Stereographic Projections Point Groups

1 9/15/20141 Point Groups (Crystal Classes) Stereographic Projections Used to display crystal morphology. X for upper hemisphere. O for 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 PointGroups:Hermann-Mauguin Symbols Three positions in H-M symbol Triclinic: No unique axis Only 1 or -1 Monoclinic: (b-unique) [010] Orthorhombic: [100], [010], [001] Tetragonal: [001], [100], [110] Trigonal: [001], [100], Hexagonal: [001], [100], [210] Cubic: [100], [111], [110]32 PointGroups (Crystal Classes) Triclinic: 1, 1 Monoclinic: 2, 2=m, 2/m Orthorhombic: 222, 2mm, 2/m2/m2/m (=mmm) Tetragonal.

2 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/mTriclinic System9/15/20142 Monoclinic SystemOrthorhombic SystemCrystal System ?A. TriclinicB. MonoclinicC. OrthorhombicD. TetragonalE. TrigonalCrystal System ? MonoclinicC. OrthorhombicD. TetragonalE. TrigonalPoint Group ?A. -1B. 2C. mD. 2/mE. 1 Point Group ? mC. 2/mD. 19/15/20143 Crystal SystemA. TriclinicB. MonoclinicC. OrthorhombicD. TetragonalE. TrigonalCrystal SystemA. TriclinicB.

3 TetragonalE. TrigonalPoint GroupA. -1B. 2/m2/m2/mE. 2/mPoint GroupA. -1B. 2 2C. 2C. 169/15/20144 Trigonal SystemTrigonal SystemTetragonal SystemTetragonal SystemTetragonal SystemHexagonal System9/15/20145 Hexagonal SystemHexagonal SystemCubic SystemCubic SystemCrystal System ?A. OrthorhombicB. TetragonalC. Isometric (cubic)D. HexagonalE. TrigonalCrystal System ?A. OrthorhombicB. TetragonalC. Isometric (cubic) Trigonal9/15/20146 Point GroupA. 4mmB. 432C. 6/m 2/m 2/mD. 4/m -3 2/mE. 2/m -3 Point GroupA. 4mmB.

4 2/m 2/mD. 4/m -3 2/mE. 2/m -3 Crystal System ?A. OrthorhombicB. TetragonalC. Isometric (cubic)D. HexagonalE. TrigonalCrystal System ?A. OrthorhombicB. (cubic)D. HexagonalE. TrigonalPoint Group ?A. 4mmB. 432C. 23D. 4/m -3 2/mE. 2/m -3 Point Group ?A. 4mmB. 4/m -3 2/mE. 2/m -39/15/2014732 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