Crystal Specimen
How to Miller index (indices) work being co-prime integers?

This system is a simple mathematical method used for labeling crystal faces on mineral specimens. What I don’t understand is what “arbitrary values” could be used for each of the three axes values and how this relates to the co-prime integers (1 or -1).
Any help with the maths on this would be greatly appreciated.

Ref: http://www.springerlink.com/index/0PQT13H3LGDLGRAC.pdf

Native Copper Crystal Specimen Michigan

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