Five Views of the Compound of the Truncated Cube and the Truncated Octahedron

Posted on 30 October 2024 by RobertLovesPi

When I first made this compound using Stella 4d (available here), these are the colors the software automatically selected.

I wanted to find a better coloring-scheme, so I told Stella to color the model as a compound. Here’s what I got.

Next, I tried “color by face type.” This yields four colors, instead of just two.

I then tried “rainbow color mode,” with this result.

One more try (color by face, unless the faces are parallel) gave me my favorite color scheme for this compound.

Which one do you like best?

A Pyritohedral Polyhedron With Only Trapezoids for Faces

Posted on 29 October 2024 by RobertLovesPi

This 24-faced polyhedron, which has pyritohedral symmetry, was formed by repeatedly tetstelling a rhombic triacontahedron, using Stella 4d: Polyhedron Navigator. If you wish, you can try this program for free right here.

A Polyhedron With Sixty Convex Pentagonal Faces

Posted on 28 October 2024 by RobertLovesPi

This polyhedron was derived from the truncated icosahedron, using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

A Polyhedron Made By Repeatedly Tetstelling the Rhombic Enneacontahedron

Posted on 27 October 2024 by RobertLovesPi

This polyhedron has pyritohedral symmetry. I made it with Stella 4d, which you can try for free right here. The red faces are rhombi, and the purple faces are kites. The blue faces look, superficially, like kites, but they don’t quite qualify as anything other than convex quadrilaterals.

The Ninth Stellation of the Dual of the Rhombic Octagonoid

Posted on 26 October 2024 by RobertLovesPi

The rhombic octagonoid, from which this polyhedron is derived, can be found here. I made this stellation of its dual using Stella 4d, which you can try for free at this website. The non-stellated dual can be found in the post immediately preceding this one.

A Symmetrohedron With All the Faces of the Icosidodecahedron, Plus Two Sets of Sixty Isosceles Triangles

Posted on 26 October 2024 by RobertLovesPi

This polyhedron is the dual of the rhombic octagonoid. I made it using Stella 4d, which you can try for free right here.

A Polyhedron Made of a Dozen Convex Heptagons and a Dozen Equilateral Triangles

Posted on 25 October 2024 by RobertLovesPi

This is the second tetstell of the icosidodecahedron. Tetstelling is like normal stellation, except you drop the symmetry of the model to tetrahedral first. It’s an easy trick with Stella 4d, the program I used to make this. You can try it, free, at this website.

Here it is, in the colors Stella chose when I made it again, just now, to double-check those “dozens” in the title of this post.