The Great Stellated Dodecahedron, Inscribed Inside a Partially-Invisible Dodecahedron

Posted on 30 November 2019 by RobertLovesPi

I made this using Stella 4d, which you can try right here.

Two Rhombic Polyhedra with Tessellated Faces

Posted on 8 September 2019 by RobertLovesPi

These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).

I made both of these using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.

A Three-Level Dodecahedron, Together with Its Dual

Posted on 29 May 2019 by RobertLovesPi

I made these using *Stella 4d*, which you can try for yourself, free, at http://www.software3d.com/Stella.php.

After I’d posted this, a helpful friend on Facebook told me the official name of the first polyhedron shown here — a pentalofted chamfered dodecahedron.

The Third Stellation of the Pentagonal Icositetrahedron Is a Compound of Two Irregular Dodecahedra

Posted on 26 April 2019 by RobertLovesPi

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 Non-Convex, Pyritohedral Dodecahedron with Non-Convex Pentagonal Faces

Posted on 13 January 2019 by RobertLovesPi

I created this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. Starting with the Platonic dodecahedron, I dropped the symmetry of the model down from icosahedral to tetrahedral, then stellated it six times. I also put the resulting polyhedron into “rainbow color mode” before making this .gif image.

Here’s a net for this solid. To build it, you’ll need six copies of this net.

41 Dodecahedra

Image

Created using *Stella 4d*, which can be tried for free at http://www.software3d.com/Stella.php.

Stellar Array

Posted on 2 January 2019 by RobertLovesPi

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

Posted on 14 October 2018 by RobertLovesPi

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

Posted on 29 September 2018 by RobertLovesPi

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

Posted on 7 June 2018 by RobertLovesPi

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.