New nomenclature for regular polytopes

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Re: New nomenclature for regular polytopes

Postby quickfur » Mon Nov 22, 2010 9:27 pm

Keiji wrote:Yes, the E-series deserve their own names, but this doesn't mean we should enumerate names for all uniform shapes up to 8 dimensions, because there are a vast number of (5..8)-dimensional shapes which are uninteresting.

Uninteresting to whom? I find each shape quite interesting in and of its own. ;)

The point of a nomenclature is to be able to consistently name all possible objects in its domain. Of course, some objects are generally more interesting than others, so it doesn't matter as much if the less interesting objects are relegated to having a name with a numerical prefix (e.g. 1,0,1,1-rhodotome). We just need more convenient names for the more interesting objects (e.g., so that we can refer to the 1,1,1,1-tomes as omnitruncates, or whatever term we come up with, without needing to pronounce "one one one one").
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Re: New nomenclature for regular polytopes

Postby wendy » Tue Nov 23, 2010 7:25 am

The general 'truncated tetrahedron' can have hexagons with alternating sides of x,y. When x=y, or x=0 or y=0, the truncation is special.
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Re: New nomenclature for regular polytopes

Postby Keiji » Sat Dec 04, 2010 7:50 pm

Ok, I split out the stuff about runes, which was interesting enough but not at all on-topic.

Have there been any other ideas for truncation prefixes?
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Re: New nomenclature for regular polytopes

Postby quickfur » Sat Dec 04, 2010 8:44 pm

It just occurred to me that we could refer to truncated polytopes in general as tomomorphs, which has a nice ring to it. :-)
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Re: New nomenclature for regular polytopes

Postby quickfur » Sat Dec 04, 2010 8:56 pm

For omnitruncates, the ad-hoc name pantome comes to mind, from Gk pan- (all) + tomo (to cut). Well actually it's a portamenteau, because the Greek root is actually pan(t)-, so properly it would be pantotome, but I do prefer shorter names. :-) So the omnitruncated 600-cell, for example, would be the rhodopantome. This is just a literal Grecification of the Latin-derived "omnitruncate", of course, except it has only half the syllables. :-)
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Re: New nomenclature for regular polytopes

Postby Tamfang » Sat Dec 04, 2010 9:01 pm

A haplology rather than a portmanteau.
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Re: New nomenclature for regular polytopes

Postby Keiji » Sun Dec 05, 2010 12:40 am

quickfur wrote:So the omnitruncated 600-cell, for example, would be the rhodopantome.


I think you mean rhodopantomochoron, to distinguish it from the omnitruncated dodecahedron/icosahedron which would be the rhodopantomohedron!

So let's see. Adopting your "meso-" for rectates (and using "dimeso-" for cantellates, since a cantellate can be obtained by rectifying twice), we now have the following for the uniform polyhedra (only missing snubs):

pyrohedron, pyrotomohedron
geohedron, geotomohedron, stauromesohedron, aerotomohedron, aerohedron, staurodimesohedron, stauropantomohedron
cosmohedron, cosmotomohedron, rhodomesohedron, hydrotomohedron, hydrohedron, rhododimesohedron, rhodopantomohedron

Alternatively, if we bring the prefix for the truncation type to the front, we get:

pyrohedron, tomopyrohedron
geohedron, tomogeohedron, mesostaurohedron, tomoaerohedron, aerohedron, dimesostaurohedron, pantomostaurohedron
cosmohedron, tomocosmohedron, mesorhodohedron, tomohydrohedron, hydrohedron, dimesorhodohedron, pantomorhodohedron

Although the second way is more analogous to what we currently do ("truncated"+"cube" => "tomo"+"geohedron", etc.), I think I prefer the first way (your way) when seeing them both together like that.

