  In this paper, we prove that the general tiling problem of the hyperbolic
plane is undecidable by proving a slightly stronger version using only a
regular polygon as the basic shape of the tiles. The problem was raised by a
paper of Raphael Robinson in 1971, in his famous simplified proof that the
general tiling problem is undecidable for the Euclidean plane, initially proved
by Robert Berger in 1966.
