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Cubitruncated Cuboctahedron

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U16

The cubitruncated cuboctahedron (called the cubotruncated cuboctahedron by Wenninger 1971, p. 121) is the uniform polyhedron with Maeder index 16 (Maeder 1997), Wenninger index 79 (Wenninger 1989), Coxeter index 52 (Coxeter et al. 1954), and Har'El index 21 (Har'El 1993). It has Wythoff symbol 34/34| and its faces are 8{6}+6{8}+6{8/3}. It is a faceted octahedron.

The cubitruncated cuboctahedron is implemented in the Wolfram Language as UniformPolyhedron["CubitruncatedCuboctahedron"]. Precomputed properties are implemented in the Wolfram Language as PolyhedronData["CubitruncatedCuboctahedron", prop].

CubitruncatedCuboctahedralGraph

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

The circumradius for a cubitruncated cuboctahedron of unit edge length is

R=1/2sqrt(7).

The dual is the tetradyakis hexahedron.

See also

Cubitruncated Cuboctahedral Graph, Tetradyakis Hexahedron, 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. "16: Cubitruncated Cuboctahedron." 1997. https://www.mathconsult.ch/static/unipoly/16.html.Wenninger, M. J. "Cubotruncated [sic] Cuboctahedron." Model 79 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 121-122, 1971.

Referenced on Wolfram|Alpha

Cubitruncated Cuboctahedron

Cite this as:

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

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