Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.Ī rhombitrihexagonal tiling: tiled floor in the Archeological Museum of Seville, Spain, using square, triangle and hexagon prototiles Tessellations are sometimes employed for decorative effect in quilting. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.Ī real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. A tiling that lacks a repeating pattern is called 'non-periodic'. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.Ī periodic tiling has a repeating pattern. Repeat all the tracing steps until the whole paper is used up.Example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles.Ī tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. Trace it from the left to the right side of the paper again, positioning it in the gaps between the successive images previously drawn.Ħ. Repeat this step until you run out of horizontal spaces.ĥ.

Slide the template horizontally to the next available empty space but still touching the previous shape. Put the template edge flushed against the edge of the lower paper when tracing.Ĥ. Trace the cutout fish template on a larger piece of paper. Trace it on a piece of construction paper and cut it out when you have finished.ģ. Leave some white spaces around the edge of the drawing paper.Ģ. Make sure that the design produces can be interlocked by making the fish template symmetrical along the diagonal axes. Draw or use the cutout image of a fish to create a template on a piece of drawing paper. You can easily make a fish tessellation by repeatedly performing the operations of translation, rotation and reflection on a basic fish shape.ġ. A tessellation is the pattern produced from the repeated arrangements of the same shape over a plane without any gaps. While many mathematical objects can appear beautiful when presented visually, tessellation is one of the easiest to appreciate. You can make a tessellation from a cutout image of a fish.

Fish tessellation