A fundamental parallelepiped of a full-rank point lattice 
with basis 
is the half-open set
 |
The translations 
for 
form a set partition
of 
,
so 
is a fundamental domain for these translations.
The closure of 
is the parallelepiped spanned
by the basis vectors. Different
bases of the point lattice
generally give different fundamental parallelepipeds, but all have the same volume,
namely the covolume of 
(Regev 2004, pp. 2, 4).
