Talk:Plesiohedron

A fact from Plesiohedron appeared on Wikipedia's Main Page in the Did you know column on 13 March 2017 (check views). The text of the entry was as follows:

Did you know... that Euclidean space can be completely filled without overlaps by copies of any plesiohedron, a type of convex shape whose known examples have up to 38 sides?

A record of the entry may be seen at Wikipedia:Recent additions/2017/March. The nomination discussion and review may be seen at Template:Did you know nominations/Plesiohedron.

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Polyhedra

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Triangular prism[edit]

I think a triangular prism fits the definition of a plesiohedron and is a recognizable enough shape to warrant mentioning if that is correct. I am holding off inserting that myself in case I am misunderstanding. Rlendog (talk) 23:04, 6 March 2017 (UTC)[reply]

Yes, I agree. I'll add it. —David Eppstein (talk) 23:15, 6 March 2017 (UTC)[reply]

I'm unsure. Do some of the Laves tiling honeycombs also apply? Tom Ruen (talk) 01:12, 7 March 2017 (UTC)[reply]

What you need is for there to be a single tile type, and for there to exist a placement of dual vertices such that every primal tiling edge bisects the corresponding dual tiling edge. So that's obviously true of the triangular tiling, and seems to be true for all the dual Laves tilings, but I'd want a source before putting it into the article. —David Eppstein (talk) 01:43, 7 March 2017 (UTC)[reply]

@Tomruen: the answer to your question is yes. For a reference that the 2d Laves tilings can all be realized as Voronoi diagrams, see https://books.google.com/books?id=jBWKSRexj-oC&pg=PA125 . I added this to the article: Special:Diff/770189153. —David Eppstein (talk) 23:12, 13 March 2017 (UTC)[reply]

Confusing sentences[edit]

Article currently has a few sentences that are unclear in their wording, each saying something to the effect of, "Every plesiohedron has at most 92 faces." Should this be, "Plesiohedra can have no more than 92 faces," or, "The maximum number of faces a plesiohedron can have is 92?" Morganfitzp (talk) 02:31, 13 March 2017 (UTC)[reply]

To me all three of these could mean the same, except that the third one is ambiguous: it could mean that there are known plesiohedra with exactly 92 faces (something that is not actually true). What do you think is wrong with the first one? Why do you think "can have" is clearer than "has"? —David Eppstein (talk) 02:47, 13 March 2017 (UTC)[reply]

It did seem a little weird. How about "It has been proved plesiohedra may exist with at most 92 faces, while none have been found with over 38." Tom Ruen (talk) 06:45, 13 March 2017 (UTC)[reply]

That is completely wrong (or more charitably, not what you meant it to say). It has *not* been proved that any exist (or may exist) with 92 faces. The only ones that have been proved to exist have 38 or fewer faces. What has been proved is that there are none with more than 92. To put it another way: for numbers of faces in the range [4,38], plesiohedra exist. For numbers in the range [93,∞], they don't exist. And for numbers in the range [39,92], we don't know. But your sentence (and one interpretation of talk:Morganfitzp's second sentence) states that we do know they exist for the whole range [3,92], we just haven't explicitly constructed them all. Such a statement would not accurately describe what we know. —David Eppstein (talk) 07:21, 13 March 2017 (UTC)[reply]

I thought that's what I said. How about "It has been proved plesiohedra can not have more than 92 faces, while the highest known has 38." Tom Ruen (talk) 09:13, 13 March 2017 (UTC)[reply]

This last description is clear. The assertion that "every plesiohedron has at most 92 faces" is logically off-kilter when plugging in specific plesiohedra. A cube, for example, does not have "at most 92 faces," and nor do the other polyhedra listed as examples. Morganfitzp (talk) 11:55, 13 March 2017 (UTC)[reply]

Yes, a cube does have at most 92 faces. 6 is a number that is at most 92. Rephrasing the bound negatively (cannot have more than 92) doesn't seem to me to be any kind of clarification of phrasing it positively (has at most 92). —David Eppstein (talk) 16:16, 13 March 2017 (UTC)[reply]

Or, to put it another way. What it says now: f(p) ≤ 92. What you seem to want it to say instead, because that's too confusing: not(f(p) > 92). Why you think not(f(p) > 92) is easier to understand than f(p) ≤ 92: I don't know. —David Eppstein (talk) 17:54, 13 March 2017 (UTC)[reply]

One should not need be a logistician or mathematician to comprehend this article's opening paragraphs. Some good suggestions were made on how to make the top section less confusing. Please regard these considerations in working toward something better as an inroad for the layperson who comes across this article. Morganfitzp (talk) 20:05, 13 March 2017 (UTC)[reply]

Which is exactly why I think more-convoluted ways of rewriting the same thing are not an improvement. —David Eppstein (talk) 20:28, 13 March 2017 (UTC)[reply]

Etymology[edit]

Once a verifiable source rears its head from the Loch Ness of the internet, feel free to copy and paste:

Plesiohedron (from Greek: πλησιος/plesios, "near to" + ἕδρα/hédra "base", "seat" or "face").

Until the eventuality of alleged coiners of such hedra publish the true reasons for their christening, this—according to some—is just folk etymology. Morganfitzp (talk) 23:35, 24 March 2017 (UTC)[reply]