## Tessellation

A TESSELLATION is the periodic repetition of the same figure covering a plane without overlapping or holes. The figures used to cover the surface, tessellations, are often polygons, regular or not, but they can also have curved sides or be without any vertices. Below are some “regular” tessellations in that they each use only one geometric shape:

In 1974 Roger Penrose and Robert Ammann discovered various irregular tessellations, that is, making use of multiple geometric figures in a single tessellation, including the kite and the dart:

## How to play

It is the periodic repetition of the same figure covering the floor without overlapping or holes. Your floor could be an example of this. It is easy to tessellate a floor with rectangular, hexagonal tiles or triangular by replicating the same figure in different positions. But what if you have edges, can you tessellate? Choose shapes and combine them to cover the whole plane, you will find that there are different ways to tessellate, but traceable to two types of tessellation:

A tessellation is PERIODIC if it involves regular repetition of the tessellation, which in such cases is always a polygon. A polygon, regular or irregular, tessellates if its interior angle is submultiple of an angle of 360°. Which polygons tessellate? Does a regular pentagon tessellate the plane?

A tessellation is NON PERIODIC if it is impossible to detect a pattern that repeats itself identically indefinitely, even if at first glance it appears to be there. Among the most famous tessellations that generate nonperiodic tessellations are those of the mathematician Penrose, the arrow and the kite, made from a rhombus with angles of 72° and 108°.

## How to build

###### EXHIBIT MATERIAL:
• no. 2 base pallet 120×180 cm
• Moulds for tessellation (in MDF)
according to drawing, as desired in
colors, but in the shapes indicated (10 cm side): kites, darts, equilateral triangles, regular pentagons, right triangles, scalene triangles.
• Red MDF frame
• no. 2 honeycomb cardboard
shelves (100x140cm)x2
• no. 4 cardboard panels (40x15cm)
with descriptions of different types
of dowel