What Is a Rotation Tessellation?

In order to explain what a rotation tessellation is, you must know what a tessellation is. A tessellation is a geometric shape repeated to form a design or mosaic. It is also called tiling.

Simple Tessellations

Some tessellations are very simple. For example, a chain linked fence found bordering backyards is a tessellation. The criss-crosses of the metal form a diamond-like pattern.

Another example of a tessellation is a window pain divided into smaller squares or rectangles much like a grid. Inside a beehive are many honeycombs and chambers of hexagonal shape. A hexagon fitting into two hexagons like a puzzle is the base for this three-dimensional tessellation.

Angles & Examples

Right triangles placed to form complimentary and supplementary angles, or acute and obtuse angles lying on top of one another in the same plane, are another form of a simple tessellation.

Tessellations are commonly seen in home improvement stores in the flooring department.

Modification

The more advanced tessellations are formed when you take a simple shape like a square and modify its sides so that each side fits into the side of its repeated, modified shape.

Mirroring

A more advanced form is when the base geometrical shape is set to mirror itself. This creates a more intricate tile design. The mirroring effect creates symmetry. Sometimes, the symmetry is just as if you mirrored your hand. Other times, the symmetry is offset by a few degrees to create a diagonal reflection. This concept is called glide reflection.

Rotational Symmetry

There are tessellations with rotational symmetry. This means that the base geometrical shape is shaped somewhat like a pinwheel, flower, star or snowflake. If you turn or rotate the star a few degrees, it will look the same as its original position. If a star has three points, it has three-fold symmetry or three-fold rotation. If the star or flower has eight points or petals, then the figure has eight-fold symmetry or eight-fold rotation. The greater the number of each n-fold rotation, the smaller the degree of the angle created by each petal in relation to the next petal on a 360 degree plane.

Tessellations Within Tessellations

You can have rotations within rotations and tessellations within tessellations. You can tell by looking at the complete tessellation and by inspecting to see if there is more than one "pinwheel" on the plane. Each pinwheel has a center point. More than one pinwheel has more than one center point. You can have a tessellation full of rotations, and the tessellation itself will be able to rotate in complete symmetry.

Changing Degrees

A figure can be rotated one degree and repeated to create a brand new tessellation. For example, the letter A can be repeated to form a tessellation. If the letter A were slanted and repeated that way, it would be a brand new tessellation.

References

• Math Forum