---
tag: JFX8ASQS3E
kind: concept
name: Tetrahedron
msc: [51M20, 52B10]
specializes: [0325SGSJAR]
sources:
  - url: https://en.wikipedia.org/wiki/Tetrahedron
same_as:
  wikidata: Q160003
  wikipedia: Tetrahedron
---

## Summary

A tetrahedron is a [[polyhedron|0325SGSJAR]] with four triangular faces, six edges and four vertices.
It is the convex hull of four points of space that do not lie in one plane.
It is the three-dimensional [[simplex|YX1DJK2QAG]], the simplest solid, and it plays the role in space that the triangle plays in the plane.

## Explanations

### L1 human

A tetrahedron is a pyramid on a triangular base.
Take four points that do not lie on one flat sheet and join each pair by a straight edge: the solid you get has four triangle faces.
The corners $(0, 0, 0)$, $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$ give a tetrahedron of volume $1/6$.
The regular tetrahedron, with all four faces equilateral, is one of the five Platonic solids.