  Twins travelling at constant relative velocity will each see the other's time
dilate leading to the apparent paradox that each twin believes the other ages
more slowly. In a finite space, the twins can both be on inertial, periodic
orbits so that they have the opportunity to compare their ages when their paths
cross. As we show, they will agree on their respective ages and avoid the
paradox. The resolution relies on the selection of a preferred frame singled
out by the topology of the space.
