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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[edit]


  • 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))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  • Lang, Robert J. "Polypolyhedra in Origami" (PDF). Retrieved 2006-12-16.