In this paper, we show that affine extensions of non-crystallographic Coxeter groups can be
derived via Coxeter-Dynkin diagram foldings and projections of affine extended versions of …

A group-theoretical discussion on the hypercubic lattice described by the affine Coxeter–
Weyl group Wa (Bn) is presented. When the lattice is projected onto the Coxeter plane it is …

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 …

We introduce a technique of projection onto the Coxeter plane of an arbitrary higher-
dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined …

The projections of lattices may be used as models of quasicrystals, and the particular affine
extension of the H2 symmetry as a subgroup of A4, discussed in this work, presents a …

We study the Weyl groups of hyperbolic Kac–Moody algebras of 'over-extended'type and
ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K= R …

This paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its
relation to the E 8 root lattice. The FIG was originally constructed to represent the …

The largest finite subgroup of O (4) is the non-crystallographic Coxeter group W (H4) of
order 14,400. Its derived subgroup is the largest finite subgroup W (H4)/Z2 of SO (4) of order …

The root systems of SO (8), SO (9) and F 4 are constructed by quaternions. Triality manifests
itself as permutations of pure quaternion units e 1, e 2 and e 3. It is shown that the …