# Tetrahedron

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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

TypePlatonic solid
ElementsF = 4, E = 6
V = 4 (χ = 2)
Faces by sides4{3}
Conway notationT
Schläfli symbols{3,3}
h{4,3}, s{2,4}, sr{2,2}
Face configurationV3.3.3
Wythoff symbol3 | 2 3
| 2 2 2
Coxeter diagram =

SymmetryTd, A3, [3,3], (*332)
Rotation groupT, [3,3]+, (332)
ReferencesU01, C15, W1
Propertiesregular, convexdeltahedron
Dihedral angle70.528779° = arccos(13)

3.3.3
(Vertex figure)

Self-dual
(dual polyhedron)

Net
Close

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]