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Title: Tetrahemihexacron  
Author: World Heritage Encyclopedia
Language: English
Subject: List of polygons, polyhedra and polytopes, List of Wenninger polyhedron models, Table of polyhedron dihedral angles
Publisher: World Heritage Encyclopedia


Type Star polyhedron
Elements F = 6, E = 12
V = 7 (χ = 1)
Symmetry group Td, [3,3], *332
Index references DU04
dual polyhedron)

In geometry, the tetrahemihexacron is the dual of the tetrahemihexahedron, and is one of nine dual hemipolyhedra.

Since the tetrahemihexahedron has three square faces passing through the model centre, the tetrahemihexacron has three vertices at infinity. In Magnus Wenninger's Dual Models, they are represented with intersecting infinite prisms passing through the model centre, cut off at a certain point that is convenient for the maker.

Topologically it is considered to contain seven vertices. The three vertices considered at infinity (the real projective plane at infinity) correspond directionally to the three vertices of the hemi-octahedron, an abstract polyhedron. The other four vertices exist at alternate corners of a central cube (a demicube, in this case a tetrahedron).


  • (Page 101, Duals of the (nine) hemipolyhedra)

External links

  • MathWorld.
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