Design Nomenclature / Form & Geometry
Rotational symmetry
Also called radial symmetry, n-fold symmetry, radial array, dihedral group
- Form & Geometry
- Composition
- 2D & 3D
Invariance under rotation about an axis by 360°/n for some integer n, called the order of the symmetry. Order 2 is a half-turn. A shape with rotational but no mirror symmetry is chiral and reads as turning. Combined with reflections these generate the dihedral groups, which classify every rosette pattern that exists.
In practice
'Radial array' is the tool; the order is worth stating out loud. Five-fold symmetry cannot tile the plane, which is why it turns up in flowers and quasicrystals and never in brickwork.