The Biaugmented Truncated Cube is the 67th Johnson Solid.
You should be able to design your own, and then watch them rotate. That would have been better.
I'm struggling to tell the difference between these
wikipedia helps a bit
Still, I'm a bit :bawa: about itThe last three operations — augmentation, diminution, and gyration — can be performed more than once on a large enough solid. We add bi- to the name of the operation to indicate that it has been performed twice. (A bigyrate solid has had two of its cupolae rotated.) We add tri- to indicate that it has been performed three times. (A tridiminished solid has had three of its pyramids or cupolae removed.)