diëdrische

Diëdrische refers to a type of symmetry in geometry and crystallography, specifically related to the arrangement of atoms or molecules in a crystal lattice. The term is derived from the Greek words "di" meaning two, and "hedron" meaning base or foundation, reflecting the two-dimensional nature of the symmetry planes in three-dimensional space.

In a diëdrische crystal, the symmetry is characterized by a twofold rotation axis perpendicular to a mirror plane. This results in a mirror symmetry across the plane and a rotational symmetry of 180 degrees about the axis. The combination of these symmetries leads to a unique arrangement of atoms, which can be visualized as a series of parallel planes with alternating layers of atoms or molecules.

Diëdrische symmetry is one of the seven crystal systems recognized in crystallography. It is less common than other crystal systems but is found in certain minerals and materials, such as some forms of calcite and gypsum. The diëdrische crystal system is further classified into two types: diëdrische pinacoidal and diëdrische domical, based on the orientation of the symmetry elements relative to the crystal faces.

Understanding diëdrische symmetry is crucial in fields such as mineralogy, materials science, and chemistry, as it provides insights into the structural properties and behavior of crystalline materials. The study of diëdrische symmetry also contributes to the broader understanding of symmetry in mathematics and physics.