Polytetrahedron Explained

Polytetrahedron is a term used for three distinct types of objects, all basedon 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" http://www.langorigami.com/science/polypolyhedra/3rd%20OSME%20Polypolyhedra.pdf. There exist two topologically distinct polytetrahedra, each made up of four intersecting triangles.

See also

• Compound of five tetrahedra
• Compound of ten tetrahedra

References

• A119602. Number of nonisomorphic polytetrahedra with n identical regular tetrahedra connected face-to-face and/or edge-to-edge (chiral shapes counted twice).
• Web site: Lang, Robert J . Polypolyhedra in Origami . . 2006-12-16 .