Chrystallography

orthorhombic

3 two-fold axes or mirror at 90 degrees

a ≠ b ≠ c α = β = γ = 90 degrees

hexagonal

1 three-fold or six-fold axis of rotation

a1 = a2 = a3  intersecting at 120 degrees and perpendicular to c

Tetragonal

1 four-fold axis of rotation

a = b ≠ c α = β = γ = 90 degrees

monoclinic

1 two-fold axis of rotation or 1 mirror plane

a ≠ b ≠ c β > 90 α = γ = 90 degrees

triclinic

one fold symmetry only

a ≠ b ≠ c  α ≠ β ≠ γ ≠ 90 degrees

cubic

4 three fold axes of rotation

a = b = c α = β = γ = 90 degrees