My previous post about platonic solids included a link to a site with printable templates for making your own solids. However, there are other easy ways to make paper platonic solids. Here are directions for making a tetrahedron using an envelope.
Step 1. Seal the envelope and then fold length-wise to mark the center line. I have marked the center line with a dotted line. (Marking the line is optional, I was just trying to make it more visible.)
Step 3. Fold opposite side over until it touches the corner that was folded down. This is to find the line perpendicular to the center line that touches point where the corner touches. I’ve marked this with another dotted line.
Step 4. Cut along the vertical line and unfold the corner.
Step 5. Fold the two corners on the open end of the envelope from the center line to the opposite top corner. These folds are marked with the highlighted lines. Fold forward and back to make a good crease.
Step 6. Open up envelope at the cut end and pop out the 4 folds you made (the highlighted folds plus the corresponding ones on the opposite side). Tape the open end together and you have your completed tetrahedron.