symmetry
[OED]: 3. b. (a) Sci. Exact correspondence in position of the several points or parts of a figure or body with reference to a dividing line, plane, or point (or a number of lines or planes); arrangement of all the points of a figure or system in pairs (or sets) so that those of each pair (or set) are at equal distances on opposite sides of such line, plane, or point.
[See also chirality.] The regular proportions in symmetrical objects or patterns are defined by ‘symmetry operations’ - (1) A physical or mental lateral shift (translation); (2) A reflection in a virtual mirror (or point) cutting through the object; or (3) A rotation of the object by some fraction of 360 degrees about an axis. At the completion of the operation the object looks identical with the starting configuration. Translational symmetry creates tiling patterns or tessellations. Frequently the only symmetry the novice recognizes is two-fold reflective (bilateral) symmetry. Rotational (or radial) symmetry occurs in such everyday objects as a double-ended threaded bolt, the recycling symbol, and a pinwheel. Terms that can be used with children for the operations are ‘slide’, ‘twist’. And ‘flip’.
