 Covolume

The covolume of a full Euclidean lattice is the Lebesgue measure of a fundamental parallelepiped in its ambient inner-product space. In orthonormal coordinates it is $|\det B|$ for a lattice basis matrix $B$. Scaling the lattice by $t>0$ multiplies the covolume by $t^n$; the dual lattice has reciprocal covolume.