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Point Groups (Crystal Classes)

Learn about crystal point groups and use stereographic projections to plot crystal faces and symmetry equivalents like Triclinic, Monoclinic, Orthorhombic, Tetragonal, Trigonal, Hexagonal, and Cubic systems.

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Point Groups (Crystal Classes)

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  1. Point Groups (Crystal Classes)

  2. Stereographic Projections • Used to display crystal morphology. • X for upper hemisphere. • O for lower.

  3. 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.

  4. 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

  5. Triclinic System

  6. Monoclinic System

  7. Orthorhombic System

  8. Trigonal System

  9. Trigonal System

  10. Tetragonal System

  11. Tetragonal System

  12. Tetragonal System

  13. Hexagonal System

  14. Hexagonal System

  15. Hexagonal System

  16. Cubic System

  17. Cubic System

  18. 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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