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] }
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] }