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The analysis of manifold valued data using embedding based methods is linkedto the problem of finding suitable embeddings. In this paper we are interestedin embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of therotation group modulo finite symmetry groups. Data on such quotient manifoldsnaturally occur in crystallography, material science and biochemistry. Weprovide a generic framework for the construction of such embeddings whichgeneralizes the embeddings constructed in arXiv:1701.01579. The centraladvantage of our larger class of embeddings is that it comprises isometricembeddings for all crystallographic symmetry groups.

Locally Isometric Embeddings of Quotients of the Rotation Group Modulo Finite Symmetries