OK, so what is this shape? As a first approximation, Straws Thingy is simply the Compound of Five Tetrahedra, a favorite among origami folders thanks to Tom Hull’s popular and supremely elegant design.
But on closer inspection, these tetrahedra break down into even smaller parts: each tetrahedron is made from four interwoven triangles, making 20 triangles in all. Here’s one such tetrahedron (left) with one of the four triangles distinguished (right):
Robert Lang describes this shape as a “polypolyhedron” (specifically, it is the mirror image of Polypolyhedron 44), and he originally classified all such shapes (there are 54) for origami—his folding of this particular polypolyhedron, a model he named K2, is especially stunning and took a full day to assemble!
I therefore like to think of Straws Thingy as origami without the origami. The straws’ flexy bits (technical term, I’m sure) do the folding for us, and instead of holding everything together with creases, we stick straws inside each other—the same beloved trick for blowing bubbles in my chocolate milk from across the room…