Truncated cube
| Truncated cube | |
|---|---|
(Click here for rotating model) |
|
| Type | Archimedean solid Uniform polyhedron |
| 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 | |
| Symmetry | Oh , [4,3], (*432) |
| Dihedral Angle | |
| References | U09, C21, W8 |
| Properties | Semiregular convex |
Colored faces |
3.8.8 (Vertex figure) |
Triakis octahedron (dual polyhedron) |
Net |
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices.
If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and 
.
Contents |
Area and volume
The area A and the volume V of a truncated cube of edge length a are:
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 = 
Related polyhedra
The truncated cube can be seen as a cube with its corners truncated, as shown in this truncation sequence:
Cube |
Truncated cube |
cuboctahedron |
Truncated octahedron |
Octahedron |
It shares the vertex arrangement with three nonconvex uniform polyhedra:
Truncated cube |
Nonconvex great rhombicuboctahedron |
Great cubicuboctahedron |
Great rhombihexahedron |
A cube can be alternately truncated producing tetrahedral symmetry, with 6 hexagonal faces, and 4 triangles at the truncated vertices.
See also
- Spinning truncated cube
- Cube-connected cycles, a family of graphs that includes the skeleton of the truncated cube
References
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)
External links
- Eric W. Weisstein, Truncated cube (Archimedean solid) at MathWorld.
- Richard Klitzing, 3D convex uniform polyhedra, o3x4x - tic
- Editable printable net of a truncated cube with interactive 3D view
- The Uniform Polyhedra
- Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
- VRML model
- Conway Notation for Polyhedra Try: "tC"
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