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# Tetrahedron

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

Euler’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

## Formulas for a Regular Tetrahedron

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For a regular tetrahedron of edge length a:

Base plane area   = A0 = ?3 a2 /4

Surface area      = A   =  4 A0   = ?3 a2

Height                = h    =  ?6a /3

Volume                  = V    = A0h /3     = ?2 a3/12

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