[Illustration]
Though we cannot really see all the sides of the octahedron at once, we
can make a projection of it that suits our purpose just as well. In the
diagram the six points represent the six angles of the octahedron, and
four lines proceed from every point under exactly the same conditions as
the twelve edges of the solid. Therefore if we start at the point A and
go over all the lines once, we must always end our route at A. And the
number of different routes is just 1,488, counting the reverse way of
any route as different. It would take too much space to show how I make
the count. It can be done in about five minutes, but an explanation of
the method is difficult. The reader is therefore asked to accept my
answer as correct.