As for polychora, let's see what we can make (I'll only list the first way for these):

pyrochoron, pyrotomochoron, pyrotomichoron, pyromesochoron, pyrodimesochoron, pyropantomochoron
geochoron, geotomochoron, geotomichoron, stauromesochoron, aerotomichoron (= 24-cell), aerotomochoron, aerochoron, staurodimesochoron, stauropantomochoron
xylochoron, xylotomochoron, xylotomichoron, xylomesochoron, xylodimesochoron, xylopantomochoron
cosmochoron, cosmotomochoron, cosmotomichoron, rhodomesochoron, hydrotomichoron, hydrotomochoron, hydrochoron, rhododimesochoron, rhodopantomochoron

I've omitted Dx numbers 5, 7, 11, 10, 14, 13 (that is, cantellate, cantitruncate and runcitruncate, and those operations applied to the dual), which don't have a prefix yet.
I obtained tomi- by combining tomo with hemicate, my word for the four-dimensional Dx 2.

It seems that the 4D cantellate (Dx 5) is equivalent to hemicating twice. So if tomi- is used for Dx 2 then ditomi- could be used for Dx 5. Then we'd have pyroditomichoron, geoditomichoron, xyloditomichoron, cosmoditomichoron and hydroditomichoron.

How's this look so far?
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Re: New nomenclature for regular polytopes

Postby Tamfang » Sun Dec 05, 2010 12:52 am

Keiji wrote:How's this look so far?

Disappointing, in one respect, but I won't beat that horse again today.
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Re: New nomenclature for regular polytopes

Postby quickfur » Sun Dec 05, 2010 1:05 am

I can't say I like the idea of compounding prefixes just so we can shoehorn all possible ringings of the CD diagrams into the system. I rather we kept the prefixes simple, and restrict them to the most "common" polytopes (the truncate, the mesotruncate, the cantellate, and omnitruncate, say), and just use numbers for the rest. I mean, c'mon, numbers aren't all that scary! There's nothing wrong with naming a rarely-specifically-discussed polytope something like 1,2,3,4-aerotome. I rather have numerical prefixes with reasonable short and pronunciable names, than to reinvent the current verbose system of cantimesotrunciwhatever hecatonicosidodecawhateveron, merely relexified.
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Re: New nomenclature for regular polytopes

Postby Keiji » Sun Dec 05, 2010 9:16 am

Well, dare I say all the 3D ones are worth having individual names for?

The 4D ones not so much, so you could just call the runcitruncated 8-cell an 11-geotomochoron.

Having said that, it would be nice to have a separate sequence for up to the mesotruncate, so that they would be in a natural order, though this would of course require another different prefix. But with this, tomi- would be a 3-something and wouldn't need its own prefix.
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Re: New nomenclature for regular polytopes

Postby Oschkar » Thu Mar 01, 2012 4:55 am

I was thinking about keeping the commonly used prefixes and shortening them.
In three dimensions:
xoo ---
oxo recto-
xxo ter-
oox (dual)
xox canti-
oxx ter(dual)
xxx omni-

In four dimensions:
xooo ---
oxoo recto-
xxoo ter-
ooxo recto(dual)
xoxo canti-
oxxo biter-
xxxo canter-
ooox (dual)
xoox runci-
oxox canti(dual)
xxox runter-
ooxx ter(dual)
xoxx runter(dual)
oxxx canter(dual)
xxxx omni-
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Re: New nomenclature for regular polytopes

Postby wendy » Thu Mar 01, 2012 7:57 am

I generally use construction names eg xsf for icosahedron) for most of the WME and WMM polytopes, and generally don't bother to give them different names. There's far too many different interesting solids out there.
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Re: New nomenclature for regular polytopes

Postby Tamfang » Thu May 10, 2012 8:01 am

I'm uneasy about ter (for trunc?) because it is a Latin word meaning 'thrice', occasionally used in science with that meaning.

Somewhere upstream I suggested pen– (Latin paene), meaning 'almost' (as in peninsula)
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Re: New nomenclature for regular polytopes

Postby wendy » Thu May 10, 2012 9:53 am

Professor Johnson already has a series of names for this. I generally disagree with this process, though since it adds no insight into the processes involved. Also it's a waste of a lot of words for no sensable gain.

xooo base t1
xxoo truncated xooo t3
oxoo rectified xooo t2
oxxo bitruncated xooo t6

These actually make sense, since these correspond to the intersection of xooo and mooo at various ratios.

xoxo cantellated xooo = rectified oxoo = rectified rectified xooo t5 ie xoxo becomes runcinated
xxxo canteruncated = truncated xoxo = truncated rectified xooo t7 ie xxxo becomes runcitruncated.

