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This paper presents several general properties of systematic absences that are available before unit-cell parameters and the space group have been determined. The properties are given in the form of distribution rules of Miller indices corresponding to systematic absences on a topograph. A topograph is a graph whose edges are associated with a set of four lattice vectors satisfying Ito's equation 2(|l1*|2 + |l2*|2) = |l1* + l2*|2 + |l1* - l2*|2. It is possible to integrate global information about extinct reflections by using topographs. As an example of the application of these rules, a new powder auto-indexing algorithm is introduced, focusing on its theoretical aspects.

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Appendices A, B, C and D

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