Truncated octahedron
From Free net encyclopedia
The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces, 6 regular square faces, 24 vertices and 36 edges. Since each of its faces has point symmetry (or 180° rotational symmetry), the truncated octahedron is a zonohedron.
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Image:Truncated octahedron flat.png
Cartesian coordinates
All permutations of (0, ±1, ±2) are Cartesian coordinates of the vertices of a truncated octahedron centered at the origin. The vertices are thus also the corners of 12 rectangles whose long edges are parallel to the coordinate axes.
Geometric relations
Image:Truncated octahedra.jpg
Truncated octahedra are able to tessellate 3-dimensional space, forming an Andreini tessellation. This tessellation can also be seen as the Voronoi tessellation of the body-centred cubic lattice.
Related polyhedra
Compare:
Image:Hexahedron.jpgImage:Truncatedhexahedron.jpgImage:Cuboctahedron.jpg Image:Truncatedoctahedron.jpg Image:Octahedron.jpg
External links
- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra
- [1] Uniform space-filling using only truncated octahedranl:Afgeknotte octaëder
![[1]](http://www.nanomedicine.com/NMI/Figures/5.5.jpg){kind=link}