Norman was not happy when i suggested the second names, and that 'cantellated' could be read as this. Still, if you use runcinated for these names, then rr = r of r, and tr = t of r, makes me more sense. Still, using runci here would line up with rhombi- for 5 and 7 in 3d. (rhombi = rr and rhombirtuncated as rt)

xoox runcinated xooo = t9 Bowers derives t9 from t6, not t1
xxox runcitruncated xooo = t11 (but bowers uses t13 here)

xxxx omnitruncated = t15 Bowers derives t15 from t6

No one's ever figured out how the other various truncates match up with the flag, save for Coxeter's use of 't' for Stott's 'e' operator. These are pretty much by custom. In any case, no one deals with the corresponding names. The iffyness of 'xxox' is that Bowers derive it from the dual, ie xoxx.

The duals have some names, based on a similar process.

apiculated = mmoo
surtegmated = omoo

This corresponds to the skinn formed over the wire-frames of the figure and its dual, in relative size.

mo..om = strombiated ...

Conway's term here actually makes sense, since the faces of these are antitegums of the margins of the figures.

mmmmm = vaniated ...

This means to make flags of, that is, the faces correspond to flags of the original, or simplexes based on the centres of e0, e1, e2, e3, ....

The snub 24 choron, makes sense with the other snubs (snub dodecahedron, snub cube), when one supposes that the only non-simplex faces belong to a the non-snub. In any case, one has sC = s3s4s sD = s3s5s, and s24 = s3s4o3o. Johnson has also runcisnub = s3s4o3x (which is not uniform).

I suppose, effort would be better put into expanding the conway-hart system, because when applied to the regular figures, give this direct.

One is still left with j5j2j5j "Di16" which has no real wythoff construction. Conway's "grand antiprism" could be used here.

Of course, the simple regular system breaks down in five and higher dimensions, where there are wythoffian figures based on non-regular figures.
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Re: New nomenclature for regular polytopes

Postby wendy » Tue Sep 18, 2012 10:51 am

The construct in -id makes a solid. So a chorid is a 3d polytope, a loose choron, so to speak.

The names for the regulars based on products, become pyrosolid, tegmasolid, and prismasolid. The three-dimensional versions replace /solid/ with /chorid/.

I'm not sure what to do with the other three. You could group 53 with 533, and 35 with 335, but 343 must by itself stand.

This gets around the ugly problem of what to call the 216-zetton (the regular orthotope in 8d), becomes the tegmayottid.

Interestingly, the tegmasolids, and prismasolids are both the basis of a coherent system of space-measure (eg 8d = yottage = measure of yottix.)
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Re: New nomenclature for regular polytopes

Postby Klitzing » Tue Sep 18, 2012 1:15 pm

wendy wrote:The construct in -id makes a solid. So a chorid is a 3d polytope, a loose choron, so to speak.

The names for the regulars based on products, become pyrosolid, tegmasolid, and prismasolid. The three-dimensional versions replace /solid/ with /chorid/.

The very beginning of this thread was Tamfangs reintruduction of the old platonic names: pyrotopes (for regular simplices), aerotopes (for orthotopes or cross-polytopes, i.e. your tegmasolids), geotopes (for hypercubes or measure poytopes, i.e. your prismasolids). Coxeter would call those alpha_d, beta_d, gamma_d (d being the dimension - in addition he used delta_d for the hypercubical honeycombs).
I'm not sure what to do with the other three. You could group 53 with 533, and 35 with 335, but 343 must by itself stand.

Tamfang and Platon would recommend: cosmotope resp. hydrotope. Tamfang later additionally introduced xylotope for 343.
This gets around the ugly problem of what to call the 216-zetton (the regular orthotope in 8d), becomes the tegmayottid.

Well, this is not fair. On the one hand you are after any polytopes on the other after the ones of a special class. You use numbers for more specificness in both cases. Facet counts at the one hand, dimension numbers on the other. The subclass itself is specified by your prefixing tegma-.
Interestingly, the tegmasolids, and prismasolids are both the basis of a coherent system of space-measure (eg 8d = yottage = measure of yottix.)

