Here is another brief model, since it is summer...

**Problem:** Build the dual to last month's
construction of an icosahedron inscribed in a cube.

**Answer:** An octahedron inscribed in a dodecahedron, so that every
octahedron vertex is at the midpoint of a dodecahedron edge. The
icosahedron's edge was centered in the cube's face, so dualizing puts the
octahedron's vertex centered in the dodecahedron's edge.

**Construction:** It is easy. With a **2b1** dodecahedron
(the smallest size that has a zomeball available at an edge midpoint),
the octahedron edge length is **g3** (which you have to make as **g1+g2**,
of course).

(If someone sends me a picture, I'll add it to this page.)