I spent the holiday weekend becoming fluent in the basics of modular origami. With practice, you can churn out the below models surprisingly quickly.
My first attempt at the octahedron can be seen here, which I found was actually a bit tougher to finagle (in terms of assembly) than the the somewhat more impressive looking icosahedron (shown below). I found Math Craft admin Cory Poole's modular origami instructions for the cube, octahedron and icosahedron easy to follow, with the exception of the assembly of the octahedron, which I eventually pieced together through trial and error (and by cross-referencing this diagram).
I went on to attempt the Pentakis Dodecahedron with Cory's instructions, but couldn't figure out the sonobe unit modification, so I will use the notorious barbabellaatje of YouTube's video demonstration, and will be posting my results soon!