Bifurcated diagam families are not cought up here so far.
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Re: New nomenclature for regular polytopes

Postby Tamfang » Tue Sep 18, 2012 7:26 pm

Klitzing wrote:The very beginning of this thread was Tamfangs reintruduction of the old platonic names: pyrotopes (for regular simplices), [...]

Tamfang and Platon would recommend: cosmotope resp. hydrotope. Tamfang later additionally introduced xylotope for 343.

Tamfang would ask you (once again) not to attribute to him a vocabulary that equates the element with the whole.

A polytope is a thing whose topoi (elements, literally 'places') are many. A hydrotope, if Tamfang had a use for that word, would be a thing whose elements are watery, e.g. {3,5,3} — not {3n,5} itself, which is a deltatope (common style) or pyrotope (Tamfang style), a thing whose elements are simplices (deltas, pyromorphs).
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Re: New nomenclature for regular polytopes

Postby wendy » Wed Sep 19, 2012 6:54 am

The approach being suggested here is that the elements continue onto four dimensions, with each of those regular polychora being an element.

When the name applies to the solid, rather than the element of surface, the style in the polygloss is to use "chorid" for 3d, ie "3d solid". So, where cosmo- applies to the pentagonal series, the style suggested by the PG would be to use cosmochorid for 'dodecahedron' and cosmoterid for the twelftychoron.

Still, it's a little known fact that each of those that exist in higher dimensions are the power of the primitives, and that one could just as well make names like prismatope, giving prismachorid for cube, tegmachorid for octahedron, both L³ on different multiples, and the pyrochorid for the simplex (being point^4). This leaves just three series (3,4,3), (..,3,5), and (5,3..), and prehaps three more for the three gossets (/...,3,B), (/G,3,...) and (G/,3,...). These extend down to two dimensions.

It is still worth noting that much of the discussion simply avoids the duals of the uniforms, a feature one derives from the graph, by replacing x with m, or / with \. This does indeed have a regular construction (you make the mirror-portion into a face-wall). So the dual of /4B is \4B, which is not uniform in the usual sense. Likewise, you can mix both symbols in separate bases of a lace-prism. eg xm3xm3oo&x is the truncated tetrahedron antipism, while xm3xm3oo&m is the corresponding truncated tetragedron antitegum.
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Re: New nomenclature for regular polytopes

Postby Klitzing » Wed Sep 19, 2012 7:07 am

Tamfang wrote:
Klitzing wrote:The very beginning of this thread was Tamfangs reintruduction of the old platonic names: pyrotopes (for regular simplices), [...]

Tamfang and Platon would recommend: cosmotope resp. hydrotope. Tamfang later additionally introduced xylotope for 343.

Tamfang would ask you (once again) not to attribute to him a vocabulary that equates the element with the whole.

A polytope is a thing whose topoi (elements, literally 'places') are many. A hydrotope, if Tamfang had a use for that word, would be a thing whose elements are watery, e.g. {3,5,3} — not {3n,5} itself, which is a deltatope (common style) or pyrotope (Tamfang style), a thing whose elements are simplices (deltas, pyromorphs).


Sorry :oops: for mixing your proposed prefixes (infact the first 5 just go back onto the association of Platon) with the so far generally used suffix. As I can deduce from this thread, you rather like to propose to have:
  • Pyromorphs {3, ..., 3}, esp. pyrogon {3}, pyrohedron {3, 3}, pyrochoron {3, 3, 3}, etc.
  • Aeromophs {3, ..., 3, 4}, esp. aerohedron {3, 4}, aerochoron {3, 3, 4}, etc.
  • Geomorphs {4, 3, ..., 3}, esp. geogon {4}, geohedron {4, 3}, geochoron {4, 3, 3}, etc.
  • Hydromorphs {3, ..., 3, 5}, i.e. just hydohedron {3, 5} and hydrochoron {3, 3, 5}
  • Cosmomorphs {5, 3, ..., 3}, i.e. just cosmogon {5}, cosmohedron {5, 3}, and cosmochoron {5, 3, 3}
  • Xylochoron {3, 4, 3} (only)

Are those correct now? Else correct me once more, please.
Did you ever consider to add the bifurcated graphs to that naming scheme as well?

