Unit crystals can have same structure after rotation around axis, reflection across axis, inversion through central point, translation along axis, or any combination {symmetry, crystal}. Nature has six symmetry groups: isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic.
Symmetry groups {hexagonal} can have rotation by 60 degrees. Hexagonal crystals have one six-fold axis, with one axis perpendicular to the other two axes but with different length, and two axes with same length at 60-degree angle to perpendicular axis, and makes seven crystal classes.
Symmetry groups {cubic symmetry group} {isometric symmetry group} can have rotation by 90 degrees, reflection, and inversion.
Symmetry groups {monoclinic symmetry group} can have rotation by 90 degrees. Crystals {monoclinic crystal}| can have one two-fold axis, two perpendicular same-length axes, and one non-perpendicular different-length axis, to make three crystal classes.
Symmetry groups {orthorhombic symmetry group} can have rotation by 180 degrees and reflection. Crystals {orthorhombic crystal} can have three two-fold axes, which are all perpendicular but have different lengths, to make three crystal classes.
Symmetry groups {tetragonal symmetry group} can have rotation by 90 degrees. Crystals {tetragonal crystal} can have one four-fold axis and three perpendicular axes but only two with same length, to make seven crystal classes.
Symmetry groups {triclinic symmetry group} can have rotation by 120 degrees. Crystals {triclinic crystal}| can have three axes, all not perpendicular but all of same length, to make two crystal classes.
5-Chemistry-Inorganic-Phase-Phases-Solid-Crystal
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Date Modified: 2022.0225