The polyhedron shown above is the snub dodecahedron, which is one of the Archimedean solids. The one shown below is its first stellation.
Next, each of the yellow faces was augmented with a tall prism.
The next step was to form the convex hull of the polyhedron above.
Finally, I used Stella 4d‘s “try to make faces regular” function on this convex hull. The result is below, and has 242 faces.
If you would like to try Stella 4d, the software I used to do all of this, simply visit http://www.software3d.com/Stella.php, and look for the free trial download.