  A ``Wick rotation'' is applied to the noncommutative sphere to produce a
noncommutative version of the hyperboloids. A harmonic basis of the associated
algebra is given. It is noted that, for the one sheeted hyperboloid, the vector
space for the noncommutative algebra can be completed to a Hilbert space, where
multiplication is not continuous. A method of constructing noncommutative
analogues of surfaces of rotation, examples of which include the paraboloid and
the $q$-deformed sphere, is given. Also given are mappings between
noncommutative surfaces, stereographic projections to the complex plane and
unitary representations. A relationship with one dimensional crystals is
highlighted.
