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In this paper, we complete the construction of paper arXiv:cs.CG/0701096v2.Together with the proof contained in arXiv:cs.CG/0701096v2, this paperdefinitely proves that the general problem of tiling the hyperbolic plane with{\it \`a la} Wang tiles is undecidable.

About the domino problem in the hyperbolic plane, a new solution: complement