Rhombic dodecahedron

{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"\n!bgcolor=#e7dcc3 colspan=2|Rhombic dodecahedron\n|-\n|align=center colspan=2|

Click on picture for large version.
Click for spinning version.\n|-\n|bgcolor=#e7dcc3|Type||Catalan\n|-\n|bgcolor=#e7dcc3|Face polygon||rhombus\n|-\n|bgcolor=#e7dcc3|Faces||12\n|-\n|bgcolor=#e7dcc3|Edges||24\n|-\n|bgcolor=#e7dcc3|Vertices||14 = 6 + 8\n|-\n|bgcolor=#e7dcc3|Face configuration||3,4,3,4\n|-\n|bgcolor=#e7dcc3|Symmetry group||octahedral (O_h)\n|-\n|bgcolor=#e7dcc3|Dual polyhedron||cuboctahedron\n|-\n|bgcolor=#e7dcc3|Properties||convex, face/edge-uniform, zonohedron\n|}\nThe Rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is the polyhedral dual of the cuboctahedron and a zonohedron. The long diagonal of each face is exactly √2 times the length of the short diagonal, so that the acute angles on each face measure 2 tan⁻¹(1/√2), or approximately 70.53°. Being the dual of an Archimedean polyhedron, the rhombic dodecahedron is face-uniform, meaning the symmetry group of the solid acts transitively on the set of faces. In elementary terms, this means that for any two faces A and B there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B. The rhombic dodecahedron is also somewhat special in being one of the nine edge-uniform convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron and the rhombic triacontahedron. \nThe rhombic dodecahedron can be used to tessellate 3-dimensional space. This tessellation can be seen as the Voronoi tessellation of the face-centred cubic lattice. Honeybees use the geometry of rhombic dodecahedra to form honeycomb from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron.\n

See also

\n*Rhombic triacontahedron

External links

\n*Rhombic Dodecahedron – from MathWorld\n*Virtual Reality Polyhedra – The Encyclopedia of Polyhedra Category:Catalan solids