In this variation of the snub cube, twenty of the triangular faces have been excavated with short triangular pyramids. Since the snub cube is chiral, it’s possible to make a compound out of it and its mirror-image:
A polyhedron which is somewhat similar to the first one shown here can be produced by faceting a snub cube:
Stella 4d was used to create these images. You can find this program at http://www.software3d.com/Stella.php.