Crystal symmetry

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Crystal Systems
System Minimum symmetry Dimensional requirements for unit cell
Triclinic none none
Monoclinic Twofold axis (parallel to b) a and c are both perpendicular to b (but not to each other)
Orthorhombic Three mutually perpendicular twofold axes a, b, and c all perpendicular
Tetragonal Fourfold axis (parallel to c) a, b, and c all perpendicular; a and b equal in length
Rhombohedral (or Trigonal) Threefold axis (parallel to c) a, b perpendicular to c and at 120° to each other; a and b equal
Hexagonal Sixfold axis (parallel to c) Same as trigonal
Cubic Threefold axes along cube diagonals a, b, and c perpendicular and equal in length

Bravais lattices

see: Bravais lattice

Space groups

see: Space groups, Overview of all space groups (in French)