The Triple Rhombicosidodecahedron

Posted on 1 February 2022 by RobertLovesPi

This is the rhombicosidodecahedron, one of the thirteen Archimedean solids.

Several of the 92 Johnson solids are modified forms of this polyhedron, such as J76, the diminished rhombicosidodecahedron (shown below). It is formed by removal of a pentagonal cupola from a rhombicosidodecahedron, exposing a decagonal face.

Another variant of this Archimedean solid may be created by removing two pentagonal cupolas, exposing decagons on opposite sides of the figure. This solid, J80, is called the parabidiminished rhombicosidodecahedron.

Two J76s and one J80 can then be joined together, at their decagonal faces, to form this: the triple rhombicosidodecahedron.

I made these using Stella 4d, a program you can try for free at this website.

The Double Rhombicosidodecahedron

Posted on 31 January 2022 by RobertLovesPi

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.

A Compound of the Rhombic Dodecahedron and a Truncation of the Octahedron

Posted on 30 January 2022 by RobertLovesPi

I made this using Stella 4d, which you can try for free at this website.

A 50-Faced Symmetrohedron Which Is Also a Zonohedron

Posted on 28 January 2022 by RobertLovesPi

I made this polyhedron by creating a zonohedron based on the edges and faces of the truncated tetrahedron. Only the blue hexagons are irregular. Stella 4d was used in its creation, and you may try this program for free at http://www.software3d.com/Stella.php.

A Zonohedron with 170 Faces

Posted on 22 January 2022 by RobertLovesPi

This zonohedron was made using the edges and vertices of the truncated tetrahedron.

I made this using Stella 4d: Polyhedron Navigator, which you can try for free right here.

Two Rhombic Triacontahedra, Each Decorated with Birthday Stars

Posted on 13 January 2022 by RobertLovesPi

In yesterday’s post, I unveiled my annual birthday star for my new age, 54. Today, I’m placing that 54-pointed star on each of the thirty faces of a rhombic triacontahedron. I use a program called Stella 4d (free trial available right here) to do this, and it allows images on polyhedron-faces to either be placed inside the face, or around the face. Here’s the “inside” version:

And here is the “around each face” version:

Which one do you like better?

A 38-Faced Symmetrohedron

Posted on 10 January 2022 by RobertLovesPi

This symmetrohedron includes, as faces, eight regular hexagons, six squares, and 24 isosceles triangles. I made it using Stella 4d, which you can try for free at this website.

The Pyritohedral Golden Icosahedron

Posted on 9 January 2022 by RobertLovesPi

Both the Platonic icosahedron and the golden icosahedron have twenty triangular faces. In the Platonic version, these faces are all equilateral triangles. The golden icosahedron has eight such triangles, but the other twelve are golden triangles, which have a leg-to-base ratio which is the golden ratio. These golden triangles appear in pairs, and the six pairs are arranged in such a way as to make this a solid with pyritohedral symmetry: the symmetry of a standard volleyball.

A net for the golden icosahedron appears below. Both images were made using a program called Stella 4d, which you can try for free right here.

A Faceted Rhombicosidodecahedron with 540 Faces

Posted on 8 January 2022 by RobertLovesPi

This beauty appeared unexpectedly when I was playing around with polyhedra related to the icosahedron and dodecahedron, using Stella 4d: Polyhedron Navigator. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.