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Point Groups (Crystal Classes)

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Point Groups (Crystal Classes). Stereographic Projections. Used to display crystal morphology. X for upper hemisphere. O for lower. Stereographic Projections. We will use stereographic projections to plot the perpendicular to a general face and its symmetry equivalents (general form hkl ).

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stereographic projections
Stereographic Projections
  • Used to display crystal morphology.
  • X for upper hemisphere.
  • O for lower.
stereographic projections1
Stereographic Projections
  • We will use stereographic projections to plot the perpendicular to a general face and its symmetry equivalents (general form hkl).
  • Illustrated above are the stereographic projections for Triclinic point groups 1 and -1.
32 pointgroups hermann mauguin symbols
32 PointGroups:Hermann-Mauguin Symbols
  • Three positions in H-M symbol
  • Triclinic: No unique axis Only 1 or -1
  • Monoclinic: [010]
  • Orthorhombic: [100], [010], [001]
  • Tetragonal: [001], [100], [110]
  • Trigonal: [001], [100],
  • Hexagonal: [001], [100], [210]
  • Cubic: [100], [111], [110]
32 pointgroups crystal classes
32 PointGroups (Crystal Classes)
  • Triclinic: 1, 1
  • Monoclinic: 2, 2=m, 2/m
  • Orthorhombic: 222, 2mm, 2/m2/m2/m (=mmm)
  • Tetragonal: 4, 4, 4/m, 42m, 422 4mm 4/m2/m2/m
  • Trigonal: 3, 3m, 32, 3, 32/m
  • Hexagonal: 6, 6, 6/m, 6m2, 622, 6mm, 6/m2/m2/m
  • Cubic: 23, 2/m3, 432, 43m, 4/m32/m
32 pointgroups crystal classes1
32 PointGroups (Crystal Classes)
  • Triclinic: 1, 1
  • Monoclinic: 2, 2=m, 2/m
  • Orthorhombic: 222, 2mm, 2/m2/m2/m (=mmm)
  • Tetragonal: 4, 4, 4/m, 42m, 422 4mm 4/m2/m2/m
  • Trigonal: 3, 3m, 32, 3, 32/m
  • Hexagonal: 6, 6, 6/m, 6m2, 622, 6mm, 6/m2/m2/m
  • Cubic: 23, 2/m3, 432, 43m, 4/m32/m
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