Patterns on an Octahedron

Most readers will be familiar with Rubik’s cube and might even be aware that similar puzzles exist with noncubic shapes. The various manufacturers advertise these puzzles as being “educational for children six years and up.” I suspect that might be a bit optimistic, but there is no doubt that for university and even high school students there is a great deal of interesting math associated with these puzzles and the patterns one can create on them.