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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Point Groups (Crystal Classes)

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Point groups crystal classes

Point Groups(Crystal Classes)


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


Triclinic system

Triclinic System


Monoclinic system

Monoclinic System


Orthorhombic system

Orthorhombic System


Trigonal system

Trigonal System


Trigonal system1

Trigonal System


Tetragonal system

Tetragonal System


Tetragonal system1

Tetragonal System


Tetragonal system2

Tetragonal System


Hexagonal system

Hexagonal System


Hexagonal system1

Hexagonal System


Hexagonal system2

Hexagonal System


Cubic system

Cubic System


Cubic system1

Cubic System


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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