In this polyhedron, the twelve rhombic faces are in the same position as the faces of a rhombic dodecahedron — but narrowed, so as to make room for the kites. As for the kites, there are 24 of them — in eight sets of three. These set-of-threes’ positions correspond to those of the faces of an octahedron.

Software credit: I made this with polyhedron-manipulation software called Stella 4d. If you wish to purchase it, or try the free trial download, here’s the site to visit:

http://www.software3d.com/Stella.php