You may be wondering to yourself, "What is a hexahexaflexagon?" A hexahexaflexaon is a fun, hexagonal paper toy that has many faces that you can flex to reveal. This instructable will walk you through how to make your own!

Supplies

All you need is:

a roll of adding machine tape, 2 1/4" or 57.15 mm wide
a glue stick
a mechanical pencil
a metric ruler
Optional - coloring medium of your choice

Step 1: Marking the Lines

To start, along one edge of the paper mark every 66 mm with your pencil until you have 10 marks. In the pictures I have put the marks in bold. From the corner, measure and mark 66 mm with your ruler diagonally to the other side of the paper. Cut on this line so you have an angle on the end. Then mark every 66 mm on that side until you have 10 marks. Using your ruler, you should now be able to connect these lines bridging across sides to form 19 perfect equilateral triangles. Cut at the last diagonal line.

Step 2: Numbering the Triangles

Using your pencil, lightly number the side still facing up by numbering 1-2-3 six times and leaving the last triangle blank as shown. Then flip the paper over and leave the first one blank and number in the pattern 4-4-5-5-6-6 three times as shown. You will have hold the paper up to the light to look through it to see where to number the back, although you don't have to be exact as you will erase them later.

Step 3: Folding

With the 1-2-3 side facing up, fold on the lines so that on the 4-5-6 side, the same numbers next to each other match up. You should end up with the flattened spiral in the first picture and have a blank triangle on each end. To fold into a hexagon, pay close attention to the second picture. Starting from the right end, fold the two 1s right next two each other, three from the right, down as shown. Then, going down, fold the other two 1s up and lift the two over the three so it is a hexagon with a 1 sticking of to the side.

Step 4: Gluing

Flip the hexagon over. There should be two blanks right next to each other. Put glue on one and press them together exactly on top of each other.

Step 5: Flexing

To flex it, push the sides in so you get a sort of three pointed star as shown in the third picture. Then pull the middle apart to form a completely new hexagon. If you did it right, there should be a different number on each of the triangles. If a side won't open, shift to a different corner and do it there instead.

Step 6: (Optional) Decorating

To make this look a little cooler, you can erase the numbers and draw a design on a side. Then flex it and do that side too until you have done all six sides. I did a planets theme but you can do anything you want. ***WARNING*** Be careful to make a design that will work in any orientation of the triangles because when it comes back up, it will not be in the same orientation.