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Different crystal systems with examples

Short answer

The seven crystal systems, defined by axis lengths and angles, are: isometric (a=b=c, all 90°; e.g., galena), tetragonal (a=b≠c, 90°; zircon), orthorhombic (a≠b≠c, 90°; topaz), monoclinic (a≠b≠c, β≠90°; gypsum), triclinic (all ≠90°; kyanite), hexagonal (a1=a2=a3≠c, 120° & 90°; beryl), and trigonal (similar axes; quartz).

Describe the different crystal systems with diagrams and examples.

Crystals are classified into seven systems by the length and mutual inclination of their three (or four) crystallographic axes a, b, c.

SystemAxesAnglesExamples
Isometric (cubic)a = b = cα = β = γ = 90°Galena, pyrite, halite, garnet
Tetragonala = b ≠ call 90°Zircon, rutile, chalcopyrite
Orthorhombica ≠ b ≠ call 90°Topaz, barite, olivine, sulphur
Monoclinica ≠ b ≠ cα = γ = 90°, β ≠ 90°Gypsum, orthoclase, mica, hornblende
Triclinica ≠ b ≠ cnone 90°Plagioclase, kyanite, microcline
Hexagonala₁ = a₂ = a₃ ≠ c (4 axes)three at 120°, c at 90°Beryl, apatite, graphite
Trigonal (rhombohedral)a₁ = a₂ = a₃ ≠ c, 3-fold axisas hexagonalQuartz, calcite, dolomite, hematite

Sketches of axes

 Isometric        Tetragonal       Orthorhombic
  c                c                 c
  |__b             |__b              |__b
 /a=b=c           /a=b<>c           /a<>b<>c
 all 90           all 90            all 90

 Monoclinic       Triclinic         Hexagonal
  c                c                  c
  |  /b            |  /b              | a2
 /|/               | /                 |/__a1
 a  beta<>90       a  none 90        a3 (120 deg)

Some books group the trigonal system under hexagonal, giving six systems.

✓ Answer checked by Claude Opus 5.5 (high effort)

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