Identical spatial lattices with different complex symbols

Abstract

In the article “Paralleloëder in kanonischer Form und deren eindeutige Beziebung zu Raumgittern” I showed that by performing a monoclinic shift, you can always obtain an identical spatial lattice, and in doing so sometimes you can reduce nonorthogonality, that is why the expression for the probability of correct orientation will increase, even though this causes the form symbols to become more complex. But I did not dwell in detail on the criterion for exactly at which shift the lattice remains identical. This is the explanation I want to make in this note.

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