Tetrahedron
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For the academic journal, see Tetrahedron (journal).
Regular Tetrahedron | |
---|---|
(Click here for rotating model) | |
Type | Platonic solid |
Elements | F = 4, E = 6 V = 4 (χ = 2) |
Faces by sides | 4{3} |
Schläfli symbol | {3,3} and s{2,2} |
Wythoff symbol | 3 | 2 3 | 2 2 2 |
Coxeter-Dynkin | |
Symmetry | T_{d} or (*332) |
References | U_{01}, C_{15}, W_{1} |
Properties | Regular convex deltahedron |
Dihedral angle | 70.528779° = arccos(1/3) |
3.3.3 (Vertex figure) | Self-dual (dual polyhedron) |
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
The surface area is
External links
- F. M. Jackson and Weisstein, Eric W., "Tetrahedron" from MathWorld.
- Weisstein, Eric W., "Tetrahedron" from MathWorld.
- Weisstein, Eric W., "Tetrahedron" from MathWorld.
- The Uniform Polyhedra
- Tetrahedron: Interactive Polyhedron Model
- K. J. M. MacLean, A Geometric Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra
- Piero della Francesca's formula for tetrahedron volume at MathPages
- Free paper models of a tetrahedron and many other polyhedra
- An Amazing, Space Filling, Non-regular Tetrahedron that also includes a description of a "rotating ring of tetrahedra", also known as a kaleidocycle.
- Tetrahedron Core Network Application of a tetrahedral structure to create resilient partial-mesh data network
- Explicit exact formulas for the inertia tensor of an arbitrary tetrahedron in terms of its vertex coordinates
- The inertia tensor of a tetrahedron