  We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no
embedded essential 2-suborbifolds, up to decomposition along embedded
hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a
3-dimensional hyperbolic polyhedral orbifold to contain an immersed (singular)
hyperbolic turnover, we classify the triangle subgroups of the fundamental
groups of orientable 3-dimensional hyperbolic tetrahedral orbifolds in the case
when all of the vertices of the tetrahedra are non-finite, and we provide a
conjectural classification of all the triangle subgroups of the fundamental
groups of orientable 3-dimensional hyperbolic polyhedral orbifolds. Finally, we
show that any triangle subgroup of a (non-orientable) 3-dimensional hyperbolic
reflection group arises from a triangle reflection subgroup.
