# Crystallographic Polyhedra

Crystallography is one of the sciences with close ties to geometry.  The above image, from G. Heck's 1851 Iconographic Encyclopedia, shows a range of polyhedra which occur as crystal forms.  The terminology used by crystallographers is somewhat different from mathematicians.  The caption to the above image is: EQUIPMENT: Figure 1.  Blowpipe 2.  Attenuated point of flame caused by the blowpipe 3.  Forceps 4.   Berzelius blowpipe 5.  Nicholson areometer 6.  Magnetic needle 7, ab. Instrument for detecting electricity in minerals 8.  Common goniometer 9.  Gambay's goniometer 10. Wollaston's goniometer FORMS OF CRYSTALLIZATION: 11, 12. Regular octahedron 13. Octahedron abbreviated to a six sided plate 14. Cube 15. Relation of the cube and octahedron 16, 17. Cubic octahedron 18. Rhombic dodecahedron 19. Relation of the rhombic dodecahedron and cube 20. Pyramidal cube 21, 24. Cube with dodecahedral faces replacing its edges 22. Octahedron with dodecahedral faces 23. Octahedron passing into a dodecahedron 24. See 21 25. Combination of cube faces and those of the pyramidal cube  26. Tetrahedron 27. Octahedron passing into a tetrahedron 28. Cube with its edges replaced by three faces 29. Pentagonal dodecahedron 30. Trapezohedron 31. Octahedron passing into a trapezohedron 32. Obtuse square octahedron 33. Acute square octahedron 34. Square octahedron with two corners truncated 35. Right square prism 36. Regular eight sided prism 37. Right square prism with its corners truncated 38. Square octahedron with truncated basal edges 39. Square octahedron with truncated lateral edges 40. Eight sided pyramid 41. Twelve sided prism 42. Six sided prism with bevelled edges 43. Right square prism with basal edges truncated 44. Rectangular octahedron 45. Rectangular octahedron truncated 46. Square octahedron with bevelled lateral edges 47, a. Obtuse rhombic octahedron b. Acute rhombic octahedron c. Rectangular octahedron 48. Rhombic octahedron with two corners bevelled 49.  Octahedron with the corners of the vertical axis replaced by four plane faces 50. Right rhombic prism 51.  Right rhombic prism with obtuse edges truncated 52. Irregular eight sided prism 53-55. Combination of prisms belonging to the trimetric system 56. Rectangular prism 57, 58. Modified octahedrons 59, 60.  Oblique six sided prism 61. Octahedron with half the edges truncated 62. Prism with half the basal edges truncated 63-65. Oblique rhomboidal prism 66. Oblique six sided prism 67. Double six sided pyramid 68.  Pyramidal six sided prism 69. Modified rhombic octahedron 70. Regular six sided prism 71. Regular six sided prism with truncated basal edges 72. Regular six sided prism with truncated corners 73. Obtuse double six sided pyramid 74. Scalene octahedron 75. Rhombohedron 76. Six sided prism with four edges bevelled 77, 78. Natural situation of two rhombohedrons 79. Grouping of crystallizations 80-87, 90, 91.    Forms of ground jewels 88, 89. Crystalline formations 90, 91. See 80, etc. 92, 93. Crystalline structure.

For a good, well illustrated, introductory work, see Martin Buerger's Elementary Crystallography, listed in the references.