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Re: New nomenclature for regular polytopes

Postby Klitzing » Wed Sep 19, 2012 7:11 am

Klitzing wrote:
Tamfang wrote:
Klitzing wrote:The very beginning of this thread was Tamfangs reintruduction of the old platonic names: pyrotopes (for regular simplices), [...]

Tamfang and Platon would recommend: cosmotope resp. hydrotope. Tamfang later additionally introduced xylotope for 343.

Tamfang would ask you (once again) not to attribute to him a vocabulary that equates the element with the whole.

A polytope is a thing whose topoi (elements, literally 'places') are many. A hydrotope, if Tamfang had a use for that word, would be a thing whose elements are watery, e.g. {3,5,3} — not {3n,5} itself, which is a deltatope (common style) or pyrotope (Tamfang style), a thing whose elements are simplices (deltas, pyromorphs).


Sorry :oops: for mixing your proposed prefixes (infact the first 5 just go back onto the association of Platon) with the so far generally used suffix. As I can deduce from this thread, you rather like to propose to have:
  • Pyromorphs {3, ..., 3}, esp. pyrogon {3}, pyrohedron {3, 3}, pyrochoron {3, 3, 3}, etc.
  • Aeromophs {3, ..., 3, 4}, esp. aerohedron {3, 4}, aerochoron {3, 3, 4}, etc.
  • Geomorphs {4, 3, ..., 3}, esp. geogon {4}, geohedron {4, 3}, geochoron {4, 3, 3}, etc.
  • Hydromorphs {3, ..., 3, 5}, i.e. just hydohedron {3, 5} and hydrochoron {3, 3, 5}
  • Cosmomorphs {5, 3, ..., 3}, i.e. just cosmogon {5}, cosmohedron {5, 3}, and cosmochoron {5, 3, 3}
  • Xylochoron {3, 4, 3} (only)

Are those correct now? Else correct me once more, please.
Did you ever consider to add the bifurcated graphs to that naming scheme as well?

--- rk


... and, from what you just wrote, the xylochoron would be a special instance of an aerotope, as its Schläfli symbol commences by {3, 4, ...}. :D
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Re: New nomenclature for regular polytopes

Postby Tamfang » Wed Sep 19, 2012 9:25 am

In (at least) the Indo-European languages there are two common kinds of noun compound, known to linguists as tatpurusa and bahuvrīhi; these names are examples (in Sanskrit) of the respective types, meaning literally that one['s] man and [possessor of] much rice. English examples of the two kinds include seaman (a kind of man) and bluegill (not a kind of gill but a kind of fish, which has blue gills).

The classic words like polygon and deltahedron and pentachoron are of the bahuvrīhi type: neither root names the thing itself, but together they describe its distinctive attribute. I hope we can agree that the name does not mean that a polygon is many of something, or that an deltahedron is a triangular something, or that a pentachoron is five of something; in each case the bold verb ought to be has. And from this analysis we can infer what gon, hedron, choron must mean (although without knowing the history we can't guess that pentagon means five angles rather than five vertices or five edges!).

Newer coinages like permutahedron result from mistaking the older __hedron words for tatpurusa compounds, describing a kind of 'hedron' (forgetting what that root means, now that one can't expect a scientist to have studied Latin let alone Greek). The result is that hedron must mean one concept (a 2d facet) in octahedron and another concept (a 3d body) in permutahedron. I guess this doesn't bother most people, because most people don't analyse the words they use. (If they did, I wouldn't have heard someone complaining recently that non-citizens are treated as "second-class citizens".) But it bothers me enough that I object to seeing my name (or pseudonym!) attached to a scheme incorporating such confusion.

In my scheme, hydromorph can be understood either as bahuvrīhi ('thing whose shape is watery') or as tatpurusa ('watery shape'), without conflict; but I definitely had tatpurusa in mind for the more specific words like hydrochoron and hydroteron, because the elements are symbolized by the whole shapes rather than by their facets. I'm willing to bend on that, but I see no good reason to abandon the definitions of –gon, –hedron, –choron as 'angle, face, cell' respectively. I necessarily tolerate existing aberrations but I try not to imitate them.

