Editing Tetrahedron (section)

==Related polyhedra and compounds==
A regular tetrahedron can be seen as a triangular [[Pyramid (geometry)|pyramid]].
{{Pyramids}}

A regular tetrahedron can be seen as a degenerate polyhedron, a uniform ''digonal [[antiprism]]'', where base polygons are reduced [[digon]]s.
{{UniformAntiprisms}}

A regular tetrahedron can be seen as a degenerate polyhedron, a uniform dual ''digonal [[trapezohedron]]'', containing 6 vertices, in two sets of colinear edges.
{{Trapezohedra}}

A truncation process applied to the tetrahedron produces a series of [[uniform polyhedra]]. Truncating edges down to points produces the [[octahedron]] as a rectified tetrahedron. The process completes as a birectification, reducing the original faces down to points, and producing the self-dual tetrahedron once again.
{{Tetrahedron family}}

This polyhedron is topologically related as a part of sequence of regular polyhedra with [[Schläfli symbol]]s {3,''n''}, continuing into the [[Hyperbolic space|hyperbolic plane]].
{{Triangular regular tiling}}

The tetrahedron is topologically related to a series of regular polyhedra and tilings with order-3 [[vertex figure]]s.
{{Order-3 tiling table}}

<gallery mode="packed" caption="Compounds of tetrahedra">
Image:CubeAndStel.svg|[[Stella octangula|Two tetrahedra in a cube]]
Image:Compound of five tetrahedra.png|[[Compound of five tetrahedra]]
Image:Compound of ten tetrahedra.png|[[Compound of ten tetrahedra]]
</gallery>

{{clear}}

An interesting polyhedron can be constructed from [[Compound of five tetrahedra|five intersecting tetrahedra]]. This [[Polyhedral compound|compound]] of five tetrahedra has been known for hundreds of years. It comes up regularly in the world of [[origami]]. Joining the twenty vertices would form a regular [[dodecahedron]]. There are both [[left-handed]] and [[right-handed]] forms, which are [[mirror image]]s of each other. Superimposing both forms gives a [[compound of ten tetrahedra]], in which the ten tetrahedra are arranged as five pairs of [[stella octangula|stellae octangulae]]. A stella octangula is a compound of two tetrahedra in dual position and its eight vertices define a cube as their convex hull.

The [[square hosohedron]] is another polyhedron with four faces, but it does not have triangular faces.

The [[Szilassi polyhedron]] and the tetrahedron are the only two known polyhedra in which each face shares an edge with each other face. Furthermore, the [[Császár polyhedron]] (itself is the dual of Szilassi polyhedron) and the tetrahedron are the only two known polyhedra in which every diagonal lies on the sides.