The Dual of the Frequency-One Geodesic Sphere Based on the Great Rhombcuboctahedron

The faces of this solid include twelve squares, six regular octagons, eight regular hexagons, and 48 irregular hexagons. I made it using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

A Curvy Tessellation #1

This is based on the well-known tessellation of squares and regular octagons, but with each line segment replaced by two semicircles.

Three Views of the Final Stellation of the Icosahedron

In this first image of the final stellation of the icosahedron, the faces are colored with a different color for each face, except for parallel faces, which are the same color.

The next image uses red and yellow to color the facelets by type.

Finally, the third image simply uses rainbow color mode.

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

Three Facetings of the Truncated Octahedron

I created these faceted polyhedra using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

Compound of Three Elongated Octahedra

This was created using Stella 4d, software you may try for free at this website.

A Great Dodecahedron, Inscribed Inside a Partially-Invisible Icosahedron

I made this using Stella 4d, which you can try for free at this website.

A Small Stellated Dodecahedron, Inscribed Inside a Partially-Invisible Icosahedron

Twelve of the icosahedron’s twenty faces have been hidden from view, exposing the small stellated dodecahedron nestled inside the icosahedron, and giving the visible parts of the model pyritohedral symmetry.

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

A Compound of the Icosahedron and the Small Stellated Dodecahedron

I found this by further stellation of the polyhedra shown in the two posts right before this one, using a program called Stella 4d: Polyhedron Navigator. You can try Stella for free at http://www.software3d.com/Stella.php.

A Compound of the Great Rhombicosidodecahedron and the Small Stellated Dodecahedron

I made this, using Stella 4d (available here), by multiple stellation of the faceted great rhombicosidodecahedron shown in the post immediately before this one.

An Interesting Faceting of the Great Rhombicosidodecahedron

I made this using the faceting function within Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.