Therefore: if aerochoron is a tatpurusa, it means 'airy cell' = {3,4}; if bahuvrīhi, it means 'figure with airy cells' = {3,4,3} or {3,4,4}, the latter being a tiling of H3 whose vertices are at infinity. It does not mean 'airy 4-polytope' {3,3,4}.
Last edited by Tamfang on Wed Sep 19, 2012 6:41 pm, edited 2 times in total.
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Re: New nomenclature for regular polytopes

Postby Tamfang » Wed Sep 19, 2012 9:31 am

The word deltahedron refers to the shape of each facet.
The word dodecahedron refers to the number of facets.
Are there any similar words derived from the arrangement or relative positions of facets?
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Re: New nomenclature for regular polytopes

Postby wendy » Wed Sep 19, 2012 9:50 am

The general pattern of describing solids is to regard them as surfaces, and describe that: in short, a solid is seen as a bag.

A dodecahedron, then is seen as a bag of 12 peices. A pentagon is a bag with 5 knee-like joints, and a fifshot (OE) is a bag made from five shots of the arrow. It's useful to push the fabric-and-cloth analogy to make words for specific dimensions, and let the bulk of words drift back to the meaning of equal-signs (ie relative to solid space).

When one starts to connect the polytopes to elements, such as tetrahedron = fire atom, octahedron = water atom, and so forth, the thing describe is the whole thing, and not a bag. So a fire-atom is a solid thing, and demands a solid element. One can not regard it as a patchwork of 2-cloth, but a singular 3-patch. The style in the pg is to use '-id' here, so 'chorid' is a solid made of chorix (or 3d cloth). A fire-atom would be a fire-chorid or pyrochorid, one of the pyrosolids. Likewise, one could have aerosolids, and geosolids, and so forth. But these are not polyhedra (ie a closure of 2d patches), but chorids (3d things).
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Re: New nomenclature for regular polytopes

Postby quickfur » Wed Sep 19, 2012 3:25 pm

wendy wrote:The general pattern of describing solids is to regard them as surfaces, and describe that: in short, a solid is seen as a bag.

A dodecahedron, then is seen as a bag of 12 peices. A pentagon is a bag with 5 knee-like joints, and a fifshot (OE) is a bag made from five shots of the arrow. It's useful to push the fabric-and-cloth analogy to make words for specific dimensions, and let the bulk of words drift back to the meaning of equal-signs (ie relative to solid space).

When one starts to connect the polytopes to elements, such as tetrahedron = fire atom, octahedron = water atom, and so forth, the thing describe is the whole thing, and not a bag. So a fire-atom is a solid thing, and demands a solid element. One can not regard it as a patchwork of 2-cloth, but a singular 3-patch. The style in the pg is to use '-id' here, so 'chorid' is a solid made of chorix (or 3d cloth). A fire-atom would be a fire-chorid or pyrochorid, one of the pyrosolids. Likewise, one could have aerosolids, and geosolids, and so forth. But these are not polyhedra (ie a closure of 2d patches), but chorids (3d things).

So IOW when we use element names then we should be using the tatpurusa compound, so pyrochorid = fire 3D-thing = tetrahedron, not {3,3,3} because chor- here describes the whole (the object is a 3D thing), rather than a part (the object's surface consists of 3D things). A pyrohedrid then would have to be a triangle (fire-kind-of 2D-thing). So {3,3,3} would have to be pyroterid, and {3,3,3,3} - pyropentid.

So one gets:
{3} - pyrohedrid
{4} - geohedrid / aerohedrid (as they are self-dual)
{5} - cosmohedrid / hydrohedrid
{3,3} - pyrochorid
{3,4} - aerochorid
{4,3} - geochorid
{3,5} - hydrochorid
{5,3} - cosmochorid
{3,3,3} - pyroterid
{3,3,4} - aeroterid
{3,4,3} - xyloterid
{4,3,3} - geoterid
{3,3,5} - hydroterid
{5,3,3} - cosmoterid

