Math 4440 Ultimate homework Due Thursday, May 1.

1. There are or 70 ways to color the edges of a regular octagon, if 4 are red and 4 are green

acts on this set of 70, and orbits are equivalent colorings. Use Burnside's formula to count the number of equivalence classes, i.e. the number of distinct colorings.

2. Use Theorem 16.16 to determine the order of the group of rotations of a regular tetrahedron.

If possible, determine this group.