A Great Rhombicosidodecahedron, Augmented With Pyramids

Posted on 22 October 2024 by RobertLovesPi

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

A Polyhedron Formed by Repeatedly Stellating the Triakis Octahedron, Along With Its Dual

Posted on 21 October 2024 by RobertLovesPi

I made these virtual models using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.

A Cube, Held Prisoner by a Stella Octangula

Posted on 21 October 2024 by RobertLovesPi

I made this three-part compound using Stella 4d (available here) to repeatedly tetstell a truncated octahedron.

A Symmetrohedron Featuring Three Regular Pentagons, One Regular Hexagon, One Equilateral Triangle, and Three Each of Two Different Isosceles Trapezoids

Posted on 20 October 2024 by RobertLovesPi

I’m 90% sure this hasn’t been found before. It has three-fold pyramidal symmetry.

Here is its net.

I used Stella 4d to make this. You can try this program for free at this website.

A Three-Part Compound Derived From the Rhombic Triacontahedron

Posted on 20 October 2024 by RobertLovesPi

I made this using Stella 4d, which you can try for free right here. It’s a continuation of the post immediately before this one.

Five Polyhedra Derived From the Rhombic Triacontahedron

Posted on 20 October 2024 by RobertLovesPi

Starting with the rhombic triacontahedron, I tetstelled it three times, and found this unusual polyhedron. It has eighteen faces: six parallelograms, and twelve trapezoids.

Here’s what happened when I used Stella 4d‘s “try to make faces regular” function on the polyhedron above.

This solid has six rhombic faces, and twelve faces which are kites. Here is its dual:

Next, I returned to the red-and-yellow solid above, and tetstelled it numerous times, producing a compound of a cube and a distorted rhombic dodecahedron.

A few more tetstells produced this interesting three-part compound.

If you’d like to try Stella yourself, the website to visit is http://www.software3d.com/Stella.php. There’s a free trial download there.

A Two-Part Compound, Derived From the Rhombicosidodecahedron

Posted on 20 October 2024 by RobertLovesPi

This is the familiar compound of the icosahedron and dodecahedron, except with both of those solids augmented on each face with short pyramids. I made it using Stella 4d, which you can try at this website.

A Two-Part Polyhedral Compound

Posted on 20 October 2024 by RobertLovesPi

The yellow component of this compound is a rhombic triacontahedron, while the red component is a slightly-stretched version of the strombic hexecontahedron (the dual of the rhombicosidodecahedron). The compound is derived from the truncated dodecahedron, and I made it using Stella 4d, which you can try for free right here.

Two Compounds Derived From the Snub Archimedeans

Posted on 20 October 2024 by RobertLovesPi

The dual of the snub cube is the pentagonal icositetrahedron. Both solids are chiral, so it is possible to make compounds out of each solid and its mirror-image. The polyhedron shown below is a compound of an enantiomorphic pair of pentagonal icositetrahedra.

The next solid shown was formed in the same way, except I started with the snub dodecahedron. This is the compound of an enantiomorphic pair of pentagonal hexecontahedra.

I did these polyhedron-transformations, as well as making these rotating .gifs, using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.

Two Compounds Derived From the Snub Cube

Posted on 19 October 2024 by RobertLovesPi

After stellating the snub cube many times (so many that I lost count), I ran into this two-part compound of irregular dodecahedra.

Like the snub cube this is derived from, this compound is chiral. Because of this, a four-part compound can be formed by combining this polyhedral compound with its mirror image.