Talk:Compound of five tetrahedra

Unusual property of duality

Restored comment on unusual chiral relationship with its dual, which was deleted on 19 November. Tom, please give a reason if you want to delete it again. Steelpillow 19:28, 24 December 2006 (UTC)

Sorry. I didn't understand it, what was unusual, or who believed what. I'm afraid I deal best with examples: (like common polyhedra A,B,C imply THIS, but this isn't true in general, for example, D,E,F.) I basically don't understand the context of this paragraph here in isolation. Tom Ruen 09:13, 25 December 2006 (UTC)

OK I've tried to make things clearer. Sorry, I just don't have time to prepare illustrations. Steelpillow 11:27, 26 December 2006 (UTC)

Is there a meaningful way in which two non-congruent figures can be said to have the "same" or "different" chirality? It seems to me that the "unusual" property only means anything when limiting ourselves to polyhedra that are self-dual (up to congruence). I think the section about the "misconception" is uninterpretable as written. 2601:645:8302:635D:DD9B:EB92:3C51:1DDD (talk) 23:01, 27 September 2015 (UTC)

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Unusual Property of Duality 2

I don't know if this is following the proper Wiki etiquette but I made a comment in the section above requesting a clarification of what it means for two non-congruent chiral polyhedra (or compounds) to have the "same chirality" or "different chirality", but I think the comment may have been overlooked because the section is old. It seems to me that the notion is only well-defined in the case of congruency (unless I'm mistaken any chiral polyhedron can be continuously deformed into its enantiomorph without passing through an achiral configuration, which would lead to the conclusion that any general classification of chiral figures into two chiralities would have to be essentially arbitrary and lack nice properties). But I don't understand the section in question to be restricting its claim to self-dual chiral figures. If it is to be interpreted as restricting its claim in that way, that should be made explicit and examples of such self-dual figures should be given. If not, then either the notion of "same" chirality across non-congruent figures its using should be made more clear, or the section should be reduced to the claim that it has the unusual property of being dual to its enantiomorph without discussion of other chiral figures (since self-duality and chirality is an interesting combination of features in general, it's still worthy of note). 166.177.251.89 (talk) 20:33, 6 November 2015 (UTC)

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density

It has a density of higher than 1.

Seems trivially true. I would assume it's 5 … ? —Tamfang (talk) 18:29, 24 August 2023 (UTC)

It's at least not trivial; I presume it's referring to its density within its convex hull, though that should probably either be clarified or removed. (I don't think it can be 5 through any reasonable definition, since not every point in the solid is in the union of all five tetrahedra; OTOH, if we're considering density within the polyhedron itself then it's trivially greater than one.) Shaterri (talk) 17:08, 7 December 2023 (UTC)

Oops — I didn't realize that there was a different concept of density at play. I agree that this seems trivial to me. Shaterri (talk) 17:10, 7 December 2023 (UTC)