ProV Logo
0
Highly symmetric fundamental domains for...
Damasco, Joseph Ray ...

Free

Highly symmetric fundamental domains for lattices in R^2 and R^3 by Damasco, Joseph Ray Clarence G. ( Author )
Lemonjar Open Access
Australian National University
26-07-2023
It is shown that most lattices $\Gamma$ in $\mathbb{R}^2$ and $\mathbb{R}^3$ possess a fundamental domain $F$ for the action of $\Gamma$ on $\mathbb{R}^2$, respectively $\mathbb{R}^3$, having more symmetries than the point group $P(\Gamma)$, i.e., the group $P (\Gamma) \subset O(d)$ fixing $\Gamma$. In particular, $P (\Gamma)$ 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.
-
Article
pdf
30.00 KB
English
-
MYR 0.01
1
-
http://arxiv.org/abs/1305.1798
Share this eBook