I made this using Stella 4d, which you can try for free right here. In the image above, the two components of this compound are given separate colors. In the second picture, below, the coloring is per face, except for parallel faces, which have the same color.
Tag Archives: great
The Truncated Great Dodecahedron

To get from the last image posted to this one, I used Stella 4d‘s “try to make faces regular” function. (You can get a free trial download of this program right here.)
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
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.
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.
In the next version, each face has its own color, except for those in parallel planes, which have the same color.
Finally, the third version is shown in “rainbow color mode.”
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.
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.
I used Stella 4d to make these images. You may try this program for yourself at http://www.software3d.com/Stella.php.
Icosahedral Cluster
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
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.
Unsquashing the Squashed Meta-Great-Rhombcuboctahedron
I noticed that I could arrange eight great rhombcuboctahedra into a ring, but that ring, rather than being regular, resembled an ellipse.
I then made a ring of four of these elliptical rings.
After that, I added a few more great rhombcuboctahedra to make a meta-rhombcuboctahedron — that is, a great rhombcuboctahedron made of rhombcuboctahedra. However, it’s squashed. (I believe the official term for this is “oblate,” but “squashed” also works, at least for me.)
So now I’m wondering if I can make this more regular. In other words, can I “unsquash” it? I notice that even this squashed metapolyhedron has regular rings on two opposite sides, so I make such a ring, and start anew.
I then make a ring of those . . .
. . . And, with two more ring-additions, I complete the now-unsquashed meta-great-rhombcuboctahedron. Success!
To celebrate my victory, I make one more picture, in “rainbow color mode.”
[All images made using Stella 4d, available here: http://www.software3d.com/Stella.php.]