  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.
