional A4 polytopes and their dual polytopes have been constructed as the orbits
of the Coxeter–Weyl group W (A4) where the group elements and the vertices of the …

This paper considers the geometry of E 8 from a Clifford point of view in three
complementary ways. Firstly, in earlier work, I had shown how to construct the four …

In this paper, we make the case that Clifford algebra is the natural framework for root
systems and reflection groups, as well as related groups such as the conformal and modular …

cell {3, 3, 5} and 120-cell {5, 3, 3} four-dimensional dual polytopes relevant to
quasicrystallography have been studied with the quaternionic representation of the Coxeter …

This paper shows how regular convex 4-polytopes–the analogues of the Platonic solids in
four dimensions–can be constructed from three-dimensional considerations concerning the …