This beauty appeared unexpectedly when I was playing around with polyhedra related to the icosahedron and dodecahedron, using *Stella 4d: Polyhedron Navigator*. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.

# Tag Archives: faceted

# A Faceted Truncated Octahedron with Twenty Faces

The twenty faces of this polyhedron are six small blue squares, six interpenetrating, larger red squares, and eight irregular, interpenetrating yellow hexagons. I made it using *Stella 4d: Polyhedron Navigator*, which you can try for free at http://www.software3d.com/Stella.php. The squares are easy to find, but it can be a challenge to see the yellow hexagons. In the .gif below, all of the yellow faces but one are hidden, which should make it easier to see where the hexagons are positioned, relative to the squares.

# A Faceting of the Rhombicosidodecahedron

I made this faceting of the rhombicosidodecahedron using *Stella 4d: Polyhedron Navigator*. You can try this program out, for free, at http://www.software3d.com/Stella.php.

# This Faceting of the Truncated Icosahedron is Also a Truncation of the Great Dodecahedron

This first version shows this polyhedron colored by face type.

In the next image, only parallel faces share a color. This is the traditional coloring-scheme for the great dodecahedron.

Both images were created with *Stella 4d*, which is available as a free trial download at this website. Also, the obvious change needed with this polyhedron — making its faces regular — is in the next post.

# 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.

# 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.

# One of Many Faceted Versions of the Great Rhombicosidodecahedron

The great rhombicosidodecahedron is also known as the truncated icosidodecahedron. I created this faceting of it using *Stella 4d: Polyhedron Navigator*, which you can try for free at http://www.software3d.com/Stella.php.

# Three Facetings of the Icosidodecahedron

I made these using *Stella 4d*, which you can try for free here.

# A Faceted Version of the Truncated Cube

This is the truncated cube, which is one of the Archimedean solids.

To make a faceted version of this solid, one must connect at least some of the vertices in different ways. Doing that creates new faces.

This faceted version of the truncated cube includes eight blue equilateral triangles, eight larger, yellow equilateral triangles, and eight irregular, red hexagons. It’s easy to spot the yellow and blue triangles, but seeing the red hexagons is harder. In the final picture here, I have hidden all faces except for three of the hexagons, so that their positions can be more easily seen.

I made all three of these images using Robert Webb’s program called *Stella 4d: Polyhedron Navigator. *It is available for purchase, or as a free trial download, at http://www.software3d.com/Stella.php.

# Seven Different Facetings of the Truncated Icosahedron

The polyhedron above is the truncated icosahedron, widely known as the pattern for most soccer balls. In the image below, the faces and edges have been hidden, leaving only the vertices.

To make a faceted version of this polyhedron, these vertices must be connected in novel ways, creating new edges and faces. There are many faceted versions of this polyhedron, of which seven are shown below.

I used *Stella 4d* to make these polyhedral images, and you’re invited to try the program for yourself at http://www.software3d.com/Stella.php.