The faces of this solid are twenty equilateral triangles, plus sixty kites, for a total of 32 faces. This is the “big brother” of the kite/triangle solid posted here. I made both using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

The faces of this solid are eight equilateral triangles, plus 24 kites, for a total of 32 faces. I made it 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 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.