User:Dc.samizdat

I am David Brooks Christie, born April 3, 1951.

• 5-cell
• 16-cell
• 8-cell
• 24-cell
• Snub 24-cell
• 600-cell
• 120-cell
• Template:Regular convex 4-polytopes
• Schläfli orthoscheme
• Tetrahedron
• Octahedron
• Kinematics of the cuboctahedron

A graph theorist, a differential topologist and a Euclidean geometer walk into a bar, in the midst of trying to decide a question about the fourth dimension. The bartender asks, "the usual?" The graph theorist says, "three eigenvectors form isomorphic paths of that diameter." The differential topologist says, "there is no symmetric Clifford torus, but it is a Hopf fibration." The Euclidean geometer says, "several distinct great circle polygons are isoclinic in that left (right) rotation." The wise bartender, who has heard it all, says "that's a yes, then," and pours them all the same drink.

It is worth remembering that the ancients who invented geometry did not have physics or mathematics to guide them, only physical experience and imagination. They did not have algebra, much less the Clifford algebra, or quaternions, or the theory of reflecting groups, or indeed any of the formulas we call the languages of mathematics except the Pythagorean theorem. Every so often, still, there comes a geometer who has not been educated in the languages of mathematics, and does great works, like Alicia Boole Stott or Thorold Gosset. The preeminent recent example of a mathematically illiterate geometer is Buckminster Fuller, who distrusted trigonometry (he thought it might be "inaccurate"), but nonetheless spotted the non-deterministic inflection point in the Möbius spinor orbit of the orientable double cover of the octahedron, without having any of that language for it, and so described it instead with physically meaningful language and actual physical demonstrations that anyone can understand,^[1] at least if they have stalled an airplane, or trimmed a submarine's ballast tanks, or can imagine doing so.