# Tetrahedron

## Polyhedron with 4 faces / From Wikipedia, the free encyclopedia

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In geometry, a **tetrahedron** (plural: **tetrahedra** or **tetrahedrons**), also known as a **triangular pyramid**, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra.[1]

**Table info: Regular tetrahedron...**▼

Regular tetrahedron | |
---|---|

(Click here for rotating model) | |

Type | Platonic solid |

Elements | F = 4, E = 6V = 4 (χ = 2) |

Faces by sides | 4{3} |

Conway notation | T |

Schläfli symbols | {3,3} |

h{4,3}, s{2,4}, sr{2,2} | |

Face configuration | V3.3.3 |

Wythoff symbol | 3 | 2 3 | 2 2 2 |

Coxeter diagram | = |

Symmetry | T_{d}, A_{3}, [3,3], (*332) |

Rotation group | T, [3,3]^{+}, (332) |

References | U_{01}, C_{15}, W_{1} |

Properties | regular, convexdeltahedron |

Dihedral angle | 70.528779° = arccos(1⁄3) |

3.3.3 (Vertex figure) |
Self-dual (dual polyhedron) |

Net |

The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a **3-simplex**.

The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid".

Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets.[1]

For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's faces.[2]