---
tag: 00C2WN1H21
kind: definition
name: Polyhedron
msc: [52B10]
defines: 0325SGSJAR
uses: [0FQSDC2EQ2, 0V3XAMF3C1]
sources:
  - url: https://en.wikipedia.org/wiki/Polyhedron
    locator: Definition
  - url: https://en.wikipedia.org/wiki/Polyhedron
    locator: lead section
---

## Definition

A convex polyhedron is the [[convex hull|0FQSDC2EQ2]] of a finite set of points of $\mathbb{R}^3$ that do not all lie in one [[plane|0V3XAMF3C1]].
A polyhedron is a bounded subset of $\mathbb{R}^3$ with a connected interior that is the union of finitely many convex polyhedra.
Its faces are the connected parts of its boundary inside the planes that cover the boundary. Its edges and vertices are the segments and points where the faces meet.

## Remarks

There is no single definition of a polyhedron that all authors use. Some definitions describe a surface in place of a solid, and some allow self-crossing faces.
A convex polyhedron is also a bounded intersection of finitely many closed half-spaces, with a nonempty interior.
Examples are the cube, the regular tetrahedron and each prism over a convex polygon.

## Explanations

### L1 human

A polyhedron is a solid with flat sides, like a box or a pyramid. A ball is not one, because its surface is curved. The cube has $8$ vertices, $12$ edges and $6$ faces.