Polyhedra obtained from Coxeter groups and quaternions
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 …
from the Coxeter-Dynkin diagrams. The vertices of a regular or semiregular polytope are the …
Quaternionic root systems and subgroups of the Aut (F4)
Cayley-Dickson doubling procedure is used to construct the root systems of some
celebrated Lie algebras in terms of the integer elements of the division algebras of real …
celebrated Lie algebras in terms of the integer elements of the division algebras of real …
Affine coxeter group Wa(A4), quaternions, and decagonal quasicrystals
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 …
dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined …
4D-POLYTOPES AND THEIR DUAL POLYTOPES OF THE COXETER GROUP W(A4) REPRESENTED BY QUATERNIONS
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 …
of the Coxeter–Weyl group W (A4) where the group elements and the vertices of the …
grand unified theory, its polytopes and 5-fold symmetric aperiodic tiling
We associate the lepton–quark families with the vertices of the 4D polytopes 5-cell (0 0 0 1)
A 4 and the rectified 5-cell (0 1 0 0) A 4 derived from the SU (5) Coxeter–Dynkin diagram …
A 4 and the rectified 5-cell (0 1 0 0) A 4 derived from the SU (5) Coxeter–Dynkin diagram …
Clifford Spinors and Root System Induction: and the Grand Antiprism
PP Dechant - Advances in Applied Clifford Algebras, 2021 - Springer
Recent work has shown that every 3D root system allows the construction of a
corresponding 4D root system via an 'induction theorem'. In this paper, we look at the …
corresponding 4D root system via an 'induction theorem'. In this paper, we look at the …
Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions
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 …
quasicrystallography have been studied with the quaternionic representation of the Coxeter …
Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system
Vertices of the 4-dimensional semi-regular polytope, snub 24-cell and its symmetry group (W
(D4)/C2): S3 of order 576 are represented in terms of quaternions with unit norm. It follows …
(D4)/C2): S3 of order 576 are represented in terms of quaternions with unit norm. It follows …
Examples of simply reducible groups
Y Luan - Journal of the Korean Mathematical Society, 2020 - koreascience.kr
Simply reducible groups are important in physics and chemistry, which contain some of the
important groups in condensed matter physics and crystal symmetry. By studying the group …
important groups in condensed matter physics and crystal symmetry. By studying the group …
Chiral polyhedra derived from Coxeter diagrams and quaternions
There are two chiral Archimedean polyhedra, the snub cube and snub dodecahedron
together with their duals the Catalan solids, pentagonal icositetrahedron and pentagonal …
together with their duals the Catalan solids, pentagonal icositetrahedron and pentagonal …