Here’s the pentagonal icositetrahedron. It is the dual of the snub cube.
And here is its third stellation. As you can see, it’s a compound of two irregular dodecahedra.
I made these images using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
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.
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.
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.
To make this using Stella 4d (available here) I started with an icosahedron, placed a dodecahedron on each of its vertices, then rendered the central icosahedron invisible. The slight pulsating effect is caused by the program fitting the polyhedra tightly into each frame of the animation.
I made this compound using Stella 4d, a program which is available here: http://www.software3d.com/Stella.php.