The above encasement of an IVM sphere (that the sphere appears to really be made of tiny dots is not unfortunate in this context), outlined in black, is the rhombic dodecahedron.
The long diagonals of each diamond facet (one is shown in red) form an octahedron, while the greens (short diagonals) form a cube. The relative volume ratios are 6:4:3.
Of special importance in Synergetics is this space-filling shape, shown in red, called the Coupler. It's a non-Platonic octahedron of volume 1 relative to the above 6:4:3 schema, and may be developed in terms of the cube (left) or in terms of the rhombic dodecahedron (right).Below is the shape most people think about when they hear the word "dodecahedron," if they think of a shape at all. Centuries of Platonic bias stacked the deck such that "dodecahedron" means the Platonic one, kind of like when some USAers say "Americans" and just mean themselves.
We needn't waste time "blaming Plato" for ignorance of the rhombic dodecahedron among the lay public. Indeed, one may correctly view Synergetics itself as a form of NeoPlatonism, although American Transcendentalism fits at least as well, if you're shopping for an "ism" with which to pigeon-hole this work.
