Systematic names for Wilson CPS structures.

IIRC, somebody found a web page from which one could derive systematic mathematical names for Wilson's CPSs. The hexany corresponds to the octahedron and the eikosany to some sort of -choron, but I don't recall the name or the naming procedure. As I recall, even the less symmetrical structures such as the dekanies could be named by this technique. Does anyone recall the name?

I did a Google search this AM and found several pages with polytopes, polychora, etc., but didn't see anything corresponding to the eikosany. Also, I'm not certain that this is an accepted nomenclature for these higher-dimensional structures.

--John

--- In tuning-math@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
>
> IIRC, somebody found a web page from which one could derive systematic
> mathematical names for Wilson's CPSs. The hexany corresponds to the
> octahedron and the eikosany to some sort of -choron, but I don't recall
> the name or the naming procedure. As I recall, even the less symmetrical
> structures such as the dekanies could be named by this technique.

I was wondering about the possibility of naming and classification deriving from graph theory.

>IIRC, somebody found a web page from which one could derive systematic
>mathematical names for Wilson's CPSs. The hexany corresponds to the
>octahedron and the eikosany to some sort of -choron, but I don't recall
>the name or the naming procedure. As I recall, even the less symmetrical
>structures such as the dekanies could be named by this technique. Does
>anyone recall the name?

Hi John,

These websites were always hard to find, and IIRC the main one was
down last I looked. Dave K. and I did put this together though:
(click here to get the right formatting:)
/tuning-math/message/18472?var=0&l=1

3-limit line segment
5-limit triangle
7-limit tetrahedron octahedron
9-limit pentachoron rectified pentachoron
11-limit hexatetron ?? uniform dodecatetron

3-limit dyad
5-limit triad
7-limit tetrad hexany
9-limit pentad dekany
11-limit hexad pentadekany eikosany

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> 3-limit line segment
> 5-limit triangle
> 7-limit tetrahedron octahedron
> 9-limit pentachoron rectified pentachoron
> 11-limit hexatetron ?? uniform dodecatetron
>
> 3-limit dyad
> 5-limit triad
> 7-limit tetrad hexany
> 9-limit pentad dekany
> 11-limit hexad pentadekany eikosany

Number of Vertices
2
3
4 6
5 10
6 15 20

According to http://en.wikipedia.org/wiki/Uniform_polyteron it seems the last line above should be changed such that the table becomes:

3-limit line segment
5-limit triangle
7-limit tetrahedron octahedron
9-limit pentachoron rectified pentachoron
11-limit hexateron rectified hexateron truncated hexateron

The main wikipedia article from which you can eventually find all of these is
http://en.wikipedia.org/wiki/Uniform_polytope

-- Dave Keenan

It is my understanding the names where derived from Greek
--

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

The names refer to the number of elements in the set, not the actual shape
--

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again