Expanding the Truncated Icosahedron, Using Augmentation with Prisms

Here’s my starting point: the truncated icosahedron, one of the thirteen Archimedean solids.

Next, each face is augmented by a prism, with squares used for the prisms’ lateral faces.

The convex hull of the polyhedron above yields what can be called an expanded truncated icosahedron, as shown below:

Could these faces be made regular, and the polyhedron still hold together? I checked, using Stella 4d‘s “try to make faces regular” function. Here’s the result:

As you can see, the faces of this polyhedron can be made to be regular, but this forces the model to become non-convex.

To try Stella for yourself, for free, just pay a visit to http://www.software3d.com/Stella.php. The trial version is a free download.