Crystal Systems Continued 

Cubic System Cubic Crystals have three equal axis lengths and three angles all at 90º. a=b=c and alpha = beta = gamma = 90º. These crystals may look like cubes, pyramids, or be almost round (like many garnets). The symmetry is very high and the system supports many many possible shapes. The cubic system is also called isometric. cubic crystals
include, fluorite, pyrite, analcime, tetrahedrite, garnet,
and galena. 

Trigonal System Trigonal crystals have three equal axis, a1=a2=a3, the angles must be less than 120º but must not be 90º. alpha1=alpha2=alpha3=60º beta ‚ 90º. The trigonal axis has a three fold axis of symmetry, but is not hexgonal (described next.) Trigonal crystals maybe described by a hexagonal unit cell, but they lack hexad rotation. They are sometimes called rhombohedral. trigonal minerals
include: calcite, sidereite, dolomite, and
rhodochrosite. 

Hexagonal System Hexagonal crystals have a1 = a2 ‚ a3 (two equal axis), beta = 90º, and alpha1 = aplpha2 = alpha3 = 60º. They have a six fold axis of symmetry. Cross sections are often perfect hexagons and fairly easy to spot in the crystal world. heagonal minerals
include: quartz, vanadinite, apatite, beryl, and
mimetite. 

For a more indepth discussion (Written by Mike Howard  Illustrated by Darcy Howard) on crystal symmetry and crystal groups you can visit: Rockhounds.com 

