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Geometrical ambiguity means the cases in which more than one powder indexing solution exists. Using a new function implemented in the powder indexing software CONOGRAPH, unit cells that involve geometrical ambiguity are exhaustively searched. As a result, many unknown cases are obtained, although the number of such unit cells is still rather limited. It is also proven that the number of solutions in powder auto-indexing is not always unique, but generally finite.

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Appendices A, B and C

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