Additions to

Zome Geometry

George W. Hart   and  Henri Picciotto

The Octahedron in the Dodecahedron

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.)