Flat fronts with polyhedral symmetry in hyperbolic three-space

Flat fronts with symmetry similar to regular polyhedrons are studied. A flat front is a flat surface in hyperbolic three-space admitting a certain kind of singularities. Explicit descriptions of regular-polyhedral flat fronts (tetrahedral, cubic, octahedral, dodecahedral and icosahedral flat fronts) are given and a characterization of them is shown.