2. Hexagonal crystal system
Image published by Solid State as public domain
A hexagonal unit cell consists of two sides of the same and one of different length. Alpha and beta have values of 90°, gamma is 120°.
Using three of these unit cells (two of them turned by 120° and 240°) we can create a structure with a hexagonal base, as can be seen here:
Image published by Daniel Mayer under CC BY-SA 3.0-License
In this picture the base of each unit cell is made up by two triangles.
A hexagonal unit cell is symmetric with respect to the lateral axis.
In this example we take a look at Beryl's unit cell. Beryl is a rather common silicate containing beryllium and aluminum. There are several variations containing different impurities which change the crystal's color, the better known of which are emerald or aquamarine. Beside these forms which are used as gems, beryl is also a source of the metal beryllium.
Here we can see the hexagonal structure generated by arranging four of beryl's unit cells. Due to the symmetry discussed above, we can also reproduce a hexagonal structure by simply placing four unit cells next to each other instead of rotating two of them an placing them next to a third one.