Fold a Tetrahedron from an Envelope

One of the simplest and most surprising ways to make a tetrahedron is to cut off the end of an envelope, make a few creases, open it up, and tape the opened edges together. This project shows you how to make the folds.

Video Instructions

Materials

• You will need an envelope of just about any size. You can use old junk-mail envelopes for this.
  

Steps

1. Fold the envelope in half lengthwise. Open again.
   
2. Fold the bottom corner of the envelope to the crease keeping the top corner of the envelope flat on the table.
   
3. Create a vertical crease at the point where the corner reached. Unfold the envelope.
   
4. Cut the envelope along this crease.
   
5. Fold a crease from the top left corner to the middle of the right edge. Fold this crease back and forth.
   
6. Do the same from the bottom corner.
   
7. Open the envelope wider and wider until the two edges meet. Tape them together.
   

Notes

• You can eliminate steps 1 - 3 by calculating the length of envelope you need to cut off. Multiply the width of the envelope by 0.866. For a U.S. #10 business envelope cut off 9cm (3 9/16 in.). Coincidentally, this is close to the length of a standard U.S. business card so those of you who are reading this at work can measure your envelope with your business card and save all sorts of calculations and folds. Continue making the tetrahedron from step 4 above.
  

References

• (Gardner, Mathematical Puzzles and Diversions 1961)