Determine the covering space of S1∨S1 corresponding to the subgroup of π1(S1∨S1) generated by the cubes of all elements. The covering space is 27-sheeted and can be drawn on a torus so that the complementary regions are nine triangles with edges labeled aaa, nine triangles with edges labeled bbb, and nine hexagons with edges labeled ababab. [For the analogous problem with sixth powers instead of cubes, the resulting covering space would have 228325 sheets! And for kth powers with k sufficiently large, the covering space would have infinitely many sheets. The underlying group theory question here, whether the quotient of Z∗Z obtained by factoring out all kth powers is finite, is known as Burnside's problem. It can also be asked for a free group on n generators.]