Twin paradox on hypertorus I will not describe the twin paradox  again. But let's suppose we have two twins, one stationary and the other moving with uniform velocity $c/2$ for instance. And let's suppose that they live in a hypertorus space, which is topological equivalent to an flat plane, so no curvature.
But the hypertorus is a finite space, it means the moving twin will meet again at an instant $t$ in time in the future. What will be their age when they cross each other again? 
 A: The answer is in Time, Topology and the Twin Paradox by J.-P. Luminet

The twin paradox is the best known thought experiment associated with
  Einstein's theory of relativity. An astronaut who makes a journey into
  space in a high-speed rocket will return home to find he has aged less
  than a twin who stayed on Earth. This result appears puzzling, since
  the situation seems symmetrical, as the homebody twin can be
  considered to have done the travelling with respect to the traveller.
  Hence it is called a "paradox". In fact, there is no contradiction and
  the apparent paradox has a simple resolution in Special Relativity
  with infinite flat space. In General Relativity (dealing with
  gravitational fields and curved space-time), or in a compact space
  such as the hypersphere or a multiply connected finite space, the
  paradox is more complicated, but its resolution provides new insights
  about the structure of spacetime and the limitations of the
  equivalence between inertial reference frames.

The inertial frames for the twins are not symmetric.

In Special Relativity theory, two reference frames are equivalent if
  there is a Lorentz transformation from one to the other. The set of
  all Lorentz transformations is called the Poincaré group – a ten
  dimensional group which combines translations and homogeneous Lorentz
  transformations called “boosts”. The loss of equivalence between
  inertial frames is due to the fact that a multiply connected spatial
  topology globally breaks the Poincaré group.

In a multiply connected spatial topology, there are more than one straight path to join 2 points.
