Cuboctahedron. I made this in the days when I thought it was cool to have every face be a different color.
Today, I'll show you the first Archimedean solid I made, the cuboctahedron. Many modular origami models are based on the Platonic solids. In a Platonic solid, every face is the same regular polygon, and each vertex has the same number of polygons around it. In an Archimedean solid, there are at least two kind of polygon faces. There are 13 kinds of Archimedean solids (under a particular definition).
The cuboctahedron can be seen as a cube, where each of its vertices have been cut off. Or it can be seen as an octahedron where each of its vertices have been cut off. Thus the name.
Funny story about the cuboctahedron. I created the model myself, using a standard square module, and inventing a simple triangle module. Later, I got a book by Tomoko Fuse, and she has the exact same method! Furthermore, she had a bunch of ideas about things you can add onto the cuboctahedron to make new shapes.
The cuboctahedron, half-way transformed into a cube. Note that I made this much later, after I figured out that it's good to repeat the same color sometimes.
As I said, the cuboctahedron can be seen as a cube with its vertices cut off. By adding extra paper, I can add those vertices back on. Here I added only four of the vertices, so it's not yet a cube. Instead it's a different polyhedron, that is neither a Platonic solid nor an Archimedean solid.