Parallelepipeds vs. Zonotopes

An n-dimensional Parallelepiped P :

spanned by n basis vectors v1 ... vn Rn

as: P = { Σ xi vi : xi ∈[-1,1] }

An n-dimensional Zonotope Z :

spanned by m⩾ n vectors v1 ... vm Rn

as: Z = { Σ xi vi : xi ∈[-1,1] }