Space Group from Absences

The determination as it is actually done: you have a data set, some classes of reflection are systematically missing, and the question is which of the 230 space groups you are allowed to be in. Answer the classes you have determined and the page names every group that fits — and the measurement that would shorten the list.

You supply

What you observe, class by class. Each menu offers only conditions some space group actually produces, so an answer can always be satisfied by something. Anything you have not determined is left alone and constrains nothing.

Reading it

A class left at not determined constrains nothing; answering it no condition asserts you looked and found nothing missing, which is what actually narrows the list. The strong answer is the one that can be wrong — and a wrong one removes the right group without saying so.

Worked examples: P2₁/c – the commonest determination there is · P2₁/c – the same data, empty classes too · Pbca – one pattern, two systems · P4cc – four groups, one reflection apart · Fd3m – diamond