Stellar Array

A great dodecahedron (red) sits in the middle of this polyhedral cluster. The polyhedra touching the one in the center are blue small stellated dodecahedra. Finally, there are yellow great stellated dodecahedra on the outside.

I assembled this polyhedral cluster using Stella 4d, which you can try for yourself at http://www.software3d.com/Stella.php.

A Compound of the Great Stellated Dodecahedron and the Great Dodecahedron

Compound of Great Stellated Dodeca and Great Dodeca.gif

In the picture above, each component of this compound has its own color. In the one below, each set of parallel faces is given a color of its own.

Compound of Great Stellated Dodeca and Great Dodeca 2

These images were made using Stella 4d, software you may try for yourself at this website.

Three Versions of a Compound of the Great and Small Stellated Dodecahedra

In the first version of this compound shown here, the great stellated dodecahedron is shown in yellow, while the small stellated dodecahedron is shown in red.

Small Stellated Dodeca and Great Stellated Dodeca.gif

In the next version, each face has its own color, except for those in parallel planes, which have the same color.

Small Stellated Dodeca and Great Stellated Dodeca 2

Finally, the third version is shown in “rainbow color mode.”

Small Stellated Dodeca and Great Stellated Dodeca 3

All three of these images were created using Stella 4d: Polyhedron Navigator, software you can try for free right here.

Augmenting the Dodecahedron with Great Dodecahedra

These two polyhedra are the dodecahedron (left), and the great dodecahedron (right).

Since the faces of both of these polyhedra are regular pentagons, it is possible to augment each of the dodecahedron’s twelve faces with a great dodecahedron. Here is the result.

Augmented Dodeca.gif

I used Stella 4d to make these images. You may try this program for yourself at http://www.software3d.com/Stella.php.

Augmenting the Icosahedron with Great Icosahedra

These two polyhedra are the icosahedron (left), and the great icosahedron (right).

 

Since the faces of both of these polyhedra are equilateral triangles, it is possible to augment each of the icosahedron’s twenty faces with a great icosahedron. Here is the result.

Augmented Icosa with 20 great icosas.gif

I used Stella 4d to make these images. You may try this program for yourself at http://www.software3d.com/Stella.php.

Icosahedral Cluster

augmented-great-icosa

The great icosahedron, one of the Kepler-Poinsot solids, is hidden from view at the center of this cluster. Each of its faces is augmented with a Platonic icosahedron, producing what you see here. Stella 4d is the software I used; more information about that program may be found here.

A Faceted Great Rhombcuboctahedron

faceted-trunc-cubocta

Some prefer to call the great rhombcuboctahedron the “truncated cuboctahedron,” instead. Whichever term you prefer, this is a faceted version of that Archimedean solid. I made it using Stella 4d: Polyhedron Navigator, software you may find here.