fivefold

Fivefold is an adjective describing something that consists of five parts or exhibits fivefold symmetry. In geometry it denotes rotational symmetry of order five, meaning an object can be rotated by 72 degrees and still look the same. Regular pentagons and pentagrams are common examples, and in three-dimensional objects the symmetry can occur about an axis, as in certain star-shaped forms. In the plane, strict fivefold symmetry cannot tile the plane periodically, a fact that helped spur the study of aperiodic tilings such as the Penrose tiling, which shows local fivefold motifs without translational repetition.

In crystallography and materials science, a fivefold axis is a rotational symmetry axis of order five. Such axes occur in quasi-crystals and in many viral capsids, but they cannot be extended to form a repeating three-dimensional lattice. The discovery of materials with fivefold or higher-order symmetry broadened the understanding of crystalline order and led to the concept of quasicrystals.

In biology and botany, fivefold symmetry appears in various life forms and structures. Pentaradial symmetry is typical of many echinoderms, including starfish and sea urchins, with bodies arranged around five radiating arms. Many flowers are pentamerous, having five petals or other floral parts arranged in a fivefold pattern.

In general usage, fivefold describes something occurring in groups of five or increasing by a factor of five. The term is used across disciplines to describe patterns, structures, or growth that relate to the number five.