2013/05/08 by Joseph Ray Clarence G. Damasco, Dirk Frettlöh, Damasco, Joseph Ray Clarence G. +3
Materials Science · Mathematics · #05B45 #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Metric Geometry (math.MG) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1305.1798
openalex publication_date 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that most lattices Γ in ℝ2 and ℝ3 possess a fundamental domain F for the action of Γ on ℝ2, respectively ℝ3, having more symmetries than the point group P(Γ), i.e., the group P (Γ) ⊂ O(d) fixing Γ. In particular, P (Γ) is a subgroup of the symmetry group S(F) of F of index 2 in these cases. Exceptions are cubic lattices in the three-dimensional case, where such an F does not exist. Possible exceptions are rhombic lattices in the plane case, where the constructions presented here do not seem to work.