Sugilite

A stone [KNa₂Li₃(Fe,Mn,Al)₂Si₁₂0₃₀] typically found in Japan, South Africa, and on Iwagi Island. Due to its vivid color, it is used primarily in jewelry making.

Chemical Composition:

    Potassium  3.80 %  K         4.58 % K2O  
    Sodium     4.47 %  Na        6.03 % Na2O  
    Lithium    2.03 %  Li        4.36 % Li2O  
    Manganese  3.21 %  Mn        4.14 % MnO  
    Aluminum   0.52 %  Al        0.99 % Al2O3  
    Iron       6.52 %  Fe        8.38 % FeO  
    Silicon   32.78 %  Si        70.12 % SiO2  
    Oxygen    46.68 %  O  
              ______             ______  
             100.00 %            98.60 % = Total Oxide

Usually purple, black, and brown in color, Sugilite forms hexagonal crystals though occurances of them are quite rare, and when found are often massive in size. With a refraction index of 1.60 and a hardness 6 - 6.5, the stone is usually found in aegirine syenite.

The stone has subconchoidal fracturing and cleavage in one direction. It has a Dana class of 63.2.1a.9, in the Milarite - Osumilite subgroup, with Cyclosilicate Condensed Rings. Overall a fairly rare stone, it is highly prized for it's rich purple colors for cabs.

The highest quality pieces are usually translucent and cabbed, thereby being used in jewelry. I find that it is most attractive set with turquoise or other similar stones, and has a similar value to it as well as lapis.

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Sources:

http://webmineral.com/data/Sugilite.shtml - Contains excellent further information on optical and physical properties of the substance.
http://www.theimage.com/gemstone/sugilite/sugilite.html