The basic facet arrangement and Proportions created by mathematician Marcel Tolkowsky and refined or adjusted by many cutters in recent years. Many shapes have been created using the same basic principles, including Round Brilliant Cut, Pear Shape Cut, Heart Shape Cut, Oval Cut, and Marquise Cut.

Additional refinements have been added by some cutters, to create Super Ideal Cut stones, as in many name brands marketed by different companies, some of which create a special pattern like the Hearts and Arrows Cut under special viewers.

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