This stone has several names. It is also called Peridot, Olivine.
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Chrysolite has been mined and used in jewelry for over 2 thousand years. Its homeland is Egypt. And now the stone is mined in Pakistan, Burma and China.
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Interestingly, Olivine makes up almost 50% of the Earth's upper mantle. But it does not always crystallize into a jewelry variety, and therefore is highly valued. As a rule, the stone is not transparent and is found in absolutely nondescript rocks.
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It is hard to believe, but in Hawaii there are entire beaches of chrysolite.
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This stone is still not grown, synthetic chrysolites do not exist.
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The most reliable way to check chrysolite is inclusions. They are inherent in natural real chrysolites.