734 W. A. T. SMITH — DETERMINATION OF CRYSTAL CLASSES 



With no singular axes, but with three 4-fold axes perpendicular to 

 each other — Hextetrahedral Class or Tetrahedral Group, Iso- 

 metric System. 



2. With no planes of symmetry: 



(a) With no or but one axis of symmetry having a period greater than 

 one-fold. 



# Opposite ends of crystals unlike (axis polar). 



Polar axis 6-fold — Hexagonal Pyramidal Class or Pyramidal- 



Hemimorphic Group, Hexagonal System. 

 Polar axis 4-fold — Tetragonal Pyramidal Class or Pyramidal- 



Hemimorphic Group, Tetragonal System. 

 Polar axis 3-fold — Trigonal Pyramidal Class or (Trigonal Pyra- 



midal-Hemimorphic Group, Hexagonal (Trigonal) System. 

 Polar axis 2-fold — Monoclinic Sphenoidal Class or Hemimorphic 



Group, Monoclinic System. 

 Polar axis 1-fold — Triclinic Asymmetric Class or Asymmetric 



Group, Triclinic System. 

 ## Opposite ends of crystals like (axis not polar). 



Axis 2-fold — Tetragonal Bisphenoidal Class or Tetartohedral 



Group, Tetragonal System. 

 (6) With more than one axis having a period greater than one-fold (some 



of them may join the mid-points of opposite edges). 



# With one or more singular axes. 



With a singular 6-fold axis — Hexagonal Trapezohedral Class or 

 Trapezohedral Group, Hexagonal System. 



With a singular 4-fold axis — Tetragonal Trapezohedral Class or 

 Trapezohedral Group, Tetragonal Systefia. 



With a singular 3-fold axis — Trigonal Trapezohedral Class or 

 Trapezohedral Group, Hexagonal (Trigonal) System. 



With three singular 2-fold axes perpendicular to each other — 

 Orthorhombic Bisphenoidal Class or Sphenoidal Group, Ortho- 

 rhombic System. 

 ## With no singular axes, but with three like axes perpendicular to 

 each other; also with four like 3-fold axes — Sometimes one set, 

 sometimes the other, the more prominent. 



The like perpendicular axes 4-fold — Pentagonal Icositetrahedral 

 Class or Plagihedral Group, Isometric System. 



The like perpendicular axes 2-fold — Tetrahedral Pentagonal Do- 

 decahedral Class or Tetartohedral Group, Isometric System. 



Table N"o. 2 



a. with no planes of symmetry 



1. With no or hut one axis of symmetry having a period greater than one-fold: 

 (a) Opposite ends of crystals unlike (axis polar) — Axial Order. 



Polar axis 6-fold — Hexagonal Pyramidal Class or Pyramidal-Hemi- 



morphic Group, Hexagonal System. 

 Polar axis 4-fold — Tetragonal Pyramidal Class or Pyramidal-Hemi- 

 morphic Group, Tetragonal System. 



