Talk:Alexandrov's uniqueness theorem/GA1

GA Review[edit]

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Reviewer: Mike Christie (talk · contribs) 23:35, 24 February 2018 (UTC)[reply]

I'll review this. Mike Christie (talk - contribs - library) 23:35, 24 February 2018 (UTC)[reply]

{tq|a space in which every distance is represented by a path}}: I don't think I follow this. Does this mean that for any distance x, there exist two points in the space for which the geodesic has length x?
- It means that for every two points at distance x, one can map a line segment of length x in a distance-preserving way onto the space from one point to the other, unlike say a space where those are the only two points and there is no line segment between them. I'll see if I can gloss this in the article without getting too technical or off-topic. —David Eppstein (talk) 06:45, 26 February 2018 (UTC)[reply]
  That works. Mike Christie (talk - contribs - library) 12:03, 26 February 2018 (UTC)[reply]
The first part of the "Limitations" section repeats information at the end of the previous section.
- Removed from the previous section. —David Eppstein (talk) 02:59, 27 February 2018 (UTC)[reply]
However, the edges of the gluing pattern will not necessarily become the edges of the polyhedron: I don't follow this. If two edges are glued together, paths across those edges exist in the metric space; if those two edges are not paths in the assembled polyhedron then those paths won't exist on the polyhedron and can't be in its development. What am I missing?
- They become part of the metric space, but they run across the middle of faces of the polyhedron rather than being its edges. Hmm. Would it help if I uploaded this image and added it to the article? It shows four ways of folding the Latin cross into different polyhedra (one being the familiar folding pattern of a cube). From it you can see that the cube edges do not all line up with folds on the other three polyhedra. —David Eppstein (talk) 06:42, 26 February 2018 (UTC)[reply]
  So would it be correct to make it "However, the edges of the gluing pattern will not necessarily become the edges of the polyhedron, since two of the polygons may be coplanar in the assembled polyhedron"? Yes, the image is helpful, though it'll be tricky to make a concise caption for it. Perhaps just use two of the patterns? Mike Christie (talk - contribs - library) 12:03, 26 February 2018 (UTC)[reply]
  I ended up adding a new image File:4-hex octahedron.svg instead, as well as more description of this issue. —David Eppstein (talk) 02:59, 27 February 2018 (UTC)[reply]

-- Mike Christie (talk - contribs - library) 11:58, 25 February 2018 (UTC)[reply]

Everything looks good; promoting. Mike Christie (talk - contribs - library) 11:02, 27 February 2018 (UTC)[reply]

Thanks! —David Eppstein (talk) 18:10, 27 February 2018 (UTC)[reply]