Rhombic Triacontahedron - Related Polyhedra

Related Polyhedra

This polyhedron is a part of a sequence of rhombic polyhedra and tilings with Coxeter group symmetry. The cube can be seen as a rhombic hexahedron where the rhombi are also rectangles.

Spherical polyhedra Euclidean tiling Hyperbolic tiling
Spherical/planar
symmetry		 *332

Td		 *432

Oh		 *532

Ih		 *632

P6m		 *732
 *832
Rhombic
figures
Cube
Rhombic dodecahedron
Rhombic triacontahedron
Rhombille
Face configuration V3.3.3.3 V3.4.3.4 V3.5.3.5 V3.6.3.6 V3.7.3.7 V3.8.3.8
Coxeter diagram

The rhombic triacontahedron forms the convex hull of one projection of a 6-cube to 3 dimensions.


The 3D basis vectors are:
u = (1, φ, 0, -1, φ, 0)
v = (φ, 0, 1, φ, 0, -1)
w = (0, 1, φ, 0, -1, φ)
Shown with inner edges hidden
There are 64 vertices and 192 unit length edges forming pentagonal symmetry along specific axis (as well as hexagonal symmetries on other axis).

Read more about this topic:  Rhombic Triacontahedron

Famous quotes containing the word related:

    “The custard is setting; meanwhile
    I not only have my own history to worry about
    But am forced to fret over insufficient details related to large
    Unfinished concepts that can never bring themselves to the point
    Of being, with or without my help, if any were forthcoming.”
    —John Ashbery (b. 1927)