The Twin Paradox seems to be a type of Mobius Strip

When one of the twins leaves the Earth at a velocity near the speed of light, then turns around and returns to Earth, he is substantially younger. To return the states to normal, the twin who stayed on Earth now leaves near the velocity of light and when he returns to Earth, both twins are now the same age. So 720 degrees has to be traversed, as in a mobius to return the twins to the original state (with time passing). There are other puzzles in Relativity, for instance, a Photon does not Lorentz Contract, although it is through Lorentz Contraction, that the two laws, Amperes and Faradays Law interact to form the chain link fluctuation that is light. Lorentz Contraction, only occurs when a particle has rest mass. It is through Lorentz Contraction that massive particles bend space-time. One can surmise that photons by themselves don't bend space-time. Another interesting deduction, is that when two light beams are sent outward, polarized light returns from each. Like the twin paradox, the return light is different. The twin, in effect, is polarized, when the light then recombines it is not polarized, so polarization is removed through a 720 degree rotation as well. There is a great mystery about how space-time is bent, and this gives a clue as to how mass does this trick.