You rotate, translate, or reflect them, do a combination of transformations and you would get a repeating pattern.Īs explained at the beginning, in order to use one regular polygon to make a tessellation, there are only three possible polygons to use: triangles, hexagons and squares. A tessellation can be created by starting with one or several figures. Staying true to these boundaries, you are able to create a pattern that can go on into infinity. Geometrical objects can’t have holes in the pattern and they must never overlap. Meaning the effect of a reflection combined with any translation is a glide reflection, with this special case just a reflection.
A so called glide reflection cannot be reduced like that. In a line and a translation in a perpendicular direction the combination of this reflection is a reflection in a parallel line. Sometimes objects or shapes have more than one line of symmetry. Reflectional symmetry occurs when a line is used to split an object or shape in halves so that each half reflects the other half. You can only rotate the figure up to 360 degrees. Rotation - A Tessellation in which the shape repeats by rotating or turning. Here we consider the rigid motions of translations, rotations, reflections, or glide reflections. A regular tessellation means that the pattern is made up of congruent regular polygons, same size and shape, including some type of movement that is, some type of transformation or symmetry. The number of times you can rotate the geometric figure so it looks exactly the same as the original figure is called rotation symmetry. Tessellation is any recurring pattern of symmetrical and interlocking shapes. Tessellation Properties and Transformations. This symmetry results from moving a figure a certain distance in a certain direction which is also called translating (moving) by a vector (length and direction) It has a translation symmetry if an image can be divided into a sequence of identical figures by straight lines. As explained in symmetry research: Translation Symmetry
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