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Hexa-hexaflexagon - three versions
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Hexa-hexaflexagons

What you will make:

Learn how to make a really fun geometric toy—a six-sided, six-faced flexagon called a hexa-hexaflexagon! It looks like an ordinary, two-dimensional, paper hexagon with a front and a back, but hidden inside are four more sides (or faces) that become visible by flexing the paper.

There are many types of flexagons. The names of flexagons tell the type of polygon and the number of faces. In this project we make a hexa-hexaflexagon—a six-sided polygon (hexagon) with six faces (hexa).

Related crafts: For other (and easier to make) versions of the flexagon, try a tri-hexaflexagon, tetra-hexaflexagon or a tri-tetraflexagon. For more about the history of flexagons, see the Flexagons project.

Here's what you need:
  • Computer paper
  • Glue or double-sided tape
  • Scissors
  • Bone folder or empty ballpoint pen
  • Ruler
  • Optional: Rubber stamps, stamp pad, tape, poster board

This project is rated AVERAGE to do.

How to Make a Hexa-hexaflexagon

Read all of the steps before starting.
Step 1: Choose a Pattern and Print It

Choose a hexa-hexaflexagon to make. Download and print the pattern.
Choose a design that prints in color, or select one of the black and white patterns and use your creativity to add color and designs. It is easiest to fold patterns that have numbers or counting dots. Make one of these flexagons first before trying any of the others. To aid in folding and decorating the blank patterns, guides that number the faces are included on the patterns.

Patterns are Adobe PDF files. The Adobe Reader is available for free.

All of Aunt Annie's project patterns are designed to be printed on standard letter-size paper (8.5"x11" or A4). When printing from Adobe Reader, you may need to select Auto-Rotate and Center or Choose paper source by PDF page size to ensure the best fit.

Step 2: Color Pattern (optional)

Color the pattern template as you like with markers, colored pencils or crayons. You don't need to color the glue tabs marked with '*'.

Tip: On blank patterns, follow the Coloring Guide.  All the triangles that make up a hexagon face have the same number, so color and decorate them with that in mind.

Step 3: Cut

Cut around the two pattern pieces on the outline. Try to make the cuts very straight and accurate. There will be two pieces with 19 triangles each.

Step 4: Double and Glue

Make a double thickness by folding each pattern piece in half lengthwise and glue. To make a sharp, straight fold, first score on the fold line. Join the two pieces of the hexa-hexaflexagon together to form a strip of 19 triangles. Glue the strips together by gluing the single triangles together, back-to-back.

Fold in half and glue, glue two pieces together

To score: Use a ruler and the empty ballpoint pen (or bone folder) to make an indent along the fold lines.

Step 5: Fold

Score and fold back and forth on all the solid lines. Do this for each of the 19 triangles of the hexa-hexaflexagon.

Place the strip of 19 triangles with the side with 6s, 5s, and 4s face up and the glue tab, *, to the left. Fold the strip back on itself matching two 6s, then two 5s, then two 4s, on like this for the entire strip (nine folds). Now you have a strip of 10 triangles.

Hexa-hexaflexagon - fold and glue

Place the strip with the side without glue tabs facing up and the 3 end to the left. Fold back on the line between the third and fourth triangles (2 and 1)—four 2s are together now. Fold back on the line between the next 2 and 1. Now you should be able to see five 2s. Pull the 2 forward that is behind the 3. There should be six 2s on top and a 1 to the side. Fold the 1 back.

The two glue tabs marked with '*' are now face-to-face. Glue them together. Wait for the glue to dry before flexing your flexagon.

Step 6: Flex How to flex the hexa-hexaflexagon

Fold the flexagon to bring together three alternate corners of the flexagon. The top of the flexagon will pop open if there is a new face to reveal. If it doesn't pop open, flatten the flexagon and try again with the other three corners.

As you flex the flexagon in this project, see if you can find all the possible combinations of faces. The hexa-hexaflexagon has six faces with 3 different arrangements each, for a total of 18 possible faces. Only 15 of the faces versions can be seen with the straight strip pattern for a hexa-hexaflexagon. Can you find all 15 possibilities?

That's it! Your flexagon is done!
Hexa-hexaflexagons

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Before you start:
  • Make a place to work.
  • Read all of the directions.
  • Gather everything you need to do the project.
  • Think about the project. Imagine how it will look and what you will do with it.

Are you ready?
Okay, get started!!!

Bonus Pattern

Hexagonal box sized to store hexaflexagons

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Tip: Make a hexagonal box to store your hexaflexagons or give a Flexagon Boxed Set as a gift.

Numbered hexa-hexaflexagon decorated with rubber stamps

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Tip: Use six different rubber stamps to decorate your numbered hexa-hexaflexagon.

Hexa-hexaflexagon with Chinese zodiac symbols

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Tip: The hexa-hexaflexagon with animals is decorated with six of the twelve Chinese zodiac symbols. Can you find them all? Can you name them?

Hexa-hexaflexagon made with poster board triangles

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Tip: A sturdier hexa-hexaflexagon can be made by taping 19 triangles together. Cut equilateral triangles from poster board and tape them together in a strip. Leave a little space between each triangle for easier folding. Decorate the strip following the scheme on the numbered pattern.

Tetra-hexaflexagon
Bonus Patterns

Pattern for tetra-hexaflexagon

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Tip:  Use this pattern, in color or black & white, to make a tetra-hexaflexagon (4 faces).

To make: Fold the pattern lengthwise on the dashed line. Glue the two sides together for a double thickness. Cut around the pattern on the outline. Score and fold back and forth on all the solid lines. Create a a straight strip by folding all the red (4) triangle pairs over to face each other. Follow the folding instructions in the Flexagon project to assemble the flexagon. Now try to find all four faces!

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