trisymmetry

Trisymmetry is a term used in geometry and crystallography to describe objects or structures that possess three identical rotational symmetries. This means that the object can be rotated by 120 degrees, 240 degrees, and 360 degrees (which brings it back to its original orientation) and appear indistinguishable from its original state. Think of an equilateral triangle; if you rotate it by 120 degrees around its center, it looks exactly the same. The same applies after a 240-degree rotation.

In the context of crystals, trisymmetry is often referred to as threefold rotational symmetry. This type of symmetry is characteristic of certain crystal systems, such as the trigonal and hexagonal crystal systems. For instance, a hexagonal pyramid exhibits trisymmetry. While objects can have multiple types of symmetry, trisymmetry specifically refers to the presence of three rotational axes of order three. It is a fundamental concept in understanding the overall symmetry of three-dimensional objects and their classification. This property implies that the object can be divided into three identical parts that are related by rotation.