Diamond edge crease pattern:
Alternate flap crease pattern for square faced construction:
With a slight modification, of the fourth step, the same basic design can be used to create a cube with twelve units. This is basically the same as Valerie Vann's 12 Biz Card Open Face Cube that I later found diagrams for at archive.org.
Using this unit to create a cube also requires a little adjustment of the tabs to get them to fit nicely, which I accomplished with a simple reverse fold.
This unit can be used to make a tetrahedron (6 units), an octahedron (12 units), and an icosahedron (30 units). The first two are fairly stable, the last is a little bit less stable, but still sturdy. I don't bother to try to actually tuck the tab on the last unit, as things are too constricted by that point.
I have made the following with variations of this unit:
Malachi B-J Brown firstname.lastname@example.org