A lattice basis of a point lattice 
is a linearly independent
collection of vectors 
such that every element of 
has a unique expression 
with integer coefficients
. Thus the integer
span, not merely the real span, must be the specified
point lattice.
For a smooth polytope, the primitive outgoing directions of the edges at each polytope vertex form a lattice basis of the ambient point lattice (Liu et al. 2026).
