The table below shows the 32 crystal classes, their symmetry, Hermann-Mauguin symbol, and class name. Note that the 32 crystal classes are divided into 6 crystal systems.
The Triclinic System has only 1-fold or 1-fold rotoinversion axes.
The Monoclinic System has only mirror plane(s) or a single 2-fold axis.
The Orthorhombic System has only two fold axes or a 2-fold axis and 2 mirror planes.
The Tetragonal System has either a single 4-fold or 4-fold rotoinversion axis.
The Hexagonal System has no 4-fold axes, but has at least 1 6-fold or 3-fold axis.
The Isometric System has either 4 3-fold axes or 4 3-fold rotoinversion axes.
Crystal System - Crystal Class - Symmetry - Name of Class
Triclinic 1 none Pedial
i Pinacoidal
Monoclinic 2 1A2 Sphenoidal
m 1m Domatic
2/m i, 1A2, 1m Prismatic
