Talk:Jessen's icosahedron/GA1

GA Review

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Reviewer: Kusma (talk · contribs) 20:55, 7 January 2022 (UTC)

I'll review this one over the next few days. —Kusma (talk) 20:55, 7 January 2022 (UTC)

Overall progress and general comments

Good Article review progress box Criteria: 1a. prose () 1b. MoS () 2a. ref layout () 2b. cites WP:RS () 2c. no WP:OR () 2d. no WP:CV () 3a. broadness () 3b. focus () 4. neutral () 5. stable () 6a. free or tagged images () 6b. pics relevant () Note: this represents where the article stands relative to the Good Article criteria. Criteria marked are unassessed

Nice article about an interesting geometric object. Great images, all correctly licensed. Happy with most things (not copyvio etc.), just some questions on what should be in the lead, a few clarifications and some minor points (see below). —Kusma (talk) 20:16, 8 January 2022 (UTC)

Prose and content review

• The six-beaked shaddock of Douady seems to have slightly more general coordinates, so it is a family of objects containing Jessen's icosahedron? (Or I misunderstand the paper). Douady isn't mentioned again outside the lead, but could be; see below.
  • You are correct; I found a source stating that Douady's family is more general but includes Jessen's icosahedron, and modified the lead to say so. —David Eppstein (talk) 00:11, 9 January 2022 (UTC)
• right angles, even though they cannot all be made parallel to the coordinate planes "made" here refers to rigid motions?
  • Rewrote, "it has no orientation where they are all parallel". —David Eppstein (talk) 22:26, 8 January 2022 (UTC)
• However, because its dihedral angles are rational multiples of pi, it has Dehn invariant equal to zero. Therefore Is this meant to be a free and modern reformulation of what Jessen says about this or are you using a different theorem about Dehn invariants here?
  • It is more or less what Jessen says in the third paragraph of his paper, except that I have substituted "rational multiples of pi" for "orthogonal", as a more general condition that would still lead to Dehn invariant zero. I wanted to avoid the false implication that only orthogonal angles would have this property. (Incidentally, if you have any suggestions for making Dehn invariant § Realizability less fearsome, I'd appreciate hearing them; the technicality of that section is a big part of why I haven't nominated that article for GA.) —David Eppstein (talk) 22:26, 8 January 2022 (UTC)
    • OK, makes sense. Basically what I was looking for is a clearer statement (e.g. in Dehn invariant) that just says "if the Dehn invariant is zero, the polyhedron can be reassembled into a cube". That is more or less in Jessen's article as you point out, so I won't argue this. —Kusma (talk) 09:56, 9 January 2022 (UTC)
• provides a counterexample to a question of Michel Demazure here you could mention Douady again, who apparently introduced the shaddock as this counterexample (or even a family of counterexamples).
  • Done. —David Eppstein (talk) 00:11, 9 January 2022 (UTC)
• constructed in 1949 by Kenneth Snelson is there a better source for this? The thesis just claims this with nothing to back it up. If it is correct, shouldn't it be in the lead?
  • Ugh. This turns out to be an enormous can of worms. The fact that Snelson introduced tensegrity to Buckminster Fuller in 1948, and then that Fuller took sole credit for the concept for some ten years until finally being cornered into giving credit to Snelson, is well documented but off-topic here. The bad blood remaining from those circumstances make all recollections of that time from either Snelson or Fuller suspect. The images of tensegrity structures in Snelson's 1958 patent [1] do not appear to include this specific shape. It is also not included in Fuller's 1961 tensegrity paper [2]. The earliest references I can find to this shape in connection with tensegrity are from the 1970s, although it's not impossible that something like this could already have been found in the 1920s by Karlis Johansons (e.g. see jstor:779210). I am not convinced the source I was using for the 1949 claim is credible for this claim (it is mostly not about history and as you say has no justification for the claim). I have edited the article to remove all historical claims about tensegrity, because it is not the place to go into the history of tensegrity in general and because we have no good sources that I know of for the history of the tensegrity application of this specific shape. —David Eppstein (talk) 01:45, 9 January 2022 (UTC)
    • I was about to suggest that you could mention Snelson with just a claim, but you are probably right that this is debate is better covered elsewhere. —Kusma (talk) 09:56, 9 January 2022 (UTC)
• certain pairs of equilateral- by it would be easier to parse if you added "triangle". (Again a bit further on).
  • Copyedited, among other changes eliminating this awkward wording.
• The vertices of Jessen's icosahedron are perturbed from these positions in order to give all the dihedrals right angles. does this say anything other than what we already know? (Jessen vertices are at different positions and have right dihedral angles).
  • Not really. I removed this sentence and instead added a little more about how it has the same combinatorial type and symmetry as Jessen's. —David Eppstein (talk) 00:18, 9 January 2022 (UTC)
• one of a continuous family of icosahedra I'm not sure I understand the construction here. Is the continuous parameter the ratio in which I divide each edge?
  • Yes. I added a sentence saying so. —David Eppstein (talk) 22:26, 8 January 2022 (UTC)
    • I added a movable gif from Wikimedia which seems to be helpful in explaining what's going on. Igorpak (talk) 05:13, 9 January 2022 (UTC)
      • User:Igorpak: Thanks, but I think this is a bad image. This same image has been removed before because the claim that it makes in its title is false. It does not stop at Jessen's icosahedron. The position that it stops at is the one with the vertices at a regular icosahedron, not Jessen. More, it only loops back and forth over the range of parameter values from octahedron to cuboctahedron, within which the shapes are all convex (the convex hulls of what you see in the image), not the parameter values past that point where it becomes non-convex. —David Eppstein (talk) 07:13, 9 January 2022 (UTC)
        • An image that does what is promised would be nice, but if we don't have one, better not include one that doesn't show the Jessen icosahedron. —Kusma (talk) 09:56, 9 January 2022 (UTC)
        • I see. Thanks for catching this issue. Would indeed be nice to have a corrected image. Igorpak (talk) 18:35, 9 January 2022 (UTC)
• to an infinite family of rigid but not infinitesimally rigid polyhedra in which way infinite? More and more vertices, or infinitely many solutions with a fixed number of vertices?
  • Added "combinatorially distinct" to clarify that more vertices was the intended meaning. —David Eppstein (talk) 22:26, 8 January 2022 (UTC)
    • I was talking about this issue with respect to the Gor’kavy/Milka claim at the bottom of the article.
• isogonal and weakly convex should probably use {{em}} per MOS:ITALIC.
  • Ok, done. —David Eppstein (talk) 22:26, 8 January 2022 (UTC)

