Truncated cube

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.

Area and volume

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

$A\; =\; 2(6+6sqrt\{2\}+sqrt\{3\})a^2\; approx\; 32.4346644a^2$

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

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 = $sqrt2\; -\; 1$

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)

See also

• Truncatedhexahedron.gif
• 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

• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra
• Printable net of a Truncated Cube Life is a Story Problem.org
• Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
• VRML model
• Conway Notation for Polyhedra Try: "tC"