The Double Rhombicosidodecahedron

This is a rhombicosidodecahedron, one of the Archimedean solids.

If one pentagonal cupola is removed from this polyhedron, the result is the diminished rhombicosidodecahedron, which is one of the Johnson solids (J76).

The next step is to take another J76, and attach it to the first one, so that their decagonal faces meet.

I’m calling the result the “double rhombicosidodecahedron.”

I did these manipulations of polyhedra and their images with a program called Stella 4d: Polyhedron Navigator. There’s a free trial download available, if you’d like to try the program for yourself, and it’s at this website.

2 thoughts on “The Double Rhombicosidodecahedron

  1. “Gyro” double rhombicosidodecahedron — you would get a different shape if you rotated one of the diminished rhombicosidodecahedra 36 degrees.

    Cutting off the cupolas is actually a very interesting thing. If we imagine the rhombicosidodecahedron as a spherical tiling instead of a polyhedron, then this is equivalent to saying that edge length at which the angles of equilateral triangle, square, and pentagon are just so that (3,4,5,4) closes perfectly is the same as the edge length where (4,5,10) closes perfectly.
    And this is a general rule. (3,4,n,4) has always the same edge as (4,n,2n). For n = 3 to 5, this is spherical, n=6 is Euclidean, so trivial (all Euclidean configurations can be considered to have edge 0), and n > 6 is hyperbolic.

    Here are some selected gyrated/diminished tilings for n = 7:

    Liked by 1 person

Leave a Reply to Anonymous Cancel reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s