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Museum Quality 20cts Colombian Emerald Crystal Specimen in Brescia Rare    US $42,000.00

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Rare Papagoite in Quartz 51 Natural Crystal Specimen from South Africa    US $6,930.00

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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

Ethiopian Opal Polished Crystal Specimen Heart Necklace JO002

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Museum Quality 20cts Colombian Emerald Crystal Specimen in Brescia Rare    US $42,000.00

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110 Extremely Rare Helvine Crystal Mineral Specimen    US $9,000.00

NATURAL CRYSTAL Yellow BALTIC AMBER Rough Genuine Specimen FREE Ship by EMS    US $8,000.00

Rare Papagoite in Quartz 51 Natural Crystal Specimen from South Africa    US $6,930.00

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