Construction of a dodecahedron, with help from Ezra Miller: the point in this construction is to construct a dodecahedron by folding from a planar shape. The most common way to construct a dodecahedron in this way is to draw "two flowers" of six pentagons each, each flower consisting of five pentagons surrounding a sixth pentagon, and then the two flowers sharing an edge. However, in this flower construction, once you fold, you have to manually hold about four or more corners to keep the shape. With Ezra we did an alternate construction:

But do a little manipulation and hand holding, and you get a true dodecahedron: