What are Tessellations

Shodor > Interactivate > Discussions > What are Tessellations

Mentor: Shapes with more than two sides are called polygons. The sides can be of any length, and where two sides meet, an angle is formed. Polygons with sides of equal length and equal angles are called regular polygons.

Triangles = three sides

Squares = four sides

Pentagons = five sides

And so on. Most of the names are derived using Latin or Greek prefixes for the number of sides.

Student: OK, so that means if we continue with the names:

6 = Hexagon 9 = Nonagon
7 = Heptagon 10 = Decagon
8 = Octagon 11 = Undecagon

Mentor: Right. So using your table above, what would this object be called?

Student: A hexagon, a six-sided shape.

Mentor: Good. Now, try picturing many hexagons placed all around each other in all directions on a flat surface. What would it be like?

Student: A honeycomb made by bees!

Mentor: Yes, that's right. It would also be what is called a tessellation: a repeating polygonal shape with no gaps or overlapping sections spread across a plane.

Student: Oh. What is "polygonal"?

Mentor: Any shape that qualifies as a polygon: any closed plane figure with more than two sides. By "closed plane," that means the shape is one that can lie flat on a plane surface, and where there are no openings in the shape--the sides join together to form one "piece".

Student: OK. So a tessellation can be any polygon that forms a repeating pattern across a flat surface and does not overlap or leave gaps anywhere. I don't think all regular polygons will tessellate.

Mentor: Good hypothesis. You will get a chance to test it! As we learn more about tessellations, you will see how they are used many places in the world. There are also many observations you can make by examining different types of tessellations, which we will see in the Tessellation Activity .

a resource from CSERD, a pathway portal of NSDL NSDL CSERD