III. Hexagonal System

A. Hexagonal Division 1. Normal Class (13) Beryl Type 2. Hemimorphic Class (14) Zincite Type 3. Pyramidal Class (15) Apatite Type 4. Pyramidal-Hemimorphic Class (16) Nephelite Type 5. Trapezohedral Class (17) B. Trigonal or Rhombohedral Division 1. Trigonal Class (18) Benitoite Type 2. Rhombohedral Class (19) Calcite Type 3. Rhombohedral-Hemimorphic Class (20) Tourmaline Type 4. Trirhombohedral Class (21) Phenacite Type 5. Trapezohedral Class (22) Quartz Type 6. Other Classes (23) 7. Other Classes (24) Mathematical Relations of the Hexagonal System 119. The HEXAGONAL SYSTEM includes all the forms which are referred to four axes, three equal horizontal axes in a common plane intersecting at angles of 60") and a fourth, vertical axis, at right angles to them. Two sections are here included, each embracing a number of distinct classes related among themselves. They are called the Hexagonal Division and the Trigonal (or Rhombohedral) Division. The symmetry of the former, about the vertical axis, belongs to the hexagonal type, that of the latter to the trigonal type. Miller (1852) referred all the forms of the hexagonal system to three equal axes parallel to the faces of the fundamental rhombohedron, and hence intersecting at equal angles, not 90". This method (further explained in Art. 169) had the disadvantage of failing to bring out the relationship between the normal hexagonal and tetragonal types, both characterized by a principal axis of symmetry, which (on the system adopted in this book) is the vertical crystallo raphic axis. It further gave different symbols to faces which are crystallographally identical. It is more natural to employ the three rhombohedra1 axes for tri- gonal forms only, as done by Groth (1905), who includes these groups in a Trigonal Syslem; but this also has some disadvantages. The indices commonly used in describing hexagonal forms are known as the Miller-Bravais indices, since the were adopted by Bravais for use with the four axes from the scheme used by Miller in the other crystal systems.