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According to Mathworld, hyperbolic geometry is well understood in 2 dimensions but not in 3 dimensions.

http://mathworld.wolfram.com/HyperbolicGeometry.html

What isn't well understood about hyperbolic geometry in 3D, that is in 2D or that is in 3D-Euclidean geometry?

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    I wouldn't take that comment on Wolfram's site too seriously.....2010-10-26

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