Talk:Stereohedron

"Isohedral"

@David Eppstein: Hello. First off let me acknowledge I made a mistake in my initial edit message, you are right that in this case the facets are 3-faces, I meant to say it is more commonly used to refer to something which is transitive on its 2-faces, (I think I got confused trying to juggle terms with multiple defitions, or maybe I just hit the wrong key) which is indeed what the linked article covers. My intention with the edit is to move away from language with multiple ambiguous meanings requiring meaning to be inferred from context, to simply what is meant. "Isohedral" in this context is intended to mean facet-transitive. I don't think this is at all unnecessary extra technicality, in fact I think it is quite the opposite, it is less technical since it decomposes the word into two smaller parts with clear meaning. I'm not sure how a reader who is not familiar is intended to understand a term like "isohedral" especially when it links to an article which gives an incompatible definition. AquitaneHungerForce (talk) 15:15, 23 March 2024 (UTC)

There is nothing specific to 2-faces in isohedral. It is always the facets, the faces of the highest dimension. I don't even know a non-compound word for 2-face-symmetric objects. I certainly wouldn't use isohedral to mean a 2-face-symmetric honeycomb or 4-polytope. As for what the reader might understand, that's why we gloss the term. —David Eppstein (talk) 17:00, 23 March 2024 (UTC)

Let me quote from the linked article:

In geometry, a tessellation of dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit.

and later:

A facet-transitive or isotopic figure is an n-dimensional polytope or honeycomb with its facets ((n−1)-faces) congruent and transitive. The dual of an isotope is an isogonal polytope. By definition, this isotopic property is common to the duals of the uniform polytopes.

• An isotopic 2-dimensional figure is isotoxal, i.e. edge-transitive.
• An isotopic 3-dimensional figure is isohedral, i.e. face-transitive.
• An isotopic 4-dimensional figure is isochoric, i.e. cell-transitive.

I can see a potential argument that "face" in the first section is intended to mean "facet". However the context strains this reading. The article Face (geometry), which it links, doesn't mention this usage. It says face is a 2-dimensional object or an element of any rank. And the same article then discusses "facet-transitive" or "isotopic" explicitly, as a concept separate from isohedral.

The gloss is actively making it harder to understand what is meant. Why use a word that is riddled with so much ambiguity when we could just say what is meant with two unambiguous words? AquitaneHungerForce (talk) 17:30, 23 March 2024 (UTC)

If "facet-transitive" is overly technical, maybe a solution would be to not use either terminology? The explanation after is perfectly servicable (and by WP:TECHNICAL should actually come first). I don't have any need for the term, I just really think we should remove isohedral as it only makes things confusing. AquitaneHungerForce (talk) 18:02, 23 March 2024 (UTC)

This is merely the standard confusing between face in low-dimensional tilings and polyhedra and facet in higher-dimensional geometry. Isohedral, for 3d honeycombs, means exactly 3-face-transitive. —David Eppstein (talk) 18:37, 23 March 2024 (UTC)

Yes, absolutely. I am non insisting that "isohedral" means anything in particular. Words don't have transcendental meaning just usage. The usage in the article isn't wrong, and sources use it that way. It's merely confusing in this context. I think we agree on this? So we should change it, to express the ideas without confusion. AquitaneHungerForce (talk) 18:54, 23 March 2024 (UTC)

How can there be confusion when the first sentence of the article immediately defines what it means by the term? "Isotope", on the other hand, is a more-familiar word with totally-unrelated meanings, and can only be understood with a technical aside explaining that it has nothing to do with the chemistry meaning. —David Eppstein (talk) 19:28, 23 March 2024 (UTC)

I make no argument in favor of "isotopic". While its meaning was instantly inferrable to me, looking into it I can't find any sources using it and I suspect it's actually a WP:NEO issue that has worked its way into the isohedral figure article. (These polyhedron related articles are brimming with WP:NEO and WP:OR garbage.)

I still don't see why this article should use an ambiguous term when a less technical non-ambigous term exists, and I especially don't see why when using that term the article should link to the other definition. Why can't this just say what is meant? AquitaneHungerForce (talk) 19:47, 23 March 2024 (UTC)

@David Eppstein: Hello again. I really don't understand your point of view here, but I would like to. I think this could be improved if we could understand each other's concerns. As I stated I believe the link to be harmful since that article defines the concept in a way which is incompatible with this one. I also think we should prefer "facet-transitive" since it is non-ambiguous and less technical. I also think that the plain explanation should come before the technical term per WP:TECHNICAL. Do you disagree with all three of these? Could you explain your disagreement? AquitaneHungerForce (talk) 17:36, 17 April 2024 (UTC)

My point of view: We have an entire article on TILINGS WHOSE TILES ARE ALL THE SAME, calling them ISOHEDRAL. That includes both tilings of the whole space (honeycombs in 3d) or the tiling of a polyhedron or polytope by its faces. For some reason you want to censor that word and the link to that article from this one, which is about the prototiles of 3d TILINGS WHOSE TILES ARE ALL THE SAME. I don't understand why you want to censor this, I don't understand why you have this wacky interpretation that isohedral means 2-face-transitive (it doesn't), and I don't understand why your changes are in any way an improvement. —David Eppstein (talk) 18:15, 17 April 2024 (UTC)

The definition you provide is not the one provided by the article. I implore you to read it again. It defines it as face-transitive. If you feel strongly that facet-transitive is somehow the correct definition of the word, I feel like your time would be better spent on that article. I don't have an opinion as to which definition is "correct", as far as I'm concerned we can define whatever word to mean whatever. My issue is entirely with linking to the definition which is wrong for this article. I may not understand, but I can except that you feel strongly that isohedral has a particular meaning. Why not use facet-transitive though? It seems to sidestep this issue. I would like to know if there's some issue with this term that makes it unacceptable. AquitaneHungerForce (talk) 18:31, 17 April 2024 (UTC)

It defines it as "face-transitive" using a definition of face that means the tiles of a tiling. You read it again. As for "it seems to sidestep the issue": yes, that is what I meant by censoring the article to avoid using the word that should be used and to avoid using the link that should be linked. It's a sidestep that should not be taken. —David Eppstein (talk) 20:03, 17 April 2024 (UTC)