In this polyhedron, there are twelve pentagons and sixty kites. It can be made by augmenting twenty of the triangles in a snub dodecahedron with short pyramids, but the pyramid-height has to be just right, in order to make those pyramids’ lateral faces coplanar with the non-augmented triangles, which produces the kites.

Since this polyhedron is chiral, a compound can be made by adding it to its own mirror image:

Both images were created using Stella 4d, software available at www.software3d.com/Stella.php.