A tetrahedron is a polyhedron consists of four triangular faces, three of which meet at each vertex. A regular tetrahedron is a tetrahedron in which the four triangles are regular or equilateral. A polyhedron is a geometric solid in three dimensions with flat faces and straight edges. The tetrahedron is a 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, all the four faces are triangles and any of the four faces can be considered the base, so a tetrahedron is also known as a triangular pyramid.

Tetrahedron is a Platonic solid. A Platonic solid is a convex polyhedron that is regular. It means that the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and angles.

There are five more Platonic solids. They are Tetrahedron, Cube (or hexahedron), Octahedron, Dodecahedron and Icosahedrons.

Tetrahedron-euler's Formula

Eulerâ€™s formula gives a relationship between the numbers of vertices (V), edges (E), and faces (F) of a geometric figure. It is given as below:

? = V - E + F

Where X - Euler characteristic, V - number of Vertices, E - number of Edges and F - number of Faces.

Name | Vertices (V) | Edges(E) | Faces(F) | Euler's characteristic (V - E + F) |

Tetrahedron | 4 | 6 | 4 | 2 |

For a regular tetrahedron of edge length a:

Base plane area = A_{0 = ?3 a}^{2 }/4

Surface area = A = 4 A_{0 }= ?3 a^{2}

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Height = h = ?6a /3

Volume = V = A_{0}h /3 = ?2 a^{3}/12