Geometrical ambiguities in the indexing of powder patterns

There are cases in which different lattices give calculated powder patterns with the identical number of distinct lines in identical 20 angular positions. The number of planes (hkl) contributing to each reflection may differ, however. The lattices having this property are related to each other by transformation matrices with simple rational elements. The resulting ambiguity in indexing of powder patterns is, in these cases, geometrical rather than accidental.