Abstract
Affine subgroups having the same Coxeter number with the affine Coxeter groups W(An), W(Dn) and W(En) are constructed by graph folding techniques. The affine groups W(Cn) and W(Bn) are obtained from the Coxeter groups W(A2n-1) and W(D2n-2), respectively. The affine groups W(E6), W(D6) and W(E8) lead to the affine groups W(F4), W(H3) and W(H4) respectively by graph folding. The latter two are the non-crystallographic groups where W(H3) plays a special role in the quasicrystallographic structures with icosahedral symmetry. A general construction of the affine dihedral subgroups is introduced, some of which describe the existing planar quasicrystallography. In the construction of the root systems, sets of orthonormal vectors are used but a special non-orthogonal set of vectors in the formulation of the root system of W(An) is also introduced which has practical applications in the construction of the lattices An and An* and their Delone and Voronoi cells.
Keywords
Publication details
- DOI
- 10.53539/2414-536x.1399
- Journal
- Sultan Qaboos University Journal for Science, 30(1), 16-22
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Koca, N. O., & Koca, M. (2025). Affine Subgroups of the Affine Coxeter Group with the Same Coxeter Number. Sultan Qaboos University Journal for Science, 30(1), 16-22. https://doi.org/10.53539/2414-536x.1399
MLA 9
Koca, Nazife Ozdes, and Mehmet Koca. "Affine Subgroups of the Affine Coxeter Group with the Same Coxeter Number." Sultan Qaboos University Journal for Science, vol. 30, no. 1, 2025, pp. 16-22. https://doi.org/10.53539/2414-536x.1399.
Chicago (author–date)
Koca, Nazife Ozdes, and Mehmet Koca. 2025. "Affine Subgroups of the Affine Coxeter Group with the Same Coxeter Number." Sultan Qaboos University Journal for Science 30 (1): 16-22. https://doi.org/10.53539/2414-536x.1399.
Harvard
Koca, N. O. and Koca, M. (2025) 'Affine Subgroups of the Affine Coxeter Group with the Same Coxeter Number', Sultan Qaboos University Journal for Science, 30(1), pp. 16-22. doi:10.53539/2414-536x.1399.
Vancouver
Koca NO, Koca M. Affine Subgroups of the Affine Coxeter Group with the Same Coxeter Number. Sultan Qaboos University Journal for Science. 2025;30(1):16-22. doi:10.53539/2414-536x.1399
IEEE
N. O. Koca, and M. Koca, "Affine Subgroups of the Affine Coxeter Group with the Same Coxeter Number," Sultan Qaboos University Journal for Science, vol. 30, no. 1, pp. 16-22, 2025, doi: 10.53539/2414-536x.1399.