Answer
A tessellation if formed by repeating the shape or pattern in order to cover a surface so that no gaps or overlaps exist. The tessellations are formed in regular tiling for decoration purpose.
Work Step by Step
A tessellation is a type of art that is used to define a relationship between geometry and the visual arts. Tessellations are created by repeated use of same figures that will leave no gap and no overlaps and thus cover whole plane.
A tessellation or tiling is done in many ways for example, regular tiling in which all the tiles have same regular polygon shape, another is semi regular tiling in which tiling of regular polygons with different shapes can be used and the non-periodic or a periodic tiling in which the tile shapes that does not form any repeating pattern is used for tessellation.
The symmetries used in tessellations are classified into three parts:
Translational symmetry: translation symmetry in tessellation is found if the geometric figure is translated to some vector and the figure remain unchanged.
Rotational symmetry: rotational symmetry exists in a tessellation if a geometric figure rotated by some angle and still remains unchanged.
Glide reflection symmetry: glide reflection symmetry is a symmetry that applies two methods. Firstly, a figure is translated by some angle and then reflected and still remain unchanged.
Tessellation exists in wide number of cultures because of its decorative characteristics like on fabrics, wall coverings, baskets, rugs and pottery.
Tessellation pattern is used in the design patterns of a quilt for example, pin wheels pattern, arrow fish pattern etc.
Decorative tiling is used as tessellations to cover the wall with design patterns.
The Alhambra is a great palace of the 14th century in Spain. The art inside the palace is a combination of geometric designs. In this palace, symmetric patterns are used for example, reflection symmetry above the window. Wall coverings are done with tiling and above that border pattern are used. Rotational symmetry showed in Rosettes. In wallpaper coverings, rotational symmetry is also applied.
M.C. Escher is a graphic artist who visited the Alhambra palace in 1922. M.C.Escher developed his interest in tessellations after analyzing the designs of the Alhambra that are based on repeating geometric patterns. He then extended his basic sketches on geometric patterns to more complex interlocking design patterns. He also contributed by developing the three-dimensional objects by including spheres, cylinders, and cubes etc in his arts.
The practical application of tessellation includes the use of geometric designs in quilts and rugs that are used in everyday life.
A unique tessellation is created by following steps:
a. Cut the paper in rectangle shape.
b. Cut the paper from middle in zig zag way.
c. Interchange the position of two pieces of paper and then join these two pieces.
d. Repeat the steps to make a design in the form of tessellation.
