Spectral Icosahedra

Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this cluster of 61 icosahedra. If you’d like to try this software for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.

A Blend of the Icosahedron and the Rhombic Enneacontahedron

This is the icosahedron, one of the Platonic solids. It has twenty faces.

The polyhedron below is the rhombic enneacontahedron, a well-known zonohedron with ninety faces.

Finally, here is a polyhedron which blends these two. It has 20 + 90 = 110 faces.

I used Stella 4d: Polyhedron Navigator to make these images. You can try this program for free at http://www.software3d.com/Stella.php.

This Faceting of the Truncated Icosahedron is Also a Truncation of the Great Dodecahedron

This first version shows this polyhedron colored by face type.

In the next image, only parallel faces share a color. This is the traditional coloring-scheme for the great dodecahedron.

Both images were created with Stella 4d, which is available as a free trial download at this website. Also, the obvious change needed with this polyhedron — making its faces regular — is in the next post.

Three Views of the Final Stellation of the Icosahedron

In this first image of the final stellation of the icosahedron, the faces are colored with a different color for each face, except for parallel faces, which are the same color.

The next image uses red and yellow to color the facelets by type.

Finally, the third image simply uses rainbow color mode.

I used Stella 4d to make these. You can try this program for free at this website.

A Small Stellated Dodecahedron, Inscribed Inside a Partially-Invisible Icosahedron

Twelve of the icosahedron’s twenty faces have been hidden from view, exposing the small stellated dodecahedron nestled inside the icosahedron, and giving the visible parts of the model pyritohedral symmetry.

I made this using Stella 4d, a program you can try for yourself at http://www.software3d.com/Stella.php.