  In this paper we present a necessary conditions, that simple close geodesics
on regular tetrahedra in the 3-dimensional hyperbolic space must satisfy.
Furthermore, we explicitly describe three classes of simple closed geodesics on
regular tetrahedra in the hyperbolic 3-space. These are so-called
2-homogeneous, 3-homogeneous and (3,2)-homogeneous geodesics. Up to a rigid
motion of a tetrahedron there exists a unique geodesic in each class.
