The trigonal crystal system is subdivision of the hexagonal crystal system. It only has one minor difference from the hexagonal system, in that trigonal minerals have threefold symmetry, whereas true hexagonal minerals have sixfold symmetry. The trigonal crystal system, like the hexagonal crystal system, has the following specifications:
Four axes, three are equal in length and lie at an angle of 120° from each other. The fourth is either longer or shorter but must be at a right angle toward the other corners.
3D Animated Illustration of a Trigonal Crystal with Axes
Crystals kindly provided by Smorf