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."
The All Five is the product of more than 40 years of mathematical puzzle making. Now retired and living in Genoa, Nev., Dr. Daniel, 78, had a distinguished career as a physicist working on engine design for General Motors Research Laboratories. His original interest in puzzling began decades ago when he set out to make a series of tetrahedral kites for his son. After he retired the hobby became a full-blown passion that has led him to become a leading designer of puzzles based on Platonic solids.
Dr. Daniel has made many such puzzles, but the All Five presented significant design challenges, he said by telephone. He made 20 of the puzzles, which sell for $400.
The major hurdle was to design pieces with one of the solids on the outside and another on the inside. Most difficult, he said, was the outermost shell, "in which a set of pieces had to assemble into an icosahedron with a dodecahedral hole in the middle."
An expert woodworker, Dr. Daniel makes all his puzzles himself, shaping each piece out of woods like peroba rosa, zebrawood, jatoba and chechen. When dreaming up a puzzle, he said, "there are two problems to be solved: how to design it geometrically, then how to actually make it." It's an art that combines the hands and the mind.
In one puzzle of which he is especially proud, the pieces fit together to form a Möbius strip, an idea that emerged while he was stuck in commute traffic and set himself the task of designing a puzzle wholly in his head. He is currently working on a new design based on a complicated soap bubble form, called a minimal surface.
"I've been thinking about this for 30 years," he said, "and no mathematician I've met can tell me what its equation is."
It has been a long time coming, he said, "but I think I've finally figured it out."
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