Tamfang wrote:By the way, what law says that truncated (for example) must be an adjective or a prefix? Chemistry gets plenty of use out of suffixes (as does Esperanto).
Oooh, I smell a fellow conlanger!
You could have (arbitrary example) –ane for the 'parent', –ene for the rectate, –ine for the birectate; –ade for the truncate, –ede for the bitruncate ... –o– and –u– for alternations ....
On another hand, in English the vowels of unstressed syllables are rarely pronounced clearly, so this scheme has obvious room for improvement.
Who says we must adopt subtle vowel variations, and who says we must restrict it to only monosyllabic suffixes? Many natural languages do just fine with polysyllabic endings (e.g. -yami/-ami in Russian for plural instrumental--and almost all adjectives have disyllabic endings), and consonants provide a much wider range of distinct sounds.
Also, to maximize distinctiveness, it's often useful to restrict any vowels to apical vowels (/a/, /i/, /u/, or in English spelling, "ah", "ee", "oo"), which have maximal contrast with each other. It's the in-between stuff, like /e/, /æ/, etc., that starts bringing in potential ambiguity.
Having said that, though, you've to realize that the number of uniform truncates grow exponentially with dimension, arising after all from the number of ways to ring the nodes in their Coxeter-Dynkin diagrams. Unfortunately, human beings (and consequently human language or naturalistic language, which is apparently what we're trying to achieve here) are rather poor at dealing with combinatorial objects. Witness, for example, the absolutely atrocious tentative naming scheme for newly synthesized chemical elements: a 1-to-1 correspondence between the numbering system (atomic number) and syllables gives us such horrors as unununium for element 111, which grates on the ears when pronounced with 3 identical vowels (oon-oon-oon-ium), and suffers heavily from distortion when one tries to pronounce it more "naturally" (e.g. yoo-nuhn-yoo-nium). Any naming scheme that does such direct translations from a numbering scheme (e.g., using n-digit binary numbers to enumerate all possible uniform truncates of dimension n) is prone to exactly the same encumbrance as names like "hecatonicosachoron".
For such cases, I've always liked the IUPAC's method of prefixing with numbers, e.g., 1,3-dimethylbenzene. I adopted the same scheme in naming duoprisms: 3,5-duoprism instead of the wordy trigonal-pentagonal-duoprism. A similar scheme for naming the uniform truncates might therefore be more appropriate here: take the Coxeter-Dynkin diagram, orient it such that the edge of highest degree lies on the left, then read it from left to right with ringed node=1 and unringed node=0, using each number as a prefix. So for example, the cuboctahedron would be a 0,1,0-stauromorph truncate (or whatever suffix you may want to invent for it), and the great rhombicuboctahedron would be a 1,1,1-stauromorph truncate. This lets you name very high dimensional objects without running out of breath, e.g., 1,0,1,1,0-stauromorph truncate instead of cantibirectifiedblahblahified hexateron.
We can still use a suffix instead of "truncate", of course; but by relegating the combinatorial stuff to arabic numerals, which is best suited for the task, we have more syllables at our disposal for the special cases, such as snubs, alternations, etc..
And if we ever feel that binary numbers waste too many syllables to pronounce, we can always convert it into its decimal value, so the cuboctahedron becomes the 2-stauromorph truncate (or 2-staurotome, if we adopt
-tom, from Greek
tomo, to cut, as a general suffix for all uniform truncates), and the great rhombicuboctahedron becomes the 7-staurotome. The omnitruncated 600-cell would then become the 15-rhodotome, which you must admit is a very sweet and simple name indeed. And we don't even have to worry about the possibility of ugly names like 0-rhodotome, because at least one node in the Coxeter-Dynkin diagram must be ringed, otherwise there's only a single point.
We may even eliminate dimensional ambiguity (e.g., a 3-polytope 0,1,0-staurotome vs. a 4-polytope 0,0,1,0-staurotome) by inserting the dimension number right after the CD number: so cuboctahedron = 2,3-staurotome, rectified 16-cell = 2,4-staurotome. So the omnitruncated 600-cell becomes the 15,4-rhodotome, but since there aren't any rhodomorphs above 4D, and the value 15 can only occur in 4D because it requires 4 binary digits, we can elide the dimensional number and just write 15-rhodotome, as before. Similarly, since the xylomorphs only occur in 4D, we can simply write 15-xylotome for the omnitruncated 24-cell.
Using this scheme, even the regular polytopes themselves are represented: the 8-xylotome is just the 24-cell, and the 1-xylotome is its dual; the 8,4-staurotome is the tesseract, and the 1,4-staurotome is the 16-cell itself. By omitting the dimension, we can make dimension-independent statements like "the 8-staurotomes tile their respective spaces".
(Is there a layman-friendly book about how the chemical suffixes were adopted?)
From my (admittedly limited) reading, they were generalizations of existing ad hoc names.