Make Your Own Truncated Cube

The 14-faced Archimedean solid with faces . It is also the uniform
polyhedron with Maeder index 9 (Maeder 1997), Wenninger index 8 (Wenninger 1989),
Coxeter index 21 (Coxeter et al. 1954), and Har'El index 14 (Har'El 1993).
It has Schläfli symbol t and Wythoff symbol . It is illustrated above together
with a wireframe version and a net that can be used for its
construction.

It is implemented in the Wolfram Language as PolyhedronData ["TruncatedCube" ]
or UniformPolyhedron ["TruncatedCube" ].
Precomputed properties are available as PolyhedronData ["TruncatedCube" ,
prop ].

The truncated cube is the convex hull of the great cubicuboctahedron , great rhombihexahedron ,
and quasirhombicuboctahedron uniform
polyhedra .

The dual polyhedron of the truncated cube is the small triakis octahedron , both of which
are illustrated above together with their common midsphere .
The inradius of the dual, midradius of the solid and dual, and circumradius of the solid for are

The distances from the center of the solid to the centroids of the triangular and octagonal faces are

The surface area and volume
are

The unit truncated cube has Dehn invariant

where the first expression uses the basis of Conway et al. (1999).

See also Archimedean Solid ,

Equilateral Zonohedron ,

Icositetrahedron ,

Truncated
Cubical Graph ,

Truncation
Explore with Wolfram|Alpha
References Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, p. 138, 1987. 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. Cundy, H. and Rollett, A. "Truncated Cube. ." §3.7.3 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 103, 1989. Geometry
Technologies. "Truncated Cube." http://www.scienceu.com/geometry/facts/solids/tr_cube.html . Har'El,
Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata 47 ,
57-110, 1993. Kasahara, K. "Two New Semiregular Polyhedrons."
Origami
Omnibus: Paper-Folding for Everyone. Tokyo: Japan Publications, p. 227,
1988. Maeder, R. E. "09: Truncated Cube." 1997. https://www.mathconsult.ch/static/unipoly/09.html . Wenninger,
M. J. "The Truncated Hexahedron (Cube)." Model 8 in Polyhedron
Models. Cambridge, England: Cambridge University Press, p. 22, 1989.
Cite this as:
Weisstein, Eric W. "Truncated Cube." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/TruncatedCube.html

Subject classifications More... Less...