Here’s how Alex created tetra-tetraflexagon Christmas cards to send to her friends:
1. Buy a pack of heavy paper at the office supply store. Regular construction paper tears too easily.
2. Measure and divide the paper into fourths one direction and thirds the other way. Fold each line backward and forward a few times.
3. Number the front and back of the paper in pencil, lightly, as shown. Then carefully cut a center flap along the dotted lines.
4. Fold the paper along the dark lines as shown, so the center flap sticks out from underneath and the right-hand column shows all 2’s.
5. Fold the flap the rest of the way around to the front and fold the right-hand column under again. (Shown as dark lines on the diagram.) This makes the front of the flexagon show 1’s in every square.
6. Carefully, tape the flap to its neighbor on the folded column. Don’t let the tape stick to any but these two squares.
7. Gently erase your pencil marks.
Find All the Faces
A tetra-tetraflexagon has four faces: front, back, and two hidden. It is shaped like a tetragon — better known as a rectangle.
Here’s how to flex your tetra-tetraflexagon card:
- Face 1 is easy to find. It’s on top when you make the card.
- Turn the card over to find Face 2.
- Face 3 is hidden behind Face 2. Fold your flexagon card in half (vertically) so that Face 1 disappears. Unfold Face 2 at the middle, like opening a book. Face 3 should appear like magic.
- Face 4 is hidden behind Face 3. Fold the card (vertically) to hide Face 2, then open the middle of Face 3. Face 2 vanishes, and Face 4 is finally revealed.
When Faces 2 and 3 are folded to the back, you will notice that any pictures you drew on them will look scrambled. What happened?
Add Your Designs
Alex wrote a holiday greeting on Face 1. Then she drew Christmas pictures on the other three faces of her card.
To Be Continued…
Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.