Creating a New Polyhedron from the Snub Dodecahedron

Posted on 13 September 2017 by RobertLovesPi

Shown below are the snub dodecahedron and its dual, the pentagonal hexecontahedron.

Seeking a way to make a “new” polyhedron (one never seen before), I augmented each face of the orange dual, above, with prisms. These prisms have a height equal to twice the average edge length of their bases.

Augmented Penta Hexeconta

Next, I used the software I use to manipulate polyhedra (Stella 4d, available here) to create the convex hull of this augmented pentagonal hexecontahedron.

starball before ttmfr expanded pentagonal hexacontahedron

Finally, I used Stella’s “try to make faces regular” function, and obtained this result, which I liked enough to stop here. There’s no way for me to know with certainty that this polyhedron has never been seen before, of course, but that didn’t stop me from having fun making it.

Unnamed starball.gif

The Cubic Rhombicosidodecahedroid

Posted on 10 September 2017 by RobertLovesPi

I call the polyhedron above the cubic rhombicosidodecahedroid because it combines a cube’s six squares (shown in green) with the overall appearance of a rhombicosidodecahedron. For comparison, the latter two polyhedra are shown below.

I made these rotating images using Stella 4d: Polyhedron Navigator. This program may be tried for free at http://www.software3d.com/Stella.php.

A Tessellation Featuring Rings of Pentagons

Image

tessellation

A Zonohedron with 7802 Faces

Posted on 2 September 2017 by RobertLovesPi

7802 faces.gif

Zonohedra with surprisingly large numbers of faces are easy to make with Stella 4d: Polyhedron Navigator. This program is sold at http://www.software3d.com/Stella.php, where there is also a free trial download offered.

An Expanded Version of the Snub Cube

Posted on 1 September 2017 by RobertLovesPi

prism-expanded snub cube convex hull after TTMFR

To make this polyhedron, I started with a snub cube. Next, I augmented all triangular faces of it with prisms, then took the convex hull of the result. Finally, I used Stella 4d‘s “try to make faces regular” function on the convex hull.

Stella 4d: Polyhedron Navigator has a free trial download available here.

A Twisted Expansion of the Truncated Octahedron

Posted on 27 August 2017 by RobertLovesPi

twisted truncated octahedron reflection one

I made this variant of the truncated octahedron using Stella 4d: Polyhedron Navigator. You may try this program for free at http://www.software3d.com/Stella.php.

An Expanded Snub Dodecahedron

Posted on 25 August 2017 by RobertLovesPi

To make this polyhedron, I started with a snub dodecahedron. Next, I augmented all triangular faces of it with prisms, then took the convex hull of the result. Finally, I used Stella 4d‘s “try to make faces regular” function on the convex hull.

An expanded snub dodecahedron

If you’d like to try the trial version of Stella for yourself, the website to visit is http://www.software3d.com/Stella.php.

The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part Two

Posted on 5 August 2017 by RobertLovesPi

Just like I did in the first part of this two-part post, I’m starting with the snub dodecahedron’s 43rd stellation.

This time, though, this polyhedral exploration is going in another direction. In the image below, the yellow kites seen above are shown augmented with prisms. The height of the prisms is equal to the average edge length of those kites.

Creating the convex hull of this augmented polyhedron is the next step.

The program I’m using to make these changes to polyhedra is called Stella 4d (it’s available here). The next step is using a function of Stella called “try to make faces regular.” The result is shown below.

Finally, I’m adjusting the coloring scheme so hexagons, pentagon, and triangles each get their own color, with a fourth color used for all three types of quadrilateral.