What should one do with Keiji's extension of the scheme to uniform polytopes, though? I.e. names like geo-tomo-choron, which was intended to refer to a 3D solid of the geo- kind that got cut in some way. But this seems out-of-order to me: interpreted as a tatpurusa compound, we have geo-(tomo-choron), that is, an earth-kind of (tomo-choron), which an earth-kind of a cut 3D-thing. It would appear that a better scheme would be to put the tomo- modifier in front: tomo-geo-chorid -- what is it? it's a chorid, a 3D-thing; what kind of 3D-thing? A geo-chorid, an earth-kind of 3D-thing; what manner of geochorid? a tomo-geochorid -- one that got cut in some way (e.g., a truncated cube -- what kind of cube? one that got cut). So one has (adjective)(noun)(noun), which makes more sense (to me) than (noun)(adjective)(noun).
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Re: New nomenclature for regular polytopes

Postby Keiji » Wed Sep 19, 2012 5:46 pm

Oh dear, this happened.
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Re: New nomenclature for regular polytopes

Postby wendy » Mon Sep 24, 2012 8:48 am

The eight gosset-elte figures diserve names. But at the moment Fb1, Fg1, Gb1, Gg2, Gg1, Hb1, Hg1, and Hg2 serve. These are 2_21, 1_22, 3_21, 2_31, 1_32, and 4_21, 2_41 and 1_42 respectively.
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Re: New nomenclature for regular polytopes

Postby wendy » Mon Jan 06, 2014 11:11 am

I'd like it to cover the regular solids, rather than the polytopes. This includes the spheres. Spheres are used to define volumes as well, so we could say, eg "geochorid inch" for P3 inch or "numiteric foot" for C4 foot.

The fabric/patch thing is built of a root stem HEDR + an i/e vowel for cloths, and a/o vowel for patches. This makes it easier when you already have things like helix etc meaning complete things, rather than patches.

So we live in a 'horochorix'. That means /euclidean + 3d fabric/.

The -ID suffix is from solid, is from SOL-ID. So a chor-id is a 3d solid. So are loose chorons, but you sew the patches together to make a mat, and the chorons generally describe what the mat makes. But a chorid is a loose thing, by itself.

You can use it as an adjective: a chorid stain is the sort of thing mould might make in bread. A hedrid stain is something ink might make on paper.

If you wack a prefix on it, you can turn a generic man into a seaman or a fireman. They're still men, but they deal with the sea and fires.

So you can use these pyro- and aeor- and geo- and xylo- and hydro- and cosmo- to make the regular figures. A pyrosolid is a simplex. A pyroyottid is a simplex in eight dimensions (litterally fire-shaped eight-solid.). I already do this with the Dt, Do, Dc, Dq, Di, Dd notation. Dg might fill the gap for the sphere.

Here's something you got to watch, though.

A glomochorix is a round 3-fabric, say S3, or the glome-surface
A glomochoron is something you make from a glomohedrix (eg by stuffing it), ie a glome-disk

So if you use 'glomochorid', the word is more likely to be a round-3solid, (ie sphere-disk), can be confused with the -ix form glome-surface.

But if you keep the prefixes far enough apart, this ought not arise.

quickfur wrote:What should one do with Keiji's extension of the scheme to uniform polytopes, though? I.e. names like geo-tomo-choron, which was intended to refer to a 3D solid of the geo- kind that got cut in some way.


Structured infixes work quite well. I've used them with electrical units, even with the same prefixes outside (as a different meaning), eg

atto-ab-deci-micro-coulomb = 1e-18 (ab) 1/4pi - 1/c (C).

You just have to make clear what's going on. I don't think that the -tomo- bit is going to be the biter here, but that there are whole families like 1_k1, k_21, which are also going to need prefixes. You get in the PG, gossetoicosa K_21 and gossetododeca 1_k2 and gossetoocta 2_k1. But you can make the gossetoocta a kind of subset to the gossetododeca, eg 1_42 = /G6, = xGo3o3o3o3o3o3o.. while the 2_41 is G/6, ie oGx3o3o3...

This would then leave the xylo- group open for the half-cube, which are charactistically oEx3.... This just recycles xylo, hydro, and cosmo- to handle respectively 1_k1, k_21, and 1_2k.
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