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Great Truncated Cuboctahedron


U20

The great truncated cuboctahedron (Maeder 1997), also called the quasitruncated cuboctahedron (Wenninger 1989, p. 145), is the uniform polyhedron with Maeder index 20 (Maeder 1997), Wenninger index 94 (Wenninger 1989), Coxeter index 67 (Coxeter et al. 1954), and Har'El index 25 (Har'El 1993). Its faces consist of 8{6}+12{4}+6{8/3}. It has Schläfli symbol t'{3/4} and Wythoff symbol 4/323|.

The great truncated cuboctahedronn is implemented in the Wolfram Language as UniformPolyhedron[], UniformPolyhedron["GreatTruncatedCuboctahedron"], UniformPolyhedron[{"Coxeter", 67}], UniformPolyhedron[{"Kaleido", 25}], UniformPolyhedron[{"Uniform", 20 }], or UniformPolyhedron[{"Wenninger", 94}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatTruncatedCuboctahedron"].

GreatRhombicuboctahedralGraph

The skeleton of the truncated tetrahedron is the great rhombicuboctahedral graph, illustrated above in a number of embeddings.

Its dual is the great disdyakis dodecahedron.

Its circumradius for unit edge length is

 R=1/2sqrt(13-6sqrt(2)).

See also

Uniform Polyhedron

Explore with Wolfram|Alpha

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. "20: Great Truncated Cuboctahedron." 1997. https://www.mathconsult.ch/static/unipoly/20.html.Wenninger, M. J. "Quasitruncated Cuboctahedron." Model 93 in Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 145-146, 1989.

Referenced on Wolfram|Alpha

Great Truncated Cuboctahedron

Cite this as:

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

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