  We describe a family of 4-dimensional hyperbolic orbifolds, constructed by
deforming an infinite volume orbifold obtained from the ideal, hyperbolic
24-cell by removing two walls. This family provides an infinite number of
infinitesimally rigid, infinite covolume, geometrically finite discrete
subgroups of the isometry group of hyperbolic 4-space. It also leads to finite
covolume Coxeter groups which are the homomorphic image of the group of
reflections in the hyperbolic 24-cell. The examples are constructed very
explicitly, both from an algebraic and a geometric point of view. The method
used can be viewed as a 4-dimensional, but infinite volume, analog of
3-dimensional hyperbolic Dehn filling.
