Talk:Isogonal figure

Poll to move contents from vertex-uniform

Vertex-transitive is a standard term for polytopes. Vertex-uniform was an incorrect term from uniform polytopes which are are vertex-transitive.

• Yes - Tom Ruen 22:25, 3 February 2007 (UTC)

• Yes and no. I would prefer to move it to Isogonal because it's shorter and has been around longer, and redirect from Vertex-transitive. Steelpillow 13:04, 6 February 2007 (UTC)

Hmmmm... no other opinions offered. Isogonal isn't as clear to me. I have to vote for clarity over compactness. I suppose it means "equal angles". A concave polygon can have equal angles and not be vertex-transitive. Tom Ruen 05:38, 10 February 2007 (UTC)

+---+
|   |
|   +--+
|      |
+------+

That figure has five interior angles of 90 deg and one of 270 deg. Those are not all equal!

Isogonal does also imply that the vertices are transitive, i.e. they lie within the same symmetry orbit, something like this:

     o---o
    /     \
   /       \
  /         \
 o           o
  \         /
   o-------o

'Isogonal' is the longest-established of the alternative synonyms we are discussing, and its meaning is beyond question. But OK, I can accept the main heading as the clