Crystallographic Restrictions for Colour Lattices with Modular Sublattices

Details Crystallographic Restrictions for Colour Lattices with Modular Sublattices Crystallographic Restrictions for Colour Lattices with Modular Sublattices

2002-05-14

arxiv.org/abs/math-ph/0205020v1

Physics

Mathematical Physics

18 pages, 2 figures

Scientific paper

The {\em d} -- dimensional $n$ -- colour lattice ${\bf \Bbb{L}}^d$ with modular sublattices are studied, when the only one crystallographic type of sublattices does exist and the only one of the colours occupies a sublattice, which is still invariant under $k$--fold rotation $C_k$. Such kind of colouring always preserves an equal fractions of the colours composed ${\bf \Bbb{L}}^d$. The $n$ -- colour lattice with modular sublattices allow to exist the crystallographic rotations $C_k$ for $k=p^r, r\geq 1$ and $n\leq p$, where $p$ is a prime number.

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