---
tag: R7V3S9V891
kind: concept
name: Vertex of a polytope
msc: [52B05, 52B11]
specializes: [KY7SB854VH]
sources:
  - url: https://en.wikipedia.org/wiki/Vertex_(geometry)
---

## Summary

A vertex of a [[convex polytope|300K6CB1KH]] is a [[face|KY7SB854VH]] of dimension zero, that is, a corner point of the polytope.
Vertices are exactly the [[extreme points|3MSGFJM2NX]] of the polytope: the points that are not inside a segment between two other points of it.
A convex polytope is the [[convex hull|0FQSDC2EQ2]] of its vertices, and no smaller set of points has this hull.
So the vertices form the most economical description of a polytope, the V-description.

## Explanations

### L1 human

The vertices of a polytope are its corners.
A square has four, a cube has eight, a tetrahedron has four.
At a vertex you can tilt a flat plane so that it touches the solid at that point only.
If you know the corners, you know the whole solid: stretch a skin tightly around them and it gives the polytope back.