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.