The $4n+2$ period conjecture for periodic trajectories on triangle tilings

A triangle tiling is the edge-to-edge tiling of the plane by congruent copies of a triangle. The period of a periodic trajectory is the number of iterations, or equivalently the number of repeated trajectory steps, in its minimal return.

$4n+2$ conjecture. Every periodic trajectory on a triangle tiling has period $4n+2$ for some positive integer $n$.

The source says that Hubert and Paris-Romaskevich subsequently proved this conjecture. It is therefore solved.