From The Gemology Project
| Crystal System
The cube is composed of 6 square faces
at 90° angles to each other. Each
face intersects one of the crystallographic
axes and is parallel to the other two.
The tetragonal system also has three axes
that all meet at 90°. It differs from the
isometric system in that the C axis is longer or
shorter than the A axes,
which are the same length.
In the hexagonal system, we have an additional axis,
giving the crystals six sides. Three of these
are equal in length and meet at 120° to each other.
The C or vertical axis is at 90° to the horizontal axes.
Mineralogists sometimes divide this into two systems,
the hexagonal and the trigonal, based on their external
appearance (see following).
The trigonal system is a subsystem of the
hexagonal system according to some institutes,
therefore some gem references will list these as
In this system, there are three axes all of which
meet at 90° to each other. However, all the axes
are of different length.
The above crystal systems all have axes sides
that meet at 90°. In the monoclinic system, all
the axes are different lengths. The A axis is inclined
to the C axis. The B axis is at 90° to them.
You can imagine this as a matchbox that slants to one side.
In this system all the axes are different
lengths and none of them meet at 90°.
You can imagine this as a matchbox which slants to two sides.