There is a whole variety of nets for the most usual polyhedra. But is it really
possible to fold a regular tetrahedron of this sheet of cardboard?

Unfold the tetrahedron into a traditional net.

Draw a segment connecting a vertex of the the big triangle and the center of the
opposite side (which is a vertex of the initial tetrahedron) and cut the cardboard
along this segment. Turn a part of the net around the point that represents the
vertex of the tetrahedron. Doing that we'll glue two edges, but in the initial
tetrahedron they were glued in the same way, so we didn't break the gluing
conditions. Now we have an additional part of the border that we'll mark as red.

Let's repeat this operation.

Once again, draw a segment from the corner to the center of the opposite side and Turn and glue. We get the same sheet of cardboard we saw in the
beginning of the movie!

Let's make sure that the resulting sheet of cardboard is a net of the initial
polyhedron. In the left upper part of the triangle there are pieces that remain
unmoved from the beginning. One of the small triangles corresponds to a part of
the initial tetrahedron's base. Let's match them.

And now we'll wind the figure round the tetrahedron. As we see, everything
matches!

All the segments of the red «false» edges connect the triangles that lie in the
same plane, that means that after gluing they will disappear. Those segments that
were painted in yellow lie on the edges of the tetrahedron and are the real edges.

The question whether one can fold a convex polyhedron out of the given sheet of cardboard
is answered by a theorem of a great Russian mathematician Alexander Danilivich
Alexandrov. It is possible to figure out where the future vertices are. But we still
don't know how will the real edges go from vertex to vertex. But it is another story
for another movie…