Trigonalis

Trigonalis is a term used in crystallography to describe a crystal system characterized by threefold rotational symmetry. In this system, the unit cell is defined by three vectors that are not necessarily equal in length, but they are symmetrically arranged around a central axis. The angles between these vectors are 120 degrees, forming an equilateral triangle when projected onto a plane perpendicular to the central axis. This symmetry is often observed in minerals and other crystalline materials, such as quartz and graphite.

The trigonal crystal system can be further classified into two subclasses: trigonal scalenohedral and trigonal trapezohedral. The scalenohedral subclass is characterized by a unit cell with three unequal vectors, while the trapezohedral subclass has two equal vectors and one unequal vector. Despite these differences, both subclasses share the fundamental threefold rotational symmetry.

Trigonal crystals exhibit unique optical and physical properties due to their symmetry. For example, they often exhibit piezoelectricity, meaning they can generate an electric charge in response to mechanical stress. Additionally, trigonal crystals can exhibit pyroelectricity, where they generate an electric charge in response to temperature changes.

In summary, trigonalis refers to a crystal system with threefold rotational symmetry, characterized by three vectors forming 120-degree angles. This system is further divided into scalenohedral and trapezohedral subclasses, and trigonal crystals exhibit unique optical and physical properties.