SYMMETRY
Etymology: Latin symmetria, from Greek, from symmetros symmetrical,
from  syn- + metron measure -- more at MEASURE
1 : balanced proportions; also : beauty of form arising from balanced proportions
2 : the property of being symmetrical; especially : correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis
3 : the property of remaining invariant under certain changes (as of orientation in space, of the sign of the electric charge, of parity, or of the direction of time flow) -- used of physical phenomena and of equations describing them
TESSELLATION
1 a : MOSAIC b : a covering of an infinite geometric plane without gaps or overlaps by congruent plane figures of one type or a few types
  (Merriam-Webster Dictionary Online)
Symmetry is detected when a shape has been moved and its shape retained. There are four ways to describe the symmetry of a pair/number of the same shape. These are Rotation, Reflection, Glide Reflection, and Translation.
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