The dodecagons are in the same planes as a cube’s faces, so there are six of them. Also, this could be constructed via an unusual truncation of the cube, using three different truncation-planes at each vertex. This polyhedron has thirty faces: the six dodecagons, and twenty-four kites (in eight sets of three).
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this polyhedron.
This is a symmetrohedron O(3,0,*,) that appeared in Kaplan & Hart’s original paper.