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:

It shares the vertex arrangement with three uniform star polyhedrons:

ee also

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

References

* (Section 3-9)

External links

*
* [http://www.mathconsult.ch/showroom/unipoly/ The Uniform Polyhedra]
* [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] The Encyclopedia of Polyhedra
* [http://www.lifeisastoryproblem.org/explore/net_truncated_cube.pdf Printable net of a Truncated Cube] [http://www.lifeisastoryproblem.org Life is a Story Problem.org]
* [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra
** VRML [http://www.georgehart.com/virtual-polyhedra/vrml/truncated_cube.wrl model]
** [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "tC"