Determining the metric and the symmetry group of finite point sets in space with an application to cyclohexane

To examine molecular geometry, we ask two questions: (1) What are the metric properties of a finite set of points in space, i.e., what are the relations of the distances between the points? (2) What is the symmetry or point group of the point set? These questions are answered by applying algebraic and algorithmic tools. Results from distance geometry are used to describe the metric. In combination with a so-called minimizing algorithm, distance geometry is also used to develop a procedure that allows generation of the symmetry group without referring to geometric intuition. The general methods presented here are applied to cyclohexane, facilitating a complete geometrical analysis of all its conformers.