3. Types of symmetry

Abstract

‘Types of symmetry’ explains different types of symmetry. Rigid motions are the easiest type of symmetry to understand, and can be explained diagrammatically. The four main types of this symmetry are translation, rotation, reflection, and glide reflection. Finite groups of rigid motions fall into several categories: cyclic groups, dihedral groups, orthogonal groups, and special orthogonal groups. Unbounded shapes have a richer range of symmetries, as seen in friezes and wallpaper patterns. Regular three-dimensional solids are symmetrical in all dimensions, and have several symmetry groups: tetrahedral, octahedral, and icosahedral. Several symmetry groups in three-diomensional space contain infinitely many transformations. Crystallographic groups have a regular shape traced to their atomic arrangement.