The secret of the small dish

So what exactly is this "secret" we made reference to last week? Look and see, gentle viewer, and all will be revealed...


Here we see the "small dish" from last week, as well as a mirror-image version. (Why a mirror-image version? That's part of the secret, folks.)


Here we see the same two dishes, each with three "flaps" extended. The flaps are normally inserted into the base of the bowl as part of the locking mechanism. However, they can be extended...


...and combined! We are now privy to the secret: the small dish can be combined with it's mirror-image counterpart to create this geometric figure, known as a regular icosahedron. (A regular icosahedron is a solid figure that consists of 20 identical triangles. Geeks like me will also recognize it as a d20.) Such shapes have been studied by mathematicians for thousands of years, and are favorite subjects for unit origami designers.

The icosahedron was constructed from 12 sheets of 5-7/8" square origami paper and stands roughly 5" tall. It was designed by Tomoko Fuse; a folding pattern for it may be found in her book Unit Origami. (Just like last week, huh?)