Polytetrahedron

Short description: Solid objects based on tetrahedrons

Polytetrahedron is a term used for three distinct types of objects, all based on the tetrahedron:

• 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. 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 nonintersecting edges" [1]. There exist two topologically distinct polytetrahedra, each made up of four intersecting triangles.

See also

• Compound of five tetrahedra
• Compound of ten tetrahedra

References

• Sloane, N. J. A., ed. "Sequence A119602 (Number of nonisomorphic polytetrahedra with n identical regular tetrahedra connected face-to-face and/or edge-to-edge (chiral shapes counted twice))". OEIS Foundation. https://oeis.org/A119602. 
• Lang, Robert J. "Polypolyhedra in Origami" (PDF). http://www.langorigami.com/science/computational/polypolyhedra/polypolyhedra.php.