---
tag: Z5SA6A67KF
kind: concept
name: Zonotope
msc: [52B12, 52B11, 52C35]
specializes: [300K6CB1KH]
sources:
  - url: https://en.wikipedia.org/wiki/Zonohedron
---

## Summary

A zonotope is a [[convex polytope|300K6CB1KH]] that is a [[Minkowski sum|7GK5417BJF]] of finitely many line segments.
Equivalently, it is the image of a cube under an affine map.
Zonotopes are centrally symmetric, and all of their faces are again zonotopes.
They are closely tied to [[hyperplane arrangements|N602W0WAVT]].
The face structure of a zonotope is dual to that of a central arrangement with one hyperplane for each generating segment.
Three-dimensional zonotopes are called zonohedra, and limits of zonotopes are [[zonoids|ZMZZ2QRFTZ]].

## Explanations

### L1 human

Take a few sticks pointing in different directions.
Sweep a point along the first stick, then sweep the resulting segment along the second stick, and so on.
The final shape is a zonotope.
Two sticks give a parallelogram; three sticks in the plane give a hexagon with opposite sides parallel; three sticks in space give a box-like parallelepiped.