NYT: A Puzzle Finally Makes the 'Cosmic Figures' Fit

A Puzzle Finally Makes the 'Cosmic Figures' Fit
By MARGARET WERTHEIM
Published: May 10, 2005


The New York Times; photograph by Tony Cenicola


At the dawn of the scientific revolution, the German astronomer Johannes Kepler was struck by a vision. Pondering the distances between the planets, he realized that the sizes of their orbits could be explained by a nested set of Platonic solids.

Known to the Greeks as the "cosmic figures," these five forms - the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron - have the property of being perfectly regular.

Kepler's vision turned out to be a mirage, as his own research on planetary orbits eventually proved. But the mystique of these solids has endured and in a small, quixotic way, Kepler's fantasy has finally been realized. Dr. Wayne Daniel, a retired physicist and puzzle expert, has designed an interlocking wooden puzzle that is a complete set of Platonic solids. Like a Russian matryoshka doll, each layer peels away to reveal a smaller form within, only in this case each layer has a different geometry.

The All Five puzzle, as Dr. Daniel has named his latest creation, is a miniature cosmos of its own. On the outside is the icosahedron, inside that a dodecahedron, inside that a cube, inside that a tetrahedron, and at the core a tiny octahedron. Each form is itself a puzzle that must be assembled from interlocking pieces, the whole constituting a tiny symphony of Platonic play.

"This is the first puzzle with all the Platonic solids in a concentric, integrated and solid form, with no voids between them," said Jerry Slocum, a puzzle expert in Beverly Hills, Calif. "It is an amazing achievement."...


http://www.nytimes.com/2005/05/10/science/10puzz.html?adxnnl=1&adxnnlx=1115732814-iU3IIbrKpRj5CklJjpcZHg

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I've seen you crapping all over my blog.

Begone foul spirit!

in the act of laying it's egg

It has been proven that there are only five regular solids but there are lots of semi-regular (whose faces are mixes of regular polygons)or truncated or stellated solids.

...all that is in the cosmos is not infinite. Boy, where we could go with that concept!

I can't recall positively, though. These five are it for a 3 dimensional manifold though.

A relative gave me a dodecahedron that he made out of wood with brass fittings. It makes a nice centerpiece for a table, and really is quite fascinating to contemplate.