## How exactly should "CRH" be expanded?

Discussion of known convex regular-faced polytopes, including the Johnson solids in 3D, and higher dimensions; and the discovery of new ones.

### How exactly should "CRH" be expanded?

We all know that "face" is ambiguous in higher dimensions. Wendy proposed "CRH" instead of "CRF". The latter means "convex regular-faced", but what about the former?
Here are some options:

"convex regular-hedrous" viewtopic.php?p=17851#p17851
"convex regularly-hedrated" viewtopic.php?p=24388#p24388
"convex regular-hedroned"
"convex with regular hedra"
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mr_e_man
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### Re: How exactly should "CRH" be expanded?

Richard Klitzing is using the 3d term 'face' to stand for a hedron

Gosset studied all the convex regular face (pg sense) beside the regulars, a scattering to eight dimensions.

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wendy
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### Re: How exactly should "CRH" be expanded?

Another way to define it is the set of polytopes whose 3D elements are regular, uniform, or Johnson. Not a super-neat definition but it works and produces the same set. So we might call them the RUJ polytopes or 3RUJ polytopes.
quickfur
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### Re: How exactly should "CRH" be expanded?

wendy wrote:Gosset studied all the convex regular face (pg sense) beside the regulars, a scattering to eight dimensions.

I doubt that he did. Else all the findings of the Blind couple would have been anticipated!
I rather assume that he just considered those which belong to a non-reducible reflectional symmetry group with (like for regulars) just a single end node of the diagram is to be ringed. (Sure this characterization more is a posteriori, i.e. already knowing about CD diagrams ...)

--- rk
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### Re: How exactly should "CRH" be expanded?

I mean, what words do the letters "CRH" stand for?

"Regular-faced" sounds more natural than all of the variant wordings I listed.
...possibly because "face" is a noun and a verb, but "hedron" is only a noun.
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mr_e_man
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### Re: How exactly should "CRH" be expanded?

convex regular hedral isthen adjective form.
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the dream we dream together is reality.

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wendy
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