There are so many cool paper projects of folks creating origami and geometric amusements out of paper or cardboard or plastic that I was inspired to try. There is a plethora of 'flexahedron' examples out there (search for 'Andreas Markus Hoenigschmid' to have your mind blown).
However, I don't have any origami paper lying about so I looked on my desk and found some 3M Post-It Notes and Scotch tape and made do. This took five minutes, tops.
The goal is to make six tetrahedrons (A tetraherdon is a polyhedron composed of four triangular faces, three of which meet at each corner or vertex. It has six edges and four vertices. Wikipedia) The six tetrahedrons will then be joined by the adhesive tape at two of each of their edges as in the image above.
Step 1: Gather Your Materials
I used a 3" x 3" pad of Post-Its and a roll of matte finish 'Magic' tape.
Step 2: Fold the Square in Half
The great thing about the square Post-It is that I didn't have to cut or rip any pieces. Two squares will make one each of the six tetrahedrons that are needed.
Step 3: Fold Twice to Create Two of the Edges
The idea is to fold the square so that you'll make an isosceles triangle with two scalene triangle flaps.
- Lightly fold the square in half so that you get a crease that runs from the middle of one side to the middle of the opposite side, creating two rectangles on either side of the Post-It. The goal is to find and mark the center of one of the sides of the square.
- Fold a sharp crease from the top of the dividing crease to the left opposite corner of the square (above, picture on the left).
- Fold a sharp crease from the top of the dividing crease to the right opposite corner of the square (above, picture in the middle).
Make these folds in two Post-It squares so that you have two identically folded pieces of paper.
Step 4: Connect the Two Halves of a Single Tetrahedron
Lay the two halves on their "backs", side-by-side.
Tear off a two inch piece of Scotch tape and carefully connect the side-by-side edges of the two inside scalene triangles so that you have a closed seam that makes the two triangles into a single isosceles triangle. You now have three sides of your tetrahedron.
Tear off another two inch piece of Scotch tape and carefully connect the other two outside scalene triangles. You will now have an almost complete tetrahedron with two edges of the pyramid unconnected.
Step 5: Close the Remaining Two Edges of the Pyramid
Tear off two more two inch pieces of Scotch tape and carefully seal the two remaining edges of the pyramid. Now you have a complete tetrahedron.
Do this five more times. (That's ten more Post-It's and twenty more pieces of tape...)
Step 6: Connect Your Tetrahedrons
Now for the fun! Connect the side of one tetrahedron to the side of another tetrahedron with a piece of tape. It may be easiest to attach two together at a time.
Step 7: Connect All Three Pairs of Tetrahedrons
Tape each of the remaining sides to create the full flexahedron.
Step 8: Ta-da! Turn the Flexahedron in Your Hands
Congratulations! Now you can turn the flexahedron in infinite loops.
Now to build it bigger...