Saturnian Rhombic Dodecahedron

Rhombic Dodeca

The image of Saturn was taken by NASA, and I put it on the faces of a rhombic dodecahedron, and created this image, with a program called Stella 4d. You can try this program for free at http://www.software3d.com/Stella.php.

The Sun, Earth, and Moon Adorning the Faces of a Great Rhombicosidodecahedron

Trunc Icosidodeca

This polyhedral image was created using Stella 4d, a program you can try for yourself, for free, at http://www.software3d.com/Stella.php.

Octahedra and Truncated Cubes Can Fill Space Without Leaving Any Gaps

Augmented Trunc Cube

I created this using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps

Augmented Cubocta

I created this image using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

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.

One Dozen Icosahedra

A dozen icosas

I made this using Stella 4d, software you can try for yourself right here.

A Zonohedron with 1382 Faces, Based on the Rhombicosidodecahedron

This zonohedron was formed from zones based on the faces, edges, and vertices of a rhombicosidodecahedron. The first image shows it colored by face type.

Zonohedrified Rhombicosidodeca 1382 faces by face type

The second image has the faces colored by number of sides.

Zonohedrified Rhombicosidodeca 1382 faces bynumber of sides per face.gif

Finally, here’s one in “rainbow color mode.”

Zonohedrified Rhombis rainbow.gif

These images were all formed using Stella 4d: Polyhedron Navigator, which you can try for free right here.

A Compound of Three Trapezohedra

I came across this little beauty while exploring stellations of the triakis octahedron, which is the dual of the truncated cube. Its three components are each eight-faced trapezohedra, and it showed up as the sixth in that stellation-series.

compound of three trapezohedra.gif

Stella 4d: Polyhedron Navigator was used to make this rotating image. You may try it for free right here.

Space-Filling Truncated Octahedra in a Rhombic Dodecahedral Cluster

The truncated octahedron is well-known as the only Archimedean solid which can fill space, by itself, without leaving any gaps. The cluster below shows this, and has the overall shape of a rhombic dodecahedron.

Augmented Trunc Octa.gif

It’s easier to see the rhombic dodecahedral shape of this cluster when looking at its convex hull:

Convex hull.gif

Both images here were made using Stella 4d, which you can try for free right here.

Three Facetings of the Icosidodecahedron

Faceted Icosidodeca.gif

Faceted Icosidodeca 2.gif

Faceted Icosidodeca 3

I made these using Stella 4d, which you can try for free here.