  This study establishes a preliminary investigation of geometric objects that
degenerate to non-planar shapes, along with their Galois covers and groups.
  The study aims to determine the fundamental groups and signatures of the
Galois covers of algebraic surfaces in general, as they are invariants of the
classification of surfaces in the moduli space. The study investigates the
tetrahedron and the double tetrahedron as first examples.
  The study's findings can advance the classification of surfaces and provide
further links between algebraic geometry, group theory, and the topology of
degenerative processes and their properties.
  The resulting groups indicate that the tetrahedron and the double tetrahedron
are in different components in the moduli space.
