To get from the last image posted to this one, I used Stella 4d‘s “try to make faces regular” function. (You can get a free trial download of this program right here.)
This first version shows this polyhedron colored by face type.
In the next image, only parallel faces share a color. This is the traditional coloring-scheme for the great dodecahedron.
Both images were created with Stella 4d, which is available as a free trial download at this website. Also, the obvious change needed with this polyhedron — making its faces regular — is in the next post.