The most common group of transforms applied to objects are termed the Euclidean group of "isometries", which are … See more

Reflectional symmetry, linear symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.
In one dimension, there is a point of symmetry a… See more

Reflection symmetry can be generalized to other isometries of m-dimensional space which are involutions, such as
(x1, ..., xm) ↦ (−x1, ..., −xk, xk+1, ..., xm)
in a certain system of Cartesian coordinates. This reflec… See more

Rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, which are isometries that preserve orientation. Therefore, a symmetry g… See more

Translational symmetry leaves an object invariant under a discrete or continuous group of translations . The illustration on the right shows four congruent footprints generated by translations along the arrow. If the line o… See more

In 2D, a glide reflection symmetry (also called a glide plane symmetry in 3D, and a transflection in general) means that a reflection in a line or plane combined with a translation along the line or in the plane, results in th… See more