I am puzzling with hyperbolic honeycombs or space filling stacking of hyperbolic regular polyhedrons and it looks all very complex to me .
As far as I tried I could not even find a stacking where two faces of different polyhedrons share the same plane.
So the only conditions I have are: * the polyhedrons together are space filling * all polyhedrons are regular (So this means all edges are the same size and the faces are equilateral triangles, squares , Pentagon's, ect)
Does this allready imply that no two faces are in the same plane?
Is this correct or am I overlooking the obvious?
If $P$ is a regular dodecahedron whose dihedral angles are right angles, then the group $G$ generated by reflections in the sides of $P$ is properly discontinuous, $P$ is a fundamental domain for $G$, and the $G$-translates of $P$ form a tiling of hyperbolic 3-space (what you call a "honeycomb" or a "space filling stacking"). This is an immediate application of the Poincare polyhedron theorem.
Furthermore, since the dihedral angles are right angles, the plane through every face of $P$ is tiled by faces of $G$-translates of $P$. This is quite the opposite behavior to what your question asserts, namely that no two faces of the tiling lie on the same plane.