127 citations · 375 across the 44 of their papers we have counts for
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Affine subgroups of the affine Coxeter group with the same Coxeter number
Nazife Ozdes Koca, Mehmet Koca
Affine subgroups having the same Coxeter number with the affine Coxeter groups W(An), W(Dn), and W(En) are constructed by graph folding technique. The affine groups W(Cn) and W(Bn)…
Affine Dihedral Subgroups of Higher Dimensional Cubic Lattices and Quasicrystallography
Nazife Ozdes Koca, Mehmet Koca, Ramazan Koc +1
Quasicrystals described as the projections of higher dimensional cubic lattices, and the particular affine extensions of the dihedral group of order , being the…
From Affine to Affine : Group Theoretical Analysis of Five-fold Tilings
Nazife Ozdes Koca, Ramazan Koc, Mehmet Koca +1
The projections of the lattices, may be used as models of quasicrystals, and the particular affine extension of the symmetry as a subgroup of , discussed in the work, pr…
4D Pyritohedral Symmetry with Quaternions, Related Polytopes and Lattices
Mehmet Koca, Nazife Ozdes Koca, Amal Juma Hamood Al-Qanobi
We describe extension of the pyritohedral symmetry to 4-dimensional Euclidean space and present the group elements in terms of quaternions. It turns out that it is a maximal subgro…
Quaternionic Representations of the Pyritohedral Group, Related Polyhedra and Lattices
Nazife Ozdes Koca, Mehmet Koca, Aida Al-Mukhaini +1
We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine Coxeter groups W(D3) and W(B3…
Group Theoretical Analysis of Quasicrystallography from Projections of Higher Dimensional Lattices Bn
Mehmet Koca, Nazife Ozdes Koca, Ramazan Koc
A group theoretical discussion on the hypercubic lattice described by the affine Coxeter-Weyl group Wa(Bn) has been presented. When the lattice is projected onto the Coxeter plane…