In hyperbolic space exist four regular platonic solids whose vertices lie in infinity.
Further details are available in the following article .
Cover shows sample scenes from Touching Soap Films . It belongs to a rare set of new compact CMC surfaces found by numerical experiments. It belongs to a family of surfaces whose fundamental domains are given as solution of free-boundary value problems in hyperbolic orthoschemes. Details are available in the following paper . Compact CMC surfaces have a long history in geometry, more details are given in Numerical Examples of Compact Constant Mean Curvature Surfaces .