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The known denitions of Farey polytopes and continued fractions are generalized and applied to diophantine approximation in n-dimensional euclidean spaces. A generalized Remak-Rogers isolation theorem is proved and applied to show that certain Hurwitz constants for discrete groups acting in a hyperbolic space are isolated. The approximation constant for the imaginary quadratic eld of discriminant 15 is found.

Farey polytopes and continued fractions associated with discrete hyperbolic groups