THE THIRTY-TWO CRYSTAL CLASSES AND THEIR SYMMETRY

(PROPER SYMMETRY OPERATIONS ONLY)

Crystal System Crystal Class Name Symmetry Content
TRICLINIC bar 1 Pedial None

1

 1 Pinacoidal i
MONOCLINIC 2 Sphenoidal 1A2

1

 m Domatic 1m

1

 2/m Prismatic i, 1A2, 1m
ORTHORHOMBIC 222 Rhombic-disphenoidal 3A2

1

 mm2 Rhombic-pyramidal 1A2, 2m

1

 2/m 2/m 2/m Rhombic-dipyramidal i, 3A2, 3m
TETRAGONAL 4 Tetragonal-pyramidal 1A4

1

1

 Tetragonal-disphenoidal i, 1A2

1

 4/m Tetragonal-dipyramidal i, 1A4, 1m

1

 422 Tetragonal-trapezohedral 1A4, 4A2

1

 4mm Ditetragonal-pyramidal 1A4, 4m

1

 bar 4 2 m Tetragonal-scalenohedral 3A2, 2m

1

 4/m 2/m 2/m Ditetragonal-dipyramidal i, 1A4, 4A2, 5m
RHOMBOHEDRAL 3 Trigonal-pyramidal 1A3

1

1

 Rhombohedral i, 1A3

1

 32 Trigonal-trapezohedral 1A3, 3A2

1

 3m Ditrigonal-pyramidal 1A3, 3m

1

 2/m Hexagonal-scalenohedral i, 1A3, 3A2, 3m
HEXAGONAL 6 Hexagonal-pyramidal 1A6

1

1

 Trigonal-dipyramidal 1A3, 1m

1

 6/m Hexagonal-dipyramidal i, 1A6, 1m

1

 622 Hexagonal-trapezohedral 1A6, 6A2

1

 6mm Dihexagonal-pyramidal 1A6, 6m

1

 m2 Ditrigonal-dipyramidal 1A3, 3A2, 4m

1

 6/m 2/m 2/m Dihexagonal-dipyramidal i, 1A6, 6A2, 7m
ISOMETRIC 23 Tetartoidal 4A3, 3A2

1

 2/m Diploidal i, 4A3, 3A2, 3m

1

 432 Gyroidal 3A4, 4A3, 6A2

1

 bar 4 3m Hextetrahedral 4A3, 3A2, 6m

1

 4/m bar3 2/m Hexoctahedral i, 3A4, 4A3, 6A2, 9m