Crystal Systems

The seven crystal systems and their characteristic symmetry elements.

crystallography symmetry identification

Overview

All crystals belong to one of seven crystal systems, classified by their unit cell
geometry and symmetry elements. Understanding these systems is fundamental to
crystallography and gem identification.

Crystal systems are defined by the relationship between crystallographic axes
(a, b, c) and the angles between them (α, β, γ). Each system has characteristic
symmetry elements that determine possible crystal forms.

Symmetry Elements

Rotation Axes

2-fold, 3-fold, 4-fold, 6-fold rotational symmetry

Mirror Planes

Reflection symmetry planes

Center of Symmetry

Inversion through a point

The Seven Systems

Cubic (Isometric)

The highest symmetry system with four threefold axes.

Axes
a = b = c
Angles
α = β = γ = 90°
Minimum Symmetry
4 threefold axes
Point Groups
m3m, 432, -43m, m3, 23
Example Gems
Diamond Spinel Garnet Fluorite
Hexagonal

Characterized by one sixfold axis.

Axes
a₁ = a₂ = a₃ ≠ c
Angles
α = β = 90°, γ = 120°
Minimum Symmetry
1 sixfold axis
Point Groups
6/mmm, 622, 6mm, -62m, 6/m, 6, -6
Example Gems
Emerald Aquamarine Morganite Apatite
Trigonal (Rhombohedral)

Characterized by one threefold axis.

Axes
a₁ = a₂ = a₃ ≠ c
Angles
α = β = 90°, γ = 120°
Minimum Symmetry
1 threefold axis
Point Groups
-3m, 32, 3m, -3, 3
Example Gems
Quartz Ruby Sapphire Tourmaline
Tetragonal

Characterized by one fourfold axis.

Axes
a = b ≠ c
Angles
α = β = γ = 90°
Minimum Symmetry
1 fourfold axis
Point Groups
4/mmm, 422, 4mm, -42m, 4/m, 4, -4
Example Gems
Zircon Rutile
Orthorhombic

Three twofold axes or two mirror planes.

Axes
a ≠ b ≠ c
Angles
α = β = γ = 90°
Minimum Symmetry
3 twofold axes or 2 planes
Point Groups
mmm, 222, mm2
Example Gems
Topaz Peridot Chrysoberyl Tanzanite
Monoclinic

One twofold axis or one mirror plane.

Axes
a ≠ b ≠ c
Angles
α = γ = 90°, β ≠ 90°
Minimum Symmetry
1 twofold axis or 1 plane
Point Groups
2/m, 2, m
Example Gems
Kunzite Orthoclase Jadeite
Triclinic

Lowest symmetry - no rotational symmetry.

Axes
a ≠ b ≠ c
Angles
α ≠ β ≠ γ ≠ 90°
Minimum Symmetry
No rotational symmetry
Point Groups
-1, 1
Example Gems
Turquoise Labradorite Rhodonite

Identifying Crystal Systems

When examining a crystal or gemstone, you can often determine its crystal system
by observing:

  • Crystal habit - The external shape and face arrangement
  • Optic character - Isotropic (cubic) vs. uniaxial vs. biaxial
  • Interference figure - Under polarized light microscopy
  • Cleavage directions - Related to internal symmetry

Quick Reference

Crystal Systems and Optic Character
System Optic Character RI Values
Cubic Isotropic Single RI (n)
Hexagonal, Trigonal, Tetragonal Uniaxial Two RI values (ω, ε)
Orthorhombic, Monoclinic, Triclinic Biaxial Three RI values (α, β, γ)

Common Gemstones by System

Cubic

  • Diamond
  • Spinel
  • Garnet (almandine, pyrope, grossular)
  • Fluorite

Trigonal

  • Quartz (amethyst, citrine)
  • Ruby
  • Sapphire
  • Tourmaline

Hexagonal

  • Emerald
  • Aquamarine
  • Morganite
  • Apatite

Orthorhombic

  • Topaz
  • Peridot
  • Chrysoberyl
  • Tanzanite