Polytetrahedron is a term used for three distinct types of objects, all based
on the
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
:
*A
uniform convex 4-polytope made up of 600
tetrahedral cells. It is more commonly known as a
600-cell or hexacosichoron. Other derivative 4-polytope are identified as polytetrahedra, where a qualifying prefix such as ''rectified'' or ''truncated'' is used.
*A connected set of
regular tetrahedra, the 3-dimensional analogue of a
polyiamond
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle. The word ''polyiamond'' is a back-formation from ''diamond'', because this word is often used to describe ...
. Polytetrahedra and polyiamonds are related as
polycubes are related to
polyominoes.
*In
origami, a polypolyhedron is "a compound of multiple linked
polyhedral skeletons with
uniform
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...
nonintersecting edges
There exist two topologically distinct polytetrahedra, each made up of four intersecting
triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, an ...
s.
See also
*
Compound of five tetrahedra
*
Compound of ten tetrahedra
The compound of ten tetrahedra is one of the five regular polyhedral compounds. This polyhedron can be seen as either a stellation of the icosahedron or a compound. This compound was first described by Edmund Hess in 1876.
It can be seen as a f ...
References
*
*
4-polytopes
Polyhedra
Paper folding
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