I think that's all I have. —Kusma (talk) 20:15, 8 January 2022 (UTC)

@Kusma: All issues responded to; please take another look. —David Eppstein (talk) 01:45, 9 January 2022 (UTC)

@David Eppstein: I think we're done once you clarify Gor’kavy/Milka. Nice work. —Kusma (talk) 09:56, 9 January 2022 (UTC)

@Kusma: I added a sentence at the bottom. I hope this suffices. Igorpak (talk) 18:49, 9 January 2022 (UTC)

@Igorpak @David Eppstein it needs a bit of copyediting. distinct from each other or from Jessen's? larger symmetry groups larger than what? no longer simplicial no longer? what is the passage of time here? Also, the sentence needs to be cited to a source.

While we're here, the external link at the bottom is nice, but could be described a tiny little bit. —Kusma (talk) 18:57, 9 January 2022 (UTC)

I copyedited the new material and removed the external link, as it didn't say much beyond what was already in the article (WP:ELNO #1). It does include a nice 3d viewable image, but it turns out to be of the icosahedral fake version, not of the actual Jessen's icosahedron. —David Eppstein (talk) 20:24, 9 January 2022 (UTC)

@David Eppstein Thanks for doing this. Igorpak (talk) 21:09, 9 January 2022 (UTC)

I was confused about the image in the link; viewing it from a better angle made clear that it is the correct orthogonal one. Restored the link, with description. —David Eppstein (talk) 21:15, 9 January 2022 (UTC)

Excellent. All done now, I'll go do the paperwork. —Kusma (talk) 22:44, 9 January 2022 (UTC)