Here's my version of his icosahedron:
I colored it in this one so that you can see the pentagonal faces of a dodecahedron:
Here I made one that looks like a cube:
Some of my students asked me how to make these and they took it a step further and made something based off of the truncated icosahedron which is one of the common stitching patterns on a soccer ball.
Three years ago I made a wreath based off of Richard Sweeney's curved triangular unit and Thomas Hull's modular origami tori:
Everything is made from flat paper. The curvature is due to the folding process.