The philosophaster's stone

I guess I was about eight or nine when I discovered the diagrams of Platonic and Archimedean solids in Mathematics: A Human Endeavor by Harold R. Jacobs and began assiduously making paper models of almost all of them. One I omitted, because it just seemed kind of tacky, was the snub cube -- the singular unattractiveness of which is best seen in Kepler's original illustration from Harmonices Mundi:

I always thought that it (like its cousin, the snub dodecahedron) shouldn't be considered a real Archimedean solid -- that it shouldn't count, just as prisms and antiprisms don't count. I mean, it's just a plain cube, gussied up with a sort of Elizabethan ruff of triangles around each face, antiprismhood taken to the next level. And the name! Kepler dubbed it cubus simus, which has something of the ring of a Life of Brian joke-name, but it is in English that it reaches the absolute nadir of polyhedral onomastics. If cellar door has often been cited (by Tolkien, H. L. Mencken, and others) as a particularly beautiful phrase, irrespective of its meaning, snub cube is the anti-cellar door. Nothing beautiful could be called a snub cube.

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Some years later, I read Timaeus, the dialogue to which the term "Platonic solid" alludes, and discovered Plato's idea that the four classical elements are made up of tiny tetrahedra (fire), cubes (earth), octohedra (air), and icosahedra (water) -- which in turn are made up of squares and triangles. (These squares and triangles are made up of two different sorts of smaller triangles, Platonic quarks.)

I realized that if you took the 6 square faces of a cube and the 4 + 8 + 20 triangular faces of the other three elemental solids, and put them all together into a single polyhedron, that polyhedron would be -- the Snub Cube, the perfect unity of the four elements. The philosophaster's stone.

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Since making that discovery, I have been using "Snub Cube" as mental shorthand for all those overly-abstract, overly-nifty schemata -- from the Kabbalah to scholastic theology to psychoanalysis -- which, despite how shiny and rectilinear they are, and how neatly everything fits together, are palpably wrong at the deepest possible level and are therefore to be treated with caution -- studied, admired, learned-from, to be sure, but never taken to heart.

"All that I have written seems like straw," Aquinas is reported to have said near the end of his life, but the metaphor is an imprecise one. What he meant was, "I see now that what I have created is, after all, only a particularly well-constructed Snub Cube."