Other kinds include translational symmetry, in which the entire pattern can be shifted rotational symmetry, in which the pattern can be rotated about a central point and glide symmetry, in which the pattern can first be reflected and then shifted (translated) along the axis of reflection. Mirror symmetry is not the only kind of symmetry present in tessellations. Likewise, every diamond-shaped cell has an identical diamond-shaped mirror image. If an imaginary mirror is placed along the axis shown, then every seed-shaped cell, such as the one shown in color, has an identical mirror image on the other side of the axis. Such is the case with the leftmost tessellation in the figure. That is, a mirror can be placed exactly in the middle of the object and the reflection of the mirrored half is the same as the half not mirrored. In everyday language, the word "symmetric" normally refers to an object with dihedral or mirror symmetry. For mathematicians, tessellations provide one of the simplest examples of symmetry. Tessellations allow an artist to translate a small motif into a pattern that covers an arbitrarily large area. The cells are usually assumed to come in a limited number of shapes in many tessellations, all the cells are identical. Tessellations of three-dimensional space play an important role in chemistry, where they govern the shapes of crystals.Ī tessellation of a plane (or of space) is any subdivision of the plane (or space) into regions or "cells" that border each other exactly, with no gaps in between. They are also widely used in the design of fabric or wallpaper. Tessellations of a plane can be found in the regular patterns of tiles in a bathroom floor, or flagstones in a patio. For centuries, mathematicians and artists alike have been fascinated by tessellations, also called tilings.
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