All these modular origami constructions are made of a single basic module, the Sonobe unit.

The basic unit has flaps and pockets.

The actual folding of the Sonobe module is quite easy, see the instructions below, taken from Michael Naughton’s excellent diagram.

This is an incredibly flexible unit, allowing us to combine it in many ways. This pdf shows how to combine different numbers of Sonobe modules to produce the shapes above, and many others. If all meeting points of the basic unit contain 3 modules, one gets a cube. If all meeting points contain 4 modules, then we produce a octahedron (with pyramids on each of its faces).

The results can be very impressive! Above is a Truncated Icosahedron, made of pentagons surrounded by hexagons (like a soccer ball). This one is made of 90 Sonobe units, see detailed instructions.