The Rhombic Dodecahedron and Its First Stellation, Decorated in Three Colors

Rhombic Dodeca

The image on the faces of these polyhedra appeared, in black and white form, in the last post here. I used Geometer’s Sketchpad and MS-Paint to make it. It took a third program, Stella 4d, to project the image onto each face of a rhombic dodecahedron (as seen above), as well as the rhombic dodecahedron’s first stellation (below), and then generate these rotating .gif images. You can try Stella for free, as a trial download, at www.software3d.com/Stella.php.

First Stellation Rhombic Dodeca

Polyhedral Porcupine

Image

Polyhedral Porcupine

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

Three Stellations of the Icosidodecahedron

Image

Three Stellations of the Icosidodecahedron

The icosidodecahedron’s 24th stellation is above, and the 32nd, then the 36th, are below.

Icosidodeca 32nd StellationIcosidodeca 36th Stellation

I made these images using Stella 4d, a program you can find at www.software3d.com/Stella.php.

The Rhombic Dodecahedron’s Third Stellation

Image

The Rhombic Dodecahedron's Third Stellation

Above is this polyhedral stellation in three colors. If every face is given its own color, though, except for parallel faces, it looks like this (click to enlarge):

RD stellation 3rd colors b

I made both images using Stella 4d, a program you can find at http://www.software3d.com/Stella.php.

Starry Dual Polyhedron

Image

Starry Dual Polyhedron

This is the dual of the polyhedron seen as the second image in the last post on this blog. If colored differently, so that only parallel faces have the same color, it looks like this (click to enlarge):

Augmented Convex hull

I used Stella 4d to make these images, and you can find that program at http://www.software3d.com/Stella.php.

Stellated Polyhedron Featuring Self-Intersecting Regular Decagons

Image

Stellated Polyhedron Featuring Self-Intersecting Regular Decagons

I created this using Stella 4d: Polyhedron Navigator, a program you can find athttp://www.software3d.com/Stella.php.

The Ninth Stellation of the Cube/Octahedron Compound

Image

The Ninth Stellation of the Cube/Octahedron Compound

Software credit: I made this using Stella 4d, which you can find at http://www.software3d.com/Stella.php.

The Twelfth Stellation of the Icosahedron/Dodecahedron Compound

Image

The Twelfth Stellation of the Icosahedron/Dodecahedron Compound

Software credit: I made this using Stella 4d, which you can find at http://www.software3d.com/Stella.php.

Two Versions of a Stellated Polyhedron with Icosidodecahedral Symmetry

Image

Two Versions of a Stellated Polyhedron with Icosidodecahedral Symmetry

The next image was produced by rendering all the blue faces above invisible, and then changing the color-scheme to “rainbow color mode.” For both of these stellated polyhedra, the convex hull would simply be an icosidodecahedron (not shown here).

Stellated DFGACoNBCnvex hull

These images were both created using Stella 4d, which you can try and/or buy at www.software3d.com/Stella.php.

Two Repeatedly-Stellated Polyhedral Compounds Which Are Dipolar

Image

Two Repeatedly-Stellated Polyhedral Compounds Which Are Dipoles

Both of these were created using Stella 4d, available at http://www.software3d.com/Stella.php. To enlarge the second image, simply click on it.

Compound of 36- Prism and dual