1394:). For the Laves graph a more intrinsic choice might be the union of four of those 17-sided plesiohedron things. For the BCC lattice, ignoring the Laves graph that it is the translational symmetries of, a simpler choice is the bottom half of the unit cube, with a tiling that arranges the half-cubes into planar checkerboards and then stacks up the checkerboards into 3d, but offset by a half-unit in each direction from one layer to the next. (These are not the parallelepipeds you would get from a basis, and their tiling is not face-to-face the way the parallelepiped tiling would be.) But you don't even need to decide on a fundamental domain in order to compute the volume. Just pile together your basis vectors as the rows of a matrix and calculate its determinant. The point of the L^3/V formula is that it is unitless, so the coordinates of your starting arrangement don't affect the result. But if we use the integer coordinates, we get four vertices and 12 halves of length-
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522:"Form" = "shape" = its geometric description in terms independent of scale and position. The integer coordinates are specific to one scale and one position. They would not be valid, for instance, for instances of this graph coming from certain crystals, unless you picked a coordinate system that was very specific to the crystal. "Arrangement", maybe? —
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1317:. Is that correct? I think the fundamental domain should be also announced as a "parallelepiped", for a slightly broader understanding—people probably wouldn't confuse it with some other random choice of parallelepiped. Also, this is why it'd be nice to supply the basis vectors, so that the reader can more quickly follow along with the
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I don't either. That looks like it could be a German pronunciation except that I'm pretty sure the vowel marked as a schwa would have a distinct sound from other schwa-vowels that most native speakers of
English would be unable to distinguish. LAH-vess not LAH-vass or LAH-vuss even though those would
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I do appreciate the spot-checking, actually. Not because it indicates a lack of trust, but because I think it should be done more generally as part of all GA reviews, and because it has a chance of turning up places where I was sloppy in sourcing or didn't myself adequately check sourcing that others
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Ah, that is nice. Appears to use WebGL-based ray marching, which is super cool but impossible for us, and as far as I know
Knowledge doesn't support 3D file formats with coloring. Conceivably the balls could have different sizes, but I think that'd only work for two colors, maybe three. Do you think
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This is all pretty standard, and much of it probably sourceable in sources that talk about the body centered cubic lattice (which is what we have here, scaled by a factor of four), but I think the details are off-topic for this article. Fundamental domains are not always parallelepipeds. They can be
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Isn't the claim that this shape is "its classic shape" the sort of editorial opinion that would need sourcing and attribution? Also at this point in the article the graph has only been stated to be a specific "system of points and line segments" so it can be recoordinatized but not given a different
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in this article, because that goes to an article that describes it in terms of crystallography rather than mathematics, and crystallographically the Laves graph is very different than the BCC lattice even though mathematically the translational symmetries of the Laves graph are a BCC lattice. (Part
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Could a version of this be done, where the eye location is a bit farther from the grid? Or maybe even at infinity? The issue is that when rotating it, it is hard to see the symmetries. So, from one angle, you can see hexagons, but due to the perspective, the other nearby hexagons are ruined. There
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But then I would have to pick a basis? The lattice itself is already described: "translations that add even numbers to each coordinate (additionally, the offsets of all three coordinates must be congruent modulo four)". So some subset of three out of four of (4,0,0), (0,4,0), (0,0,4), (2,2,2) (but
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could include a simple example in R^n that's not just a parallelepiped. It makes sense that the choice is arbitrary. Is it too off topic for even a footnote? The determinant calculation seems straightforward, and perhaps enlightening in lieu of a detailed diagram of the integer coordinates/simple
479:"Its points can be given integer coordinates" Understanding this statement requires a somewhat subtle understanding that the Laves graph enjoys the same label after any isometry. How about "In its classic shape, its points have integer coordinates", something like that
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Added before "gyroid". But in the specific "soap film structures" phrase, I really meant actual physical soap films, summarizing the later text "has also been observed experimentally in soap-water systems", and not their mathematical abstraction as minimal surfaces.
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So, to rephrase, this graph may be constructed by taking a particular fourth of all integer-coordinate points and connecting every pair that's sqrt(2) apart? I think the phrasing might be a confusing here; it should be made clear that the points under consideration
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Seeing as the EMST review is finishing up, I'll grab another one. Excepting the more abstract graph theoretic concepts, I feel like this topic can be made pretty accessible to the layperson, so I'll try make suggestions toward that.
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are other symmetries too, but the perspective blurs them out, making them very hard to discern. Ever-so-slightly smaller spheres and cylinders might help, so they don't collide when viewed from some of the symmetric directions.
1666:: Thoughts on this STL model? I might try reduce the file size; not sure why it's so large. (Edit: silly me, the cylinders are doubled.) I can also remove extraneous points, or perhaps omit points that aren't fully connected.
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any shape that tiles space under lattice translations. Escher's animals, maybe. For something I did recently involving 2d lattices I found it more convenient to use axis-parallel non-convex hexagons (see last image in
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It is possible to interleave two copies of the structure, filling one-fourth of the points of the integer lattice, while preserving the fact that the adjacent vertices are exactly the pairs of points that are
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Mention the minimum-count cycle in the Laves graph in the lead, I think. It's interesting, and the lead image is a bit... dense. My first impression was that the cycle count was eight, a la cyclooctasulfur.
1074:, which is ridiculous. Haven't seen anyone instating an inferior alternative, but maybe that guideline should be adjusted to reflect actual practice. I kind of understand deprecating references like
1140:. For instance, "Coxeter (1955) named..." is a piece of text, but "The Laves graph is embedded in this skew polyhedron (Coxeter 1955)." would be the deprecated format of parenthetical referencing. —
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while preserving the fact that the adjacent vertices are exactly the pairs of points that are sqrt(2) units apart, and all other pairs of points are farther apart
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629:"add even numbers to each coordinate" ah, but we've only been speaking in abstract terms so far in this section. Perhaps prepend "interpreted geometrically"
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1187:: All good. : Fine : All good. For the first ref I like how it talks about duality but that's too much for this article. : Can't access : Fine, also
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316:? Googling the 8-srs network turns up a few results - should a proper paper be cited, or does the youtube video qualify as a citable source?
677:"but does not give it the same geometric layout" doesn't have the same geometric layout, or doesn't endow it with a geometric layout at all?
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all sound almost the same to
English and American ears and be pronounced so briefly as to be heard as a schwa. But that's only a guess. —
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Cool, will do that going forward. I definitely don't want to be a rubber stamp, although I don't think I've been thus far in my reviews.
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How about "In one form"? That's not editorializing. The thing is that "points can be given" is more confusing than simply "points have".
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The source doesn't appear to say, and it's not obvious just from looking at the source's illustration of these two interleaved copies. —
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of the issue is those other symmetries that are not translations.) So the link would be much more likely to confuse than illuminate. —
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Beyond that, I'm quite happy with the article. Discussion regarding improvements/location of my STL can go on the article talk.
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not the first three) can be used as a basis, but I'm not sure of a source that picks out one of those bases or any other one. —
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572:"The two copies are mirror images of each other" specify whether it's simply a reflection, or a less intuitive rotoreflection
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is the statement elsewhere that the whole graph is chiral, so mirroring in the plane of the three edges doesn't work. —
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1629:, not partially lie within, the fundamental domain—cleared my remaining confusion. Will probably pass tomorrow.
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That's all for now. Will do a second pass per usual after we discuss. As an aside, I realize that the letter of
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better but I don't know that it's possible to incorporate anything like that here except as an external link. —
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to the vertices, which one can think of as a layout that is different than the standard one for this graph. —
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Having a 3d model seems like a useful addition. I like the color and animation and smoother rendering in
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Unfortunate. Anyway, I quite enjoyed your new explanation, in particular the part that the edges should
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I agree with your interpretation; I just think the guideline should be edited to make that clear.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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can be realized by a symmetry." The only part missing from that sentence to be sure it's really
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448:"soap film structures" Maybe link to somewhere about minimal surfaces? Dunno the best link
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Any way to put a period after the OEIS parentheses? Can't seem to figure that out.
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Four by four by two unit cells of the Laves graph, connecting adjacent points
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https://11011110.github.io/blog/2022/04/03/dissection-into-rectangles.html
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Two different bases and two different fundamental domains for a 2d lattice
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shape. The more abstract graph-theoretic view is only introduced later. —
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as I don't think there's particularly special place it should be put.
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to apply). If that particular calculation is unsourceable then meh.
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I rewrote this paragraph to try to make it more self-contained. —
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Done. You just put a period after the OEIS template, like "{{
644:"form a three-dimensional lattice" supply the basis vectors?
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the one-fourth subset, not the integer lattice as a whole.
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That makes sense, visually as well. Any source for that?
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calculation. Is there a verifiability/OR concern there?
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But the same term is already linked only one line up? —
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The article mentions two networks can be interleaved:
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1504:{\displaystyle (6{\sqrt {2}})^{3}/32=27/{\sqrt {2}}}
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848:|A342235}}." —
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102:Did you know
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91:Did you know
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80:A fact from
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1172:Second pass
814:Ok, done. —
399:transcluded
246:Mathematics
237:mathematics
193:Mathematics
120:Fritz Laves
107:Laves graph
96:check views
82:Laves graph
27:Laves graph
1770:Categories
1098:references
352:Authorship
338:GA toolbox
111:(pictured)
37:under the
1198:put in. —
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411:Reviewer:
375:Templates
366:Reviewing
331:GA Review
318:JasonHise
142:Knowledge
86:Main Page
1094:WP:PAREN
1062:WP:PAREN
424:contribs
380:Criteria
164:GA-class
47:reassess
1541:WP:CALC
1191:: Fine
1135:harvtxt
1105:harvtxt
273:on the
88:in the
1720:Ovinus
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1178:WP:ANI
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1130:, not
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170:scale.
54:Review
1649:Model
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265:Low
49:it.
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