Cubohemioctahedron

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The cubohemioctahedron is the uniform polyhedron with Maeder index 15 (Maeder 1997), Wenninger index 78 (Wenninger 1989), Coxeter index 51 (Coxeter et al. 1954), and Har'El index 20 (Har'El 1993). It has Wythoff symbol 👁 4/34|3
. Its faces are 👁 4{6}+6{4}
, making it a (non-regular) decahedron with intersecting faces. It is a faceted version of the cuboctahedron.

The cubohemioctahedron is implemented in the Wolfram Language as [78], [], [👁 {
, 51👁 }
], [👁 {
, 20👁 }
], [👁 {
, 15👁 }
], or [👁 {
, 78👁 }
]. It is also implemented in the Wolfram Language as [].

Its skeleton is the cuboctahedral graph, illustrated above in a number of embeddings.

Its circumradius for unit edge length is 👁 R=1
.

Its dual is the hexahemioctacron.

See also

Hexahemioctacron, 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. "15: Cubohemioctahedron." 1997. https://www.mathconsult.ch/static/unipoly/15.html.Wenninger, M. J. "Cubohemioctahedron." Model 78 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 121-122, 1971.

Referenced on Wolfram|Alpha

Cubohemioctahedron

Cite this as:

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

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