Many math puzzles and game rely on the mathematical study of shapes and spaces called topology.

Topology involves looking at the shapes that result through stretching, transforming, deforming, folding and twisting. Tearing, on the other hand, is not allowed!

Some of the shapes involved include polygons and circles which can be manipulated in space to create different shapes. These are a great way for students to explore 2-dimensional shapes in 3-dimensional space.

Trihexaflexagons are ingenious paper contraptions that change their faces as they are folded and flipped. Watch this series for a humorous history of hexaflexagons.

In this activity, students make a paper foldable that changes its faces as it is manipulated.

### Objectives

• Develop mathematical reasoning.

• Make connections and solve problems.

• Explain the importance of observation when doing math.

### Key Questions

• How many different faces does the trihexaflexagon have? How can you tell?

### What To Do

1. Cut out the two large strips of paper along the solid line.
2. Glue the white sides together, ensuring to match up the shapes.
3. Crease the paper both ways along each dashed line.This will allow your trihexaflexagon to flex easily.

Lay your strip out as shown.

Fold the left hand-side up to begin forming the maple leaf image.

Fold the right side under to complete the maple leaf image.

Tuck the top flap over. Tape the blank triangle to the triangle with words on it.

### Extensions

• Design your own trihexaflexagon. HINT: Determining which pieces of the puzzle go where in the shape may be easiest if you start by drawing a whole picture and cut the elements to glue in the spaces from the template.
• Can you make a trihexaflexagon with two different images?

Survivors

Artist: Jeff Kulak

Jeff is a senior graphic designer at Science World. His illustration work has been published in the Walrus, The National Post, Reader’s Digest and Chickadee Magazine. He loves to make music, ride bikes, and spend time in the forest.

Egg BB

Artist: Jeff Kulak

Jeff is a senior graphic designer at Science World. His illustration work has been published in the Walrus, The National Post, Reader’s Digest and Chickadee Magazine. He loves to make music, ride bikes, and spend time in the forest.

Comet Crisp

Artist: Jeff Kulak

Jeff is a senior graphic designer at Science World. His illustration work has been published in the Walrus, The National Post, Reader’s Digest and Chickadee Magazine. He loves to make music, ride bikes, and spend time in the forest.

T-Rex and Baby

Artist: Michelle Yong

Michelle is a designer with a focus on creating joyful digital experiences! She enjoys exploring the potential forms that an idea can express itself in and helping then take shape.

Buddy the T-Rex

Artist: Michelle Yong

Michelle is a designer with a focus on creating joyful digital experiences! She enjoys exploring the potential forms that an idea can express itself in and helping then take shape.

Geodessy

Artist: Michelle Yong

Michelle is a designer with a focus on creating joyful digital experiences! She enjoys exploring the potential forms that an idea can express itself in and helping then take shape.

Science Buddies

Artist: Ty Dale

From Canada, Ty was born in Vancouver, British Columbia in 1993. From his chaotic workspace he draws in several different illustrative styles with thick outlines, bold colours and quirky-child like drawings. Ty distils the world around him into its basic geometry, prompting us to look at the mundane in a different way.

Western Dinosaur

Artist: Ty Dale

From Canada, Ty was born in Vancouver, British Columbia in 1993. From his chaotic workspace he draws in several different illustrative styles with thick outlines, bold colours and quirky-child like drawings. Ty distils the world around him into its basic geometry, prompting us to look at the mundane in a different way.