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.

I did all of this using a program called Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Thirty-Faced Polyhedron Made of Six Squares and 24 Kites

Posted on 18 October 2024 by RobertLovesPi

This is the first stellation of the snub cube, one of the Archimedean solids. I made this image using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A 72-Faced Polyhedron Made of a Dozen Regular Pentagons and Sixty Kites

Posted on 17 October 2024 by RobertLovesPi

This polyhedron is the first stellation of the snub dodecahedron, which is one of the Archimedean solids. I made this with Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Faceting of the Icosidodecahedron, in Purple, Pink, and Blue

Posted on 15 October 2024 by RobertLovesPi

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

Three Polyhedra Which Each Contain Four Regular Dodecagonal Faces

Posted on 14 October 2024 by RobertLovesPi

I stumbled upon these while playing with tetrahedral-symmetry alterations of a great rhombicuboctahedron, using Stella 4d. You can try this program for free at http://www.software3d.com/Stella.php.

A Symmetrohedron Featuring Twelve Regular Pentadecagons and Sixty Kites

Posted on 12 October 2024 by RobertLovesPi

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

A 72-Faced Faceted Rhombicosidodecahedron

Posted on 8 October 2024 by RobertLovesPi

Twelve of the faces of this polyhedron are star pentagons, and they are easy to spot. The other sixty faces are isosceles trapezoids, and they’re harder to find because parts of them are hidden inside in the solid. The image below shows where these trapezoids can be found.

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

Expanding the Rhombic Octagonoid, Using Equilateral Triangles

Posted on 8 October 2024 by RobertLovesPi

I first named the rhombic octagonoid, a ninety-faced zonohedron, right here. I’ve added a new twist to it now, though, and that is to expand this polyhedron using twenty equilateral triangles. This causes the octagons of the rhombic octagonoid to become decagons. This new solid has 110 faces, and is not a zonohedron, although it is a “zonish” polyhedron. The only faces it has which are not zonogons are the triangles.

I built this new polyhedron with Zome. If you’d like to try out Zome for yourself, the website to visit is at http://www.zometool.com.

24 Kites in One Polyhedron

Posted on 7 October 2024 by RobertLovesPi

I made this by stellating a triakis octahedron multiple times, using Stella 4d, which you can try for yourself at http://www.software3d.com/Stella.php.