A very modular origami model. In the video I only demonstrate the triangle and square modules, but there are also pentagon, hexagon, octagon and decagon modules, basically you can do all sorts of polyhedra with these (tetrahedron, icosahedron, icosidodecahedron, rhombicosidodecahedron…).
If you do not have the patience to make all 18 square modules you can go for a cuboctahedron with 8 triangle modules and 6 square modules, but it’s more difficult to assemble. Otherwise if you’re super dedicated you can go ahead and make 32 triangle modules and 6 square modules to make a snub cube. You can even make a snub dodecahedron, but it requires pentagon modules which aren’t shown in the video.
Music in the video (in order) from Incompetech:
- Kevin MacLeod – Cold Funk
- Kevin MacLeod – Hypnothis
- Kevin MacLeod – Chill
- Kevin MacLeod – Dirt Rhodes
Paper to use
I used A4 paper, but as long as you’re using the same paper size to make the triangles and squares you’re good, the important thing is to keep the height of the triangle equal to the side of the square.
I would recommend thick paper, it makes the model very sturdy, but might make it harder to assemble. A general rule would be to use thicker paper when using lots of modules, otherwise it won’t be sturdy enough and will lose it’s ball-like shape.
All the module diagrams (triangle, square, pentagon, hexagon…), assembly instructions and lots and lots of information about polyhedra are in Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality by Rona Gurkewitz and Bennett Arnstein. You can also get a small preview in Google Books.