STEM & Quilting with Kids: Tessellations

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What is a Tessellation? 

We are surrounded by shapes that interact with each other in amazing ways that display beauty and order. One way that finds itself repeated in every aspect of our lives is called Tessellation.

 To get an idea of what a tessellation is, let us envision one of the most common Tessellations – a Checkerboard. A Checkerboard is composed of Black and Red squares in a Grid-like pattern. There are no gaps between the squares and no overlapping of squares. This illustrates simply what Tessellations are- Polygons or shapes that fit together perfectly with no gaps and no overlap.

Tessellations in Nature, Art, and Industry

Nature-Animals, Insects, and Plants

The natural world gives us many examples of Tessellations. Let‘s start with our bodies.  Skin Cells, Bone Cells, and Muscle Cells all come together and tessellate to form one system that protects the body, keeps it upright, and strong. Imagine a body with no skin, bones, or muscles. That would be a scary sight!!!

Skin cells

Have you ever noticed a turtle’s shell? The plates of the shell come together to form a strong compartment that the turtle can pull itself into to avoid being eaten by animals of prey. The shapes on a turtle’s back Tessellate, they leave no gaps and they do not overlap. 

Tessellation on a tutle's shell

Many insects also display tessellations. The eyes of a fly, when seen under a microscope appear to be made of tiny hexagons that come together to make a compound eye. Each of the fly’s eyes is composed of 3,000 to 6,000 simple eyes. The hexagonal shape allows for hundreds of simple eyes to be on the surface of the eye because hexagons can pack together with no gaps or overlap. 

Closeup of a fly's eye

Bees also take advantage of the compact structures that are created from Hexagons. Worker Bees use wax to build walls of hexagonal cells in their hive to store honey and to make homes for baby bees. The hexagon is the most compact shape known in nature so bees can store lots of honey inside the hive. 

Bee's in their hive

A Dragonfly’s wings display tessellations that combine regular and irregular polygons. The wings look like iridescent lace that shimmer in the sunlight as they fly above the surface of the stream.

Dragonfly wings

Art: Crafts, Fine Art, and M.C. Escher

Artists have observed tessellations in nature and have been inspired to incorporate them into their work. Tessellations appear in the artwork of craftspeople and artists - by intent and unintentionally. M.C. Escher, a visual artist that loved to draw and paint, decided to focus on tessellating shapes and forms in his artwork. He has created some of the world’s best-known tessellating images in the world of fine art. He was inspired by animals and architecture.

Reptile Tessellation by M.C. Escher

On the other hand, when basket weaver, Eva Wolfe, makes baskets with raw materials like reeds and cane, she manipulates the raw materials to develop patterns that often tessellate even though she is not trying to. Notice how this basket pattern is composed of tessellating rectangles and squares

A basket by Eva Wolfe

Industry: Technology, Engineering, Fashion, and Gaming (Minecraft)

Engineers and architects have discovered that building structures with aspects that tessellate are not only beautiful but are able to withstand the weight of construction without collapsing. Tessellation is used in the manufacturing industry to reduce the wastage of material such as sheet metal when cutting out shapes for objects like car doors or drinks cans. Tessellations have also found their way into the world of Fashion. Designers that are creating contemporary garments find fresh ideas in the observation of Tessellations.

Tank tops featuring a tessellating design

Quilts that Tessellate: Regular and Irregular Polygons

Polygons are shapes that are made with straight lines that do not cross. They have at least 3 straight lines and angles, however, they can also have 5 or more. Regular Polygons are the ones that we might see every day, like triangles, squares, pentagons, and hexagons. In a regular polygon, all the sides are the same. Irregular polygons have sides that are not the same.  An example of an irregular polygon is a rectangle. 

Two Quilts that Tessellate by O.V. Brantley

Quilters have been fascinated with the idea of creating quilts using polygons that tessellate for decades. Even though polygons can be simple shapes, their combinations in quilts can make some interesting and engaging quilt patterns. It is no surprise that there are tessellating quilts in the collection of the Smithsonian Institute’s Museum of American History.

Two quilts with tessellating triangles by Amanda Hines Bernay

Contemporary quilters also create quilts with tessellating shapes. However, Modern quilters have computers, large printers, and quilt programs to help them develop tessellations that they can use in their artwork. They also have many different kinds of tools for measuring and cutting. The modern quilter uses technology to simplify complex designs to make quilting tessellations easier. 

 “Flying South” by Linda Asbury

These are just a few examples of how quilters use Squares and Triangles to create quilts that tesselate. They use precision measuring tools to create blocks and shapes that tessellate. They are inspired by traditional patterns and are challenged to come up with original patterns to make connections with the world of Math and Technology.

Tessellating Triangles by Marquetta Johnson

The Hexagon

A regular and irregular hexagon

A Hexagon is a shape with six sides. They are called regular or irregular hexagons.  In a Regular Hexagon, all six sides are equal. An irregular hexagon is a six-sided shape whose sides are not equal. Quilters have been challenged by this shape because of its multiple sides and angles. All hexagons do not tessellate. Only regular hexagons tessellate.

Quilts that incorporate Hexagons

There are many ways to make a quilt with hexagons. You can baste fabric onto paper hexagons and sew them together at the edge. You can sew 6 equilateral triangles together and make hexagons that can be sewn together.  I would like to show you a way to make regular hexagons from circles of fabric. You can make them and sew them together to make craft items and quilts. If you make them precisely or even approximately, they will Tessellate!

An English Paper Pieced quilt made out of hexagons.

How to Make a Hexagon

You Will Need:

  • Sewing Thread

  • 7” Fabric Circle

  • Needle

  • Scissors

  • One Button

  • #2 Pencil

1.      Trace the circle onto the fabric and cut it out.

2.     Fold the circle in half and finger press. Then, fold it into fourths and finger press. This allows you to find the center of the circle.

3.     Thread Your Needle.

4.     Fold the bottom edge of the circle to the center and finger press.

5.     Fold left end of fold to the center and finger press. Repeat this three more times.

6.     Fold the 5th corner to the center and finger press. Finally, fold the top point to the center and finger press.

7.     Sew up through the middle of the hexagon then anchor each fold with a stitch in the middle of the hexagon.

8.     While the needle is still attached, sew a button in the middle of the front with 3-5 stitches through the holes of the button.

9.     Sew through the button to the back of the hexagon. 

10.     Sew three backstitches into the middle of the hexagon and clip the thread to complete the process.

Create several to make them tessellate!