Sublattice (Euclidean geometry)
= Sublattice
{disambiguate=Euclidean geometry}
= Sublattice
{synonym}
A sublattice is a <subgroup> of a <Euclidean lattice>. It is a <Euclidean lattice> in its real <linear span>, which may have smaller <dimension> than the original ambient <Euclidean space>. The equal-parity integer points in $\mathbb Z^d$ form a full-rank <sublattice> of index $2^{d-1}$: reduction of all coordinate differences modulo two gives the quotient.