sixfold

Sixfold is an adjective and adverb describing multiplication by six or a property characterized by six components or repetitions. In everyday language it often appears as sixfold, meaning six times as much or as many. In more technical contexts, the term denotes a specific kind of symmetry or scaling, such as sixfold rotational symmetry.

In geometry and crystallography, sixfold symmetry refers to invariance under rotation by 60 degrees. Objects with this property, such as regular hexagons or hexagonal tilings, exhibit a repeating pattern that remains unchanged under sixfold rotation. The mathematical framework for such patterns is associated with the dihedral group D6, which describes the 12 symmetries of a hexagonal structure, including rotations and reflections. Hexagonal lattices and crystals commonly display sixfold symmetry along a principal axis.

In chemistry and materials science, sixfold symmetry appears in molecules and crystal structures with hexagonal arrangements. Benzene, for example, has a sixfold rotational axis, contributing to its characteristic symmetry. Many nanoparticles and viral capsids also exhibit sixfold symmetry along certain axes.

In broader usage, sixfold serves as a multiplier: a sixfold increase means a quantity becomes six times larger. The term is often interchangeable with sextuple in mathematical or statistical contexts, though sixfold is more common when describing symmetry or multiplicative scaling rather than numerical labels.