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

To make this, I started with the cuboctahedron, then augmented its triangular faces with tetrahedra. Next, I excavated the square faces with square-based regular pyramids, producing what you see here. I did this using Stella 4d, a program you may try for free at this website.

This faceted is shown above is colored by face type. The one below is in “rainbow color mode.”

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

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

To make this, I augmented the pentagonal faces of an icosidodecahedron with pyramids, while the triangular faces of this icosidodecahedron had pyramids excavated from them. The result, as you can see, looks like an icosahedron with tetrahedral indentations is the middle of each face. I made it using Stella 4d, which you can try for free at http://www.robertlovespi.net/Stella.php.

Here’s a second view, in “rainbow color mode.”

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