Wolfram Language

Exploring Symmetries of Crystal Systems

"CrystalSystem" entities consist of the seven named crystal systems in three dimensions: cubic, hexagonal, monoclinic, orthorhombic, tetragonal, triclinic and trigonal.

In a crystal system, a set of point groups and their corresponding space groups are assigned to a lattice system. In three dimensions, the crystal families and systems are identical except that the hexagonal and trigonal crystal systems are combined into the single hexagonal crystal family.

A comprehensive set of properties is available for each crystal system and family.

It is easy to create a table summarizing the symmetry properties of crystal systems using the built-in data.

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Similarly, a concise tabular encapsulation of crystal system edge and angle relations can also be constructed using built-in data.

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