# Talk:Parallelohedron

This review is transcluded from Talk:Parallelohedron/GA1. The edit link for this section can be used to add comments to the review.
Nominator: David Eppstein (talk · contribs) 07:13, 6 April 2025 (UTC)
Reviewer: Dedhert.Jr (talk · contribs) 05:55, 30 July 2025 (UTC)
I have added the new image to the lead section. Please wait for the comments. Dedhert.Jr (talk) 05:57, 30 July 2025 (UTC)


### Spotcheck
Spotchecking the citations and sources according to the oldid=1303158496, as follows:

[1]: okay, with explaining the five polyhedra
[2]:
(a): okay, in p. 349
(b): Hermann Minkowski's theorem mentioned on p. 349, okay
(c): okay, but excluding the Voronoi statement on p. 359
(d), (e), (f), (g), (h), (i): It turns out I could not find the symmetric forms of the five polyhedra you have written so far, as well as how they can be generated. Perhaps I missed the pages
(j): okay per (b)'s statement of mine.
(k): okay per (c)'s but including Voronoi statement
(l): okay per (k)'s
[5]:
(a): okay
(b): mentioned 
  
    
      
        
          2
          
            d
            +
            1
          
        
        −
        2
      
    
    {\displaystyle 2^{d+1}-2}
  
, okay
(c): mention the higher-dimensional parallelotope at Voronoi's conjecture of P4; might have to check it twice
[7]: at p. 753, okay
[9]: mentioned in the abstract section, okay
[10]: oookay
[11]: mentioned in the abstract section, okay
[12]: (a,b) are okay, although it's hard to keep the connection to the source with (a)—any interpretation?
[13]: okay, perhaps some WP:CALC that I could not find the number of parameters for every five polyhedral
[14]: historically, okay. However, what I could not understand is whether it even allows for translating Russian journals. I won't mind if you answer it or not.
[19]: okay
[20]:
(a): in the conclusion section via arXiv, okay
(b, c, d): okay
[21]: perfectly fine in the abstraction section via arXiv
For [3, 4, 6, 8, 15, 16, 17, 18, 22], can't access. So I'll pass them. Dedhert.Jr (talk) 07:10, 30 July 2025 (UTC)


### Comments
Just a small number of comments

Since some parallelohedral articles mention the generators, zones, and belts, perhaps you could illustrate a picture of what they are?
Do elongated dodecahedron has Coxeter–Dyankin diagram? Otherwise, you could have removed the already existing four.
Awaiting the replies. Dedhert.Jr (talk) 07:17, 30 July 2025 (UTC)

It doesn't need a new illustration; we already have one that works. I added an explanation of the generators, zones, and belts to the caption of the lead image.
I removed the Coxeter–Dynkin diagrams, also because I don't know where if anywhere they are sourced. —David Eppstein (talk) 18:13, 30 July 2025 (UTC)
@David Eppstein. Okay, just one more: 2(d), (e), (f), (g), (h), (i) in the spotcheck. I'll pass after you reply. Dedhert.Jr (talk) 02:47, 31 July 2025 (UTC)
Okay. I see no problems with the images and writings. Topic is broad. No edit war. Everything is neutral. Sources are fine, alongside with verification. These are all according to WP:GACR.  Pass. Dedhert.Jr (talk) 03:59, 31 July 2025 (UTC)
The five types are below Fig.143 on p.357 of reference [2] but the generators and most symmetric form are listed there only for the truncated octahedron. For the others, I added a new reference by Horváth for their most symmetric forms (see Theorem 10, p. 40) and another new reference to an old paper by myself for their generators (because I did not find these described elsewhere). It does describe each set of generators, but mostly as formulas for vectors rather than as text. I took out the part about using one edge and the long diagonals of a cube for the extended rhombic dodecahedron because the source uses different generators that produce regular hexagon faces.