What is "axiality"

n. 1 The state of being axial 2 The degree which something is axial

Axiality may refer to:

• Axiality (geometry), a measure of the axial symmetry of a two-dimensional shape
• Axiality and rhombicity in mathematics, measures of the directional symmetry of a three-dimensional tensor
• Axiality, a principle behind the art and poetry of George Quasha
• Axiality in architecture, organization around a strong central axis, especially in the architecture of cathedrals and great churches and Beaux-Arts architecture

In the geometry of the Euclidean plane, axiality is a measure of how much axial symmetry a shape has. It is defined as the ratio of areas of the largest axially symmetric subset of the shape to the whole shape. Equivalently it is the largest fraction of the area of the shape that can be covered by a mirror reflection of the shape (with any orientation).

A shape that is itself axially symmetric, such as an isosceles triangle, will have an axiality of exactly one, whereas an asymmetric shape, such as a scalene triangle, will have axiality less than one.