Pop Up Card V fold
This post has been revised and updated. See the new post here.
The most basic, 45 degree angle, V fold.
Fold your paper in half. Draw a square with one side on the fold. Cut along the solid black line.
Fold and unfold along the dotted line to set the foldline.
Push out the pop up from the back.
This way, it looks like a vase or a spout or a bottom lip. Turned upside down it resembles a tree, or a skirt, a hat, a beak. Sideways it could be a megaphone or a telescope.
The V fold is actually a box with one short side and one long side. Try it! Draw a box pop up. Now shorten one side. Now try it with an even shorter side. Now so short there isn't a side at all. Oh look, it's a V fold!
Some examples
Vary the shape of the cut and the angle of the fold to make a heart or a nose.