  The present paper is a new version of the arXiv paper revisiting the proof
given in a previous paper of the author published in 2008 proving 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. The present
construction improves that of the recent arXiv paper. It also strongly reduces
the number of prototiles.
