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A theoretical framework to construct wavelets adapted to compact domains has already been established, however technical considerations must be addressed to implement the construction on a larger variety of domains. In this article we generalize the theory further and provide a methodology to explicitly construct the wavelets. Examples of the construction for a rectangular surface, a triangular surface, and a smooth simplex in 驴3 are given. An extension of the theory to triangulated manifolds of finite distortion in n dimensions is also explained.