diff --git a/docs/src/lib/interfaces.md b/docs/src/lib/interfaces.md index 5b3bf14d87..5752e3144f 100644 --- a/docs/src/lib/interfaces.md +++ b/docs/src/lib/interfaces.md @@ -210,6 +210,17 @@ isempty(::AbstractCentrallySymmetricPolytope) A zonotope is a specific centrally symmetric polytope characterized by a center and a collection of generators. +Mathematically, a zonotope is defined as the set + +```math +Z = \\left\\{ c + ∑_{i=1}^p ξ_i g_i,~~ ξ_i \\in [-1, 1]~~ ∀ i = 1,…, p \\right\\}, +``` +where ``c \\in \\mathbb{R}^n`` is its center and ``\\{g_i\\}_{i=1}^p``, +``g_i \\in \\mathbb{R}^n``, is the set of generators. +This characterization defines a zonotope as the finite Minkowski sum of line +segments. +Zonotopes can be equivalently described as the image of a unit infinity-norm +ball in ``\\mathbb{R}^n`` by an affine transformation. ```@docs AbstractZonotope