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Tetrahemihexahedron

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U04

The tetrahemihexahedron is the uniform polyhedron with Maeder index 4 (Maeder 1997), Wenninger index 67 (Wenninger 1989), Coxeter index 36 (Coxeter et al. 1954), and Har'El index 9 (Har'El 1993). It has Schläfli symbol r^'{3; 3} and Wythoff symbol 3/23|2. Its faces are 4{3}+3{4}. It is a faceted form of the octahedron.

The tetrahemihexahedron is implemented in the Wolfram Language as UniformPolyhedron[67], UniformPolyhedron["Tetrahemihexahedron"], UniformPolyhedron[{"Coxeter", 36}], UniformPolyhedron[{"Kaleido", 9}], UniformPolyhedron[{"Uniform", 4}], or UniformPolyhedron[{"Wenninger", 67}]. It is also implemented in the Wolfram Language as PolyhedronData["Tetrahemihexahedron"].

Its dual polyhedron is the tetrahemihexacron and its skeleton is the octahedral graph.

For unit edge lengths, its circumradius is

R=1/2sqrt(2).
U04Hull

The convex hull of the tetrahemihexahedron is the octahedron.

See also

Uniform Polyhedron

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References

Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform Polyhedra." Phil. Trans. Roy. Soc. London Ser. A 246, 401-450, 1954.Har'El, Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47, 57-110, 1993.Maeder, R. E. "04: Tetrahemihexahedron." 1997. https://www.mathconsult.ch/static/unipoly/04.html.Wenninger, M. J. "Tetrahemihexahedron." Model 67 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 101-102, 1971.

Referenced on Wolfram|Alpha

Tetrahemihexahedron

Cite this as:

Weisstein, Eric W. "Tetrahemihexahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Tetrahemihexahedron.html

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