reflectional

Reflectional describes symmetry with respect to a reflection across a line (in the plane) or a plane (in space). An object is reflectionally symmetric if there exists a line or plane such that reflecting the object across it yields an identical image. The line or plane is called the axis or plane of symmetry. In two dimensions, common examples include letters like A, which has a vertical line of symmetry, and H, which has two; a circle has infinitely many axes of symmetry.

The number of reflection axes depends on the figure’s symmetry. Regular polygons have a finite set of reflection lines; a circle has infinitely many. Irregular shapes may have none at all.

In three dimensions, reflectional symmetry is defined with respect to a mirror plane. Such symmetry is important in chemistry and crystallography, where the presence or absence of reflection planes affects molecular properties and crystal behavior.

Mathematically, reflections are isometries that preserve distances but reverse orientation. They form part of the symmetry group of an object. The full symmetry group of objects with both rotations and reflections is typically a dihedral group for polygons, or a point group in three dimensions for three-dimensional objects.

In common usage, reflectional is often paired with symmetry to denote mirror-like, or mirror-image, symmetry. The term is used across disciplines, including mathematics, design, biology, and art, to describe structures that resemble their mirror image across a line or plane, as distinct from rotational symmetry.