Selected Stellations of the Truncated Dodecahedron

Posted on 17 July 2017 by RobertLovesPi

This is the truncated dodecahedron. It is one of the Archimedean solids.

Trunc Dodeca

This polyhedron has a long stellation-series, from which I selected several on aesthetic grounds. The figure immediately below is the truncated dodecahedron’s 16th stellation.

16th stellation of Trunc Dodeca

Here is the 21st stellation.

21st stellation of Trunc Dodeca

It’s easy to stellate polyhedra rapidly, and make many other changes to them, with Stella 4d: Polyhedron Navigator. You can try it for free at http://www.software3d.com/Stella.php.

25th stellation of Trunc Dodeca.gif

The stellation shown immediately above is the 25th, and the one shown immediately below is the 27th.

27th stellation of Trunc Dodeca

Here is the next stellation: the 28th. Unlike the ones shown above, it is chiral.

28th stellation of Trunc Dodeca.gif

This is the truncated dodecahedron’s 31st stellation.

31st stellation of Trunc Dodeca.gif

This one is the 38th stellation.

38th stellation of Trunc Dodeca.gif

This one is the 44th.

44th stellation of Trunc Dodeca.gif

The last one shown here is called the truncated dodecahedron’s final stellation because, if it is stellated once more, it returns to the original truncated dodecahedron.

Final stellation of Trunc Dodeca

Nine Zonohedra

Posted on 3 July 2017 by RobertLovesPi

Software used to make these gifs: Stella 4d, available here.

A Rhombic Dodecahedron, Made of Icosahedra, and Tall Triangular Antiprisms

Posted on 10 June 2017 by RobertLovesPi

Augmented Icosa

Software used: Stella 4d, available at http://www.software3d.com/Stella.php.

Honeycomb Made of Cuboctahedra and Octahedra

Posted on 6 June 2017 by RobertLovesPi

Augmented Cubocta.gif

This is the three-dimensional version of what is called a tessellation in two dimensions. It fills space, and can be continued in all directions.

Software used: Stella 4d, available here.

Spectral Circles on a Cuboctahedron

Posted on 3 June 2017 by RobertLovesPi

Cubocta

I used three programs to make this: Geometer’s Sketchpad, MS-Paint, and Stella 4d. The third of these may be tried for free at http://www.software3d.com/Stella.php.

Spectral Circles on a Truncated Icosahedron

Posted on 29 May 2017 by RobertLovesPi

Trunc Icosa

I used MS-Paint and Geometer’s Sketchpad to make the designs on the faces, and then used Stella 4d (here) to put the whole thing together.

Augmenting the Octahedron with Octahedra, Repeatedly.

Posted on 15 May 2017 by RobertLovesPi

This is an octahedron.

If you augment each face of an octahedron with more octahedra, you end up with this.

One can then augment each triangular face of this with yet more octahedra.

Here’s the next iteration:

This could, of course, go on forever, but one more step in the series is all you will see here. I don’t want to get caught in an infinite loop.

Performing various manipulations of polyhedra is easy with Stella 4d: Polyhedron Navigator, which I used to make all five of these rotating images. If you’d like to try this program for yourself, just check out http://www.software3d.com/Stella.php.