12.2.2 Tessellations Key Objectives • Use transformations to draw tessellations. • Identify regular and semiregular tessellations and figures that will tessellate. Key Terms • A pattern has translation symmetry if it can be translated along a vector so that the image coincides with the preimage. • A frieze pattern is a pattern that has translation symmetry along a line. • A pattern with glide reflection symmetry coincides with its image after a glide reflection. • A tessellation , or tiling, is a repeating pattern that completely covers a plane with no gaps or overlaps. • A regular tessellation is formed by congruent regular polygons. • A semiregular tessellation is formed by two or more different regular polygons, with the same number of each polygon occurring in the same order at every vertex. Example 1 Art Application The symmetry of a frieze pattern is identified in this example. This frieze pattern has translational symmetry.
Translating the frieze pattern using a vector parallel to the long axis and as long as one of the figures produces an image that coincides with the preimage.
The symmetry of a frieze pattern is identified in this example. This frieze pattern has translational symmetry. Translating the frieze pattern using a vector parallel to the long axis and as long as a unit in the pattern produces an image that coincides with the preimage. The frieze pattern also has glide reflection symmetry. Translating the frieze pattern half the distance used for the translational symmetry and then reflecting the pattern across the horizontal midline produces an image that coincides with the preimage.
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