Tetrahedron

In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.[1]

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.[2]

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.[3]

  1. ^ Weisstein, Eric W. "Tetrahedron". MathWorld.
  2. ^ Uehara, Ryuhei (2020). "Fig. 4.6: All nets of a regular tetrahedron and a regular octahedron by edge-unfolding". Introduction to Computational Origami: The World of New Computational Geometry. Singapore: Springer. p. 64. doi:10.1007/978-981-15-4470-5. ISBN 978-981-15-4469-9. MR 4215620.
  3. ^ Ford, Walter Burton; Ammerman, Charles (1913), Plane and Solid Geometry, Macmillan, pp. 294–295
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