This document describes 32 cardboard models that represent the different crystal classes. It provides details on the symmetry elements that define each crystal class, including axes of rotation, planes of symmetry, and centers of symmetry. The crystal classes are grouped into cubic, tetragonal, orthorhombic, monoclinic, triclinic, and hexagonal systems. Each crystal class entry lists the symmetry elements that characterize its specific symmetry.

1. Crystal Classes
32 Cardboard Models
Stephen Joseph Boylan 2022

2. Crystal Classes, 32 Cardboard Models
Presenting 32 cardboard models of crystal systems as described in Crystal and
Crystal Growing by Alan Holden and Phyllis Morrison, MIT Press 1999

3. Cubic
Crystal Class

5. Crystal Class 4/m bar 3 2/m - Oh
Three 4-fold axes through opposite faces
Four 3-fold axes through opposite corners
Six 2-fold axes through opposite edges
Three planes parallel to faces, cubic planes
Six planes through opposite edges, dodecahedral planes
Center of symmetry

8. Crystal Class Bar 4 3 m - Td
Four 3-fold axes
Three 2-fold axes through opposite faces
Six dodecahedral planes

10. Crystal Class 2/m bar 3 - Th
Four 3-fold axes
Three 2-fold axes through opposite faces
Three cubic planes
Center of symmetry

12. Crystal Class 4 3 2 - O
Three 4-fold axes
Four 3-fold axes
Six 2-fold axes through opposite edges

14. Crystal Class 2 3 - T
Four 3-fold axes
Three 2-fold axes through opposite faces

16. Tetragonal
Crystal Class

18. Crystal Class - 4/m 2/m 2/m D4h
One 4-fold axes through the two square faces
Four 2-fold axes perpendicular to the 4-fold axis, two of them throuth opposite
faces and the other two through opposite edges
Five planes (a) 0ne perpendicular to the 4-fold axis (b) two containing that axis
and parrallel to opposite faces (c) two containing that axis and passing through
opposite edges
Center of symmetry

21. Crystal Class - 4mm C4v
One four-fold axis
Four planes containing that axis

24. Crystal Class - 4/m C4h
One four-fold axis
One plane perpendicular to that axis

27. Crystal Class - 422 D4
One four-fold axis
Four two fold axis

30. Crystal Class - bar 4 2 m D2d
4-fold alternating axis
Two 2-fold axes perpendicular to the 4-fold alternating axis through opposite
edges
Two planes containing the 4-fold alternating axis parrallel to opposite faces

33. Crystal Class - 4 C4
One four-fold axes

36. Crystal Class - bar 4 S4
One 4-fold alternating axis

39. Orthorhombic
Crystal Class

41. Crystal Class 2/m 2/m 2/m - D2h
Three mutually perpendicular 2 fold axes through opposite faces
Three planes parallel to opposite faces
Center of symmetry

44. Crystal Class mm2 - C2v
One 2 fold axis
Two planes containing that axis

47. Crystal Class 2 2 2 - D2
Three 2-fold axes

50. Monoclinic
Crystal Class

52. Crystal Class 2/m - C2h
One 2-fold axis
One plane perpendicular to that axis
Center of symmetry

55. Crystal Class m - Cs
One plane

58. Crystal Class 2- C2
One 2-fold axis

61. Triclinic
Crystal Class

63. Crystal Class bar 1
Center of symmetry

66. Crystal Class 1
No symmetry

69. Hexagonal
Crystal Class

71. Crystal Class 6/m 2/m 2/m D6h [1]
One 6 fold axis
Six 2 fold axes perpendicular to the 6 fold axis three of them through opposite
faces and three through opposite edges
Seven planes a) one perpendicular to the 6 fold axis
b) three containing that axis and passing through opposite faces
c) three containing that axis and passing through opposite edges
Center of gravity

74. Crystal Class 6mm - C6v [2]
One 6 fold axis, six planes containing that axis

77. Crystal Class 6/m - C6h [3]
One 6 fold axis, one palne perpendicular to that axis center of symmetry

80. Crystal Class 622 - D6 [4]
One 6 fold axis, six 2-fold axes

83. Crystal Class 6 - C6 [5]
One 6-fold axis

86. Crystal Class bar 6 m 2 - D3h [6]
One 3-fold axis, three 2-fold axes through opposite faces, three planes through
opposite faces, one plane perpendicular to the 3-fold axis

89. Crystal Class bar 6 - C3h [7]
One 3-fold axis
One plane perpendicular to that axis

92. Crystal Class 8
One 3-fold axis which is a 6-fold alternating axis, inversion axis
Three 2-fold axes passing through opposite faces
Three planes passing through opposite edges
Center of symmetry

95. Crystal Class 3 m - C3v [9]
One 3-fold axis,three planes through opposite edges

98. Crystal Class bar 3 2/m - D3d [10]
One 3-fold axis
Three 2-fold axes through opposite faces

101. Crystal Class bar 6 - C3h [11]
One 6-fold alternating axis
Center of symmetry

104. Crystal Class 3 - C3 [12]
One 3-fold axis

107. References
Alan Holden and Phyllis Morrison, Crystals and Crystal Growing, MIT Press 1999

108. The End

109. Thank you for taking the
time to watch.
Stephen Joseph Boylan
2022