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Tetrahedron

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For the academic journal, see Tetrahedron (journal).
Regular Tetrahedron
Tetrahedron
(Click here for rotating model)
TypePlatonic solid
ElementsF = 4, E = 6
V = 4 (χ = 2)
Faces by sides4{3}
Schläfli symbol{3,3} and s{2,2}
Wythoff symbol3 | 2 3
| 2 2 2
Coxeter-DynkinCDW ringCDW 3CDW dotCDW 3CDW dot
CDW holeCDW 2cCDW holeCDW 2cCDW hole
CDW holeCDW 4CDW dotCDW 2cCDW hole
CDW holeCDW 4CDW dotCDW 3CDW dot
SymmetryTd
or (*332)
ReferencesU01, C15, W1
PropertiesRegular convex deltahedron
Dihedral angle70.528779° = arccos(1/3)
Tetrahedron vertfig
3.3.3
(Vertex figure)
Tetrahedron
Self-dual
(dual polyhedron)
Tetrahedron flat
Net

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids.

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 triangular pyramid or Digonal Deltahedron.

Formulas for regular tetrahedron

The volume is V=\frac{\sqrt3}{12}S^3

The surface area is SA=\sqrt3S^2

External links

Template:Commonscat

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