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Great Cubicuboctahedron


U14

The great cubicuboctahedron is the uniform polyhedron with Maeder index 14 (Maeder 1997), Wenninger index 77 (Wenninger 1989), Coxeter index 50 (Coxeter et al. 1954), and Har'El index 19 (Har'El 1993). It has Wythoff symbol 34|4/3 and its faces are 8{3}+6{4}+6{8/3}. It is a faceted version of the cube.

The great cubicuboctahedron is implemented in the Wolfram Language as UniformPolyhedron[77], UniformPolyhedron["SmallDitrigonalIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 50}], UniformPolyhedron[{"Kaleido", 19}], UniformPolyhedron[{"Uniform", 14}], or UniformPolyhedron[{"Wenninger", 77}]. It is also implemented in the Wolfram Language as PolyhedronData["GreatCubicuboctahedron"].

SmallRhombicuboctahedralGraph

The skeleton of the great cubicuboctahedron is the small rhombicuboctahedral graph, illustrated above.

The circumradius of a great cubicuboctahedron with unit edge lengths is

 R=1/2sqrt(5-2sqrt(2)).
u14hull

The convex hull of the great cubicuboctahedron is the Archimedean truncated cube, whose dual is the small triakis octahedron, so the dual of the great cubicuboctahedron (i.e., the great hexacronic icositetrahedron) is one of the stellations of the small triakis octahedron (Wenninger 1983, p. 57).

Its dual polyhedron is the great hexacronic icositetrahedron.


See also

Great Hexacronic Icositetrahedron, 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. "14: Great Cubicuboctahedron." 1997. https://www.mathconsult.ch/static/unipoly/14.html.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, pp. 57-58, 1983.Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 118-119, 1989.

Referenced on Wolfram|Alpha

Great Cubicuboctahedron

Cite this as:

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

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