The domino problem of the hyperbolic plane is undecidable, new proof

The present paper is a new visit to a proof given in a previous paper of the author 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 strongly reduces the number of prototiles.