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• The Plato's octahedron and probabilities of combinatorial types of crystal-polyhedron in the nature

The Plato's octahedron and probabilities of combinatorial types of crystal-polyhedron in the nature

Rakin V. I.

Zapiski RMO (Proceedings of the Russian Mineralogical Society). 2015. V. 144. N 2. P. 119-130

Full text is available

Language: Russian

Abstract

For the simple crystallographic form of octahedron, the Monte-Carlo experiments were used to calculate the probability of combinatorial crystallographic varieties, including the ideal Plato’s octahedron. Results of these calculations correspond to empirical probabilities of occurrence of octahedron morphotypes among synthetic diamonds. Suggested techniques of theoretical evaluation of probabilities to find different combinatorial types of crystals-polyhedrons in the nature may be also applied for other enclosed simple forms of mineral crystals.

Key words: polyhedron, octahedron, simple crystal form, combinatorial type, probability.