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Symmetry elements, crystal systems, rock-forming minerals

Short answer

Symmetry elements are planes, axes, and centre of symmetry. The six crystal systems are isometric, tetragonal, orthorhombic, monoclinic, triclinic, and hexagonal/trigonal. Rock-forming minerals like quartz, feldspar, and mica influence rock strength and durability.

Describe the symmetry elements and crystal systems with figures. Explain the engineering significance of rock-forming minerals.

Elements of symmetry

Symmetry is the repetition of faces and edges in a crystal. There are three elements.

  1. Plane of symmetry: a plane dividing the crystal into two mirror-image halves. Axial planes pass through two axes; diagonal planes pass through one axis and bisect the angle between the other two.
  2. Axis of symmetry: a line about which rotation by 360° repeats the form 2 (diad, 180°), 3 (triad, 120°), 4 (tetrad, 90°) or 6 (hexad, 60°) times.
  3. Centre of symmetry: a point at which any line through it meets similar faces at equal distance on both sides.

A cube has 9 planes, 13 axes and 1 centre.

Crystal systems

SystemAxesAnglesSymmetry (normal class)Example
Isometrica = b = c90°, 90°, 90°9 P, 13 A, 1 CGalena, garnet
Tetragonala = b ≠ call 90°5 P, 5 A, 1 CZircon
Orthorhombica ≠ b ≠ call 90°3 P, 3 A, 1 CTopaz, barite
Monoclinica ≠ b ≠ cβ ≠ 90°1 P, 1 A, 1 CGypsum, orthoclase
Triclinica ≠ b ≠ cnone 90°1 C onlyPlagioclase
Hexagonala₁ = a₂ = a₃ ≠ c120° and 90°7 P, 7 A, 1 CBeryl, apatite
Trigonalas hexagonal, 3-fold axisas hexagonal3 P, 4 A, 1 CCalcite, quartz
 Isometric     Tetragonal    Orthorhombic   Monoclinic
   c             c              c              c  /
   |_b           |_b            |_b            |_/b
  /a=b=c        /a=b<>c       /a<>b<>c        /a   beta<>90

Engineering significance of rock-forming minerals

  • Quartz: hard, stable, no cleavage; gives strong, durable rocks; may react with cement alkalis if amorphous.
  • Feldspar: common, hardness 6, but weathers to clay and weakens rock.
  • Mica: perfect cleavage; mica-rich rocks (schist, phyllite) are weak and cause slope and tunnel failures.
  • Calcite: soft and soluble; limestone makes cement but has cavities that cause leakage.
  • Amphibole, pyroxene and olivine: dense and strong, found in dark rocks such as basalt and gabbro, but they weather faster than quartz.

✓ Answer checked by Claude Opus 5.5 (high effort)

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