Two Rhombic Triacontahedra, Each Decorated with Birthday Stars

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?

The Pyritohedral Golden Icosahedron

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

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.

A Polyhedron with 98 Faces

This polyhedron has six faces which are regular octagons, sixty quadrilateral faces, and 32 triangular faces, eight of which are regular. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.