The octahemioctahedron, also called the octatetrahedron, is the uniform polyhedron with Maeder index 3 (Maeder 1997), Wenninger index 68 (Wenninger 1989), Coxeter index 37 (Coxeter et al. 1954), and Har'El index 8 (Har'El 1993). It has Wythoff symbol 3/23|3 and its faces are 8{3}+4{6}. It is a dodecahedron with intersecting faces, and its hull is a faceted cuboctahedron.

The octahemioctahedron is implemented in the Wolfram Language as UniformPolyhedron[68], UniformPolyhedron["SmallDitrigonalIcosidodecahedron"], UniformPolyhedron[{"Coxeter", 37}], UniformPolyhedron[{"Kaleido", 8}], UniformPolyhedron[{"Uniform", 3}], or UniformPolyhedron[{"Wenninger", 68}]. It is also implemented in the Wolfram Language as PolyhedronData["Octahemioctahedron"].


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


The convex hull of the octahemioctahedron is the cuboctahedron.

For unit edge lengths, its circumradius is


Its dual polyhedron is the octahemioctacron.

See also

Uniform Polyhedron

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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. "03: Octahemioctahedron." 1997., M. J. "Octahemioctahedron." Model 68 in Polyhedron Models. Cambridge, England: Cambridge University Press, p. 103, 1989.

Referenced on Wolfram|Alpha


Cite this as:

Weisstein, Eric W. "Octahemioctahedron." From MathWorld--A Wolfram Web Resource.

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