In mathematics, a Fuchs group is a particular type of a group of isometrics of the hyperbolic plane.
A Fuchs group is always a discrete group in the semi-simple Lie group, PSL (2, C). The Fuchs group was named by German poet Lazarus Fuchs by Henri Poincaré.
Fuchs groups are used to construct Fuchs models of Riemann surfaces. In a sense, Fuchs groups for non-Euclidean geometry do what crystallographic groups do for Euclidean geometry, but the theory is much richer. Some Escher charts are based on Fuchs groups (for the hyperbolic geometry disk model).
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