Here’s the small dodecahemiicosahedron, which is one of the uniform polyhedra. It has 22 faces: the twelve star pentagons shown in red, and the ten regular hexagons shown in yellow.

This solid has a long and interesting stellation-series. Three excerpts from that series are shown below. First, the tenth stellation.

Next, the eighteenth stellation.

Finally, the thirtieth stellation.

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