Rhombic triacontahedron
A Rhombentriakontaeder is a catalanischer body and dual to the icosahedron. It is also the enveloping body, which is described by the union of the penetration of a dodecahedron and icosahedron. Also obtained a Rhombentriakontaeder by just touches pyramids on an icosahedron, and dodecahedron, of which two sides complement each other to a.
The Rhombentriakontaeder has 30 rhombic faces, 32 vertices and 60 edges. At 12 the corners borders five edges and to the other 20 vertices are adjacent to 3 edges. The aspect ratio of the diagonal of the Rhombenflächen corresponds exactly to the golden section.
Related polyhedra
Deltoidalhexakontaeder
Will the 30 boundary surfaces of the Rhombentriakontaeders pyramids with edge lengths and placed, creating a general Hexakisikosaeder, if the following condition is satisfied:
- The special Hexakisikosaeder with the same dihedral angles at the edges and arises when is.
- If the maximum value previously mentioned, the Hexakisikosaeder degenerates into a Deltoidalhexakontaeder with the edge lengths and.
Formulas
For the polyhedron
For the diamonds
Applications
- In role-playing games, the Rhombentriakontaeder as a cube ( W30 ) will be used.