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Dodecahedral Structures with Mosseri-Sadoc Tiles
Nazife Ozdes Koca, Ramazan Koc, Mehmet Koca +1
3D-facets of the Delone cells representing the deep and shallow holes of the root lattice D6 which tile the six-dimensional Euclidean space in an alternating order are projected in…
Icosahedral Tiling with Dodecahedral Structures
Mehmet Koca, Ramazan Koc, Nazife Ozdes Koca +1
Icosahedron and dodecahedron can be dissected into tetrahedral tiles projected from 3D-facets of the Delone polytopes representing the deep and shallow holes of the root lattice D_…
Icosahedral Polyhedra from D6 lattice and Danzer's ABCK tiling
Abeer Al-Siyabi, Nazife Ozdes Koca, Mehmet Koca
It is well known that the point group of the root lattice D_6 admits the icosahedral group as a maximal subgroup. The generators of the icosahedral group H_3, its roots and weights…
Prototiles and Tilings from Voronoi and Delone cells of the Root Lattice A_n
Nazife Ozdes Koca, Abeer Al-Siyabi, Mehmet Koca +1
We exploit the fact that two-dimensional facets of the Voronoi and Delone cells of the root lattice A_n in n-dimensional space are the identical rhombuses and equilateral triangles…
Explicit Construction of the Voronoi and Delaunay Cells of W(An) and W(Dn) Lattices and Their Facets
Mehmet Koca, Nazife Ozdes Koca, Abeer Al-Siyabi +1
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 centered cubic (fcc) and body centered cubi…