Curler units

The curler unit by Hermann Van Goubergen is one of the most interesting modules to build amazing origami models.  This unit is a simple but ingenious variation of the waterbomb base. 

Actually it is really easy to fold and you can find the diagram here!

Figure 1. Cuboctahedron with curler units

Using the curler units several models of polyhedra can be folded . With only twelve modules you can get the elegant cuboctahedron of Figure 1.

The cuboctahedron is an Archimedean solid and also a uniform polyhedron. Many people mistakenly believe that Archimedean and uniform are equivalent concepts.

The Archimedean polyhedra can be defined using the following local criterion

Local criterion: All faces are regular polygons, and the cyclic arrangement of the faces around each vertex is the same.

The uniform polyhedra are defined using a global criterion 

Global criterion: All faces are regular polygons, and all vertices form one orbit under isometric symmetries of the polyhedron.

There are fourteen convex polyhedra that satisfy the local criterion and should be called "Archimedean", but only thirteen that satisfy the global criterion and are appropriately called "uniform" (or "semiregular").

The interested reader can delve into this aspect by reading the interesting paper of Branko Grünbaum entitled An enduring error (avaliable online).