What is a reflexive property in geometry?

A reflexive property is a property that reverses the orientations of all points in a figure. In other words, a reflexive property returns the original figure to its original position. The easiest way to describe this concept mathematically is through rotation about the origin (0, 0).

A reflexive symmetry is one which commutes with rotations around 0 combined with translations by x and y. So an example would be if translation was not possible.

The most famous example is when points are reflected across the line mn so that each point becomes a mirror image of itself (in each quadrant) across mn. This kind of filling creates what’s called ambient polygonal tiling where all lines on intersecting tiles are congruent. In this context, the right angle is a reflexive property as well since it has rotational symmetry of order 4.