Tessellations and Symmetry There are several kinds of symmetry used in geometry, and especially in tesselations. One of the most common kinds of symmetry is reflectional symmetry. The letter A has reflectional symmetry. A plane figure has reflectional symmetry if and only if its reflection image through a line coincides with the original figure. The line is called and axis of symmetry. Some examples of figures with reflectional symmetry would be letters of the alphabet( A, H, I, T, B, E, W, Y, U, O, S, D, K, Z, X, C, V, N, M) and shapes such as regular squares, polygons, hexagons, triangles, and others. Examples of reflectional symmetry:
Horizontal Symmetry

Vertical Symmetry

Vertical and Horizontal Symmetry



Rotational Symmetry

A figure has rotaional symmetry if and only if it has at least one rotation image that coincides with the original image. We say that a figure has a rotation image of "n" degrees if a rotation by "n" degrees about a fixed point results in an image that coincides with the original. Rotation images that are only symmetrical at 0 degrees or mutiples of 360 degrees do not have rotational symmetry. This regular hexagon could be rotated 60,120,180, 240, or 300 degrees and be the same as the original:



Tessellations

There are several types of tesselations. One is the translation tessellation. This type of tessellation slides either to the left or the right to copy the original image exactly.

Translation Tessellations For Example:


Rotational Tessellation

Another type of tessellation is the rotational tessellation. This kind of tessellation will rotate or turn a certain number of degrees to copy the previous shape. For example this shape is rotated 180 degrees: