To make the image above, using Stella 4d (available here), I started with a uniform polyhedron called the octahemioctahedron, and then made the triangular faces of it invisible. Here’s what this polyhedron looks like without its triangles hidden:
The convex hull of either of these figures is a cuboctahedron, which is shown below.
To make the image above, using Stella 4d (available here), I started with a uniform polyhedron called the small icosihemidodecahedron, and then made the triangular faces of it invisible. Here’s what this polyhedron looks like without its triangles hidden:
The convex hull of either of these figures is an icosidodecahedron, which is shown below.
This zonohedron is made from the truncated octahedron’s vertices, edges, and faces. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
There’s one cuboctahedron in the center of this cluster, with each of its fourteen faces augmented by another cuboctahedron. The image below uses coloring of each face by its number of sides, while the next one is in “rainbow color mode.”
I made these images using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I made this using Stella 4d, which you can try for yourself, free, at this website: http://www.software3d.com/Stella.php.
I found this compound by repeatedly stellating the small hexacronic icositetrahedron, which is the dual of the small cubicuboctahedron, one of the uniform solids. I used Stella 4d: Polyhedron Navigator to do this, and you can try this program, as a free trial download, at http://www.software3d.com/Stella.php.
This has many more different polygons than most of my tessellations, so I’m including a color key.
Using Stella 4d (available here), I put this tessellation on the octagonal faces of a truncated octahedron, while hiding the triangular faces. The tessellation itself was made using Geometer’s Sketchpad.
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