Sorry to disappoint people who were expecting a turtle! That’s just what the model is called. If you want a turtle, go look at this one.
This is a fairly old photo, from 2014. I can tell just based on the photography sensibility. I just put the model on top of the textbook I was using as a flat surface for folding, and put a tape measure in there for scale.
The polyhedron is an icosidodecahedron, one of the Archimedean solids. There are 12 pentagonal faces and 20 triangular faces. You can add up all the edges of the face like so: 12*5 + 20*3 = 120. However, this double-counts each edge, since each edge is part of one triangle and one pentagon. So in total, there are 60 edges. This model uses one piece of paper per edge, so that’s 60 pieces of paper.
Tomoko Fuse’s original suggestion was to make a model with 4, 6, 12, 24, or 30 units. I thought I’d go one step further and do a 60-unit model. Turns out this may have been too ambitious. 60 units doesn’t hold very well, and soon it was like a deflated ball. Lesson learned: the icosidodecahedron may be a perfect mathematical ideal, but a piece of origami is still a physical object.