Three Views of The 27th Stellation of the Small Icosihemidodecahedron

First, here is this polyhedron colored by face type.

Next, the faces are each given their own color, except for parallel faces, which have the sme color.

Finally, here’s what this polyhedron looks like in “rainbow color mode.”

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

A Non-Convex Polyhedron With Sixty Each of Two Types of Kites

I made this by stellating the small icosihemidodecahedron, one of the uniform solids, once. I did this using Stella 4d, which you can try for free right here.

A Great Rhombicosidodecahedron, Augmented With Pyramids

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