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+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.

Cartesian coordinates

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

(±?, ±1, ±1),

(±1, ±?, ±1),

(±1, ±1, ±?)

where ? = \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

• Spinning truncated cube
• Cube-connected cycles, a family of graphs that includes the skeleton of the truncated cube

References

• (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"

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