The Pythagoreans, legend has it, saw each of the regular solids as a symbol of one of the elements: tetrahedron fire, octahedron air, icosahedron water, cube earth — leaving the dodecahedron to stand for the universe, or quintessence, or spirit. It’s rather a pity that they weren’t so named, pyromorph, aeromorph, hydromorph, geomorph, cosmomorph; the nomenclature of the other uniform polytopes (particularly those of four dimensions) would be somewhat cleaner.
2004 Oct 04: It is a charming coincidence that the cosmos was briefly suspected of being cosmomorphic.
In four dimensions there are six convex regular figures, five of which are analogous to the five Platonic solids. Suggested names:
Where the Greeks counted four elements the Chinese counted five: fire, water, earth, wood and metal. So I arbitrarily adopted ‘wood’, Greek xylon, for the extra four-dimensional figure, whose symmetry group includes that of the ‘air’ and ‘earth’ hypersolids.
interesting nomenclature with one minor flaw in logic.
if you are migrating from the greek four element system to the chinese five element system, air (aero) should become wood (xylo) and metal (metallo), since there is no air in the chinese system. thus, using your naming conventions the 16-cell, hexadecachoron would be a metallotetron.
or perhaps 16 should be xylo- and 24 should be metallo-. i don’t claim to know enough about chinese astrology and its elements to be able to “order” them and map them to the regular chorons (your tetrons) as the greeks did to the regular hedrons.
consultation with an eastern astrologer may be in order. (or perhaps a psychic to channel Kepler?) lol
It’s not “migrating from the Greek four-element system to the Chinese five-element system”, it’s the Greek system extended by one element so as to maintain the analogies as much as possible. If not wood, what would you suggest for the extra element?
I see I didn’t explain another aspect of my terminology. hedra means ‘face’ (actually ‘seat’) and choron means ‘cell’. I call the [number]-hedron an [element]-choron because the element is a quality of the whole body, not of the faces. I deprecate terms such as symmetrohedron (a body isomorphic to a symmetry group, whose faces need not be symmetrical) whose coiners treat the second element of polyhedron (‘many-faced’) as a synonym for the whole.
There’s nothing wrong with the prefixes, like aero- etc. But using ‘hedron’ is not the go here. Hedron is a patch you do something with. You make a bag out of 12 or triangular patches, and stuff it with wool. What you really need is something that means ‘solid’.
In the polygloss, we have a different word from solid, meaning 3d solid (chorid). You just make the -ons into -id, and the seamstress won’t come looking for your patches to sew together! So a xyloterid is a wood-element 4solid. So once you figure out wood-element is -343- you get the idea.
I’d like to see sphere make this list, because it is the the ultimate of regularity. I suggest numi- (coin-shaped), eg numichorid (3d sphere-disk).
Perhaps the distinction between endocentric and exocentric compounds would have been clearer had I named the 3-solids –chore rather than –choron.