Rhombic triacontahedron

{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"\n!bgcolor=#e7dcc3 colspan=2|Rhombic triacontahedron\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||30\n|-\n|bgcolor=#e7dcc3|Edges||60\n|-\n|bgcolor=#e7dcc3|Vertices||32 = 20 + 12\n|-\n|bgcolor=#e7dcc3|Face configuration||3,5,3,5\n|-\n|bgcolor=#e7dcc3|Symmetry group||icosahedral (I_h)\n|-\n|bgcolor=#e7dcc3|Dual polyhedron||icosidodecahedron\n|-\n|bgcolor=#e7dcc3|Properties||convex, face/edge-uniform, zonohedron\n|}\nThe Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It is the polyhedral dual of the icosidodecahedron and a zonohedron. The ratio of long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 tan⁻¹(1/φ), or approximately 63.43°. Being the dual of an Archimedean polyhedron, the rhombic triacontahedron 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 triacontahedron 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 dodecahedron.

See also

\n*Rhombic dodecahedron

External links

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