Talk:Folded cube graph
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Possible visual ambiguity in the figure
[edit]The current figure is intended to show the dimension-5 folded cube graph, i.e. the Clebsch graph, as a 4-dimensional hypercube with an added antipodal matching. This agrees with the construction described in the article.
However, I find the drawing visually confusing: the light-gray antipodal matching edges appear to meet at the center of the figure, but that center point is not a vertex of the graph. Thus the image may give the impression that the graph contains an additional central vertex, or that the gray edges are incident at a common point, neither of which is true.
Would it be possible to clarify the caption, for example by saying that the light-gray edges are matching edges and that their crossings at the center are not vertices? Alternatively, a version with the added matching edges drawn as curved arcs, or otherwise separated, might avoid this ambiguity.
Kounnas (talk) 19:18, 7 May 2026 (UTC)
- This graph is not planar. It is not possible to draw its edges so that they do not cross each other. —David Eppstein (talk) 20:28, 7 May 2026 (UTC)
- Thank you. I agree that the graph is non-planar, so a crossing-free drawing is impossible. My concern is slightly different. The dimension-5 folded cube has 16 vertices and 40 edges: 32 edges from the Q_4 skeleton, plus 8 antipodal matching edges. In the current drawing, the light-gray matching edges are difficult to interpret visually, because they appear to meet at a central point which is not a vertex. As a result, it is not immediately clear from the figure that there are 8 added matching edges, rather than edges incident with an apparent central point. Even if crossings are unavoidable, perhaps the caption could clarify that the gray lines are the 8 antipodal matching edges and that the apparent central intersection is not a vertex. Alternatively, drawing those 8 edges as slightly separated curves might make the 40-edge structure clearer. Kounnas (talk) 10:53, 8 May 2026 (UTC)
- Lots of edges meet at points which are not vertices. This is a necessary consequence of the graph being not planar. The vertices are very different in appearance. "Slightly separated curves" would only exacerbate the problem by creating many more crossings, while also breaking the symmetry of the drawing. —David Eppstein (talk) 17:33, 8 May 2026 (UTC)
- Thank you. I now understand the drawing. In particular, I see now that the light-gray edges are intended to extend all the way to the opposite vertices, rather than ending at a central point. Kounnas (talk) 20:07, 8 May 2026 (UTC)
- Lots of edges meet at points which are not vertices. This is a necessary consequence of the graph being not planar. The vertices are very different in appearance. "Slightly separated curves" would only exacerbate the problem by creating many more crossings, while also breaking the symmetry of the drawing. —David Eppstein (talk) 17:33, 8 May 2026 (UTC)
- Thank you. I agree that the graph is non-planar, so a crossing-free drawing is impossible. My concern is slightly different. The dimension-5 folded cube has 16 vertices and 40 edges: 32 edges from the Q_4 skeleton, plus 8 antipodal matching edges. In the current drawing, the light-gray matching edges are difficult to interpret visually, because they appear to meet at a central point which is not a vertex. As a result, it is not immediately clear from the figure that there are 8 added matching edges, rather than edges incident with an apparent central point. Even if crossings are unavoidable, perhaps the caption could clarify that the gray lines are the 8 antipodal matching edges and that the apparent central intersection is not a vertex. Alternatively, drawing those 8 edges as slightly separated curves might make the 40-edge structure clearer. Kounnas (talk) 10:53, 8 May 2026 (UTC)