This is a frequency-4 geodesic icosahedron, made by request using Stella 4d, which you can try for yourself, free, at this website.
I made this using Stella 4d: Polyhedron Navigator, a program you can try for free at this website. It shows Hexagon the Cat riding in circles on the twenty hexagonal faces of a rotating truncated icosahedron. We don’t know of a cat named Pentagon, so I hid the twelve pentagonal faces.
“Error Code M7353-5101” apparently means “We stopped playing Star Trek for you because your cat is sitting on the keyboard.” Hexagon strikes again!
This cuboctahedron has an edge length of two. If you’d like to compare it to a Lux model with a edge length of one, just check the post right before this one. Lux Blox are fun to build with, and are sold online at http://www.luxblox.com.
This particular truncated icosahedron has an edge length of one. I may build one with a longer edge length at some point; this would have the effect of shrinking the white edges, and magnifying the orange and blue faces, as fractions of the overall model. The individual Lux square pieces are identical, except for their color.
If you’d like to try Lux Blox for yourself, the site to visit is http://www.luxblox.com.