Tetrahedron
I made a tetrahedron. I chose to make this polyhedron because it has the fewest number of faces and I wanted to make something simple.
Preparation
Determine size of face. I chose a 4" equilateral triangle, since i wanted my polyhedron to be small and regular. This created an end result that fit in my hand.
Then, draw paper template. Cut it out of paper.
Cut Fabric
Lay paper template on fabric of choice (I used felt, but a sturdy cotton should do just as well. The shape may not hold as well if using a fabric of a lighter weight.) and trace AROUND paper template, leaving seam allowance (I used 1/4").
Then cut on traced lines.
Sew
Sew three triangles together with 3 vertices at a point. Then sew the last one to the base of the tetrahedron, remembering to leave an inch or two unsewn so that you have room to turn it inside out.
Note: I used a serger because I made this to practice using the serger. It is unnecessary and silly to use the serger on felt, a fabric that will not fray. Do not use the serger for this project, unless you want the seams facing outward (in which case, skip turning it inside out), which I guess looks cool.
Stuff
Carefully turn it inside out, and stuff with stuffing. I used some polyfill variant. Put enough so that the tetrahedron can sit on any side and still look like a tetrahedron, but not so much that it becomes bulbous and loses its shape.
Then handstitch the opening closed.
Done
Now you can squish it at your leisure. It should also have a slight bounce, depending on what you used to stuff it, so you can throw it.