Truncated cube

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Truncated cube
Truncated cube
(Click here for rotating model)
Type Archimedean solid
Elements F = 14, E = 36, V = 24 (χ = 2)
Faces by sides 8{3}+6{8}
Schläfli symbol t{4,3}
Wythoff symbol 2 3 | 4
Coxeter-Dynkin Image:CDW_ring.pngImage:CDW_4.pngImage:CDW_ring.pngImage:CDW_3.pngImage:CDW_dot.png
Symmetry Oh
References U09, C21, W8
Properties Semiregular convex
Truncated cube color
Colored faces		 Truncated cube
3.8.8
(Vertex figure)

Triakis octahedron
(dual polyhedron)		 Truncated cube Net
Net

The truncated cube, or truncated hexahedron, is an Archimedean solid. It has 6 regular octagonal faces, 8 regular triangular faces, 24 vertices and 36 edges.

Contents

[edit] Area and volume

The area A and the volume V of a truncated cube of edge length a are:

A = 2(6+6\sqrt{2}+\sqrt{3})a^2 \approx 32.4346644a^2
V = \frac{1}{3}(21+14\sqrt{2})a^3 \approx 13.5996633a^3.

[edit] Cartesian coordinates

The following Cartesian coordinates define the vertices of a truncated hexahedron centered at the origin with edge length 2ξ:

(±ξ, ±1, ±1),
(±1, ±ξ, ±1),
(±1, ±1, ±ξ)

where ξ = \sqrt2 - 1

[edit] Related polyhedra

Compare:


Cube
Truncated cube
cuboctahedron
Truncated octahedron
Octahedron

It shares the vertex arrangement with three uniform star polyhedrons:


(4.8/3.4/3.8/5)
(8/3.3.8/3.4)
(4.3/2.4.4)

[edit] See also

[edit] References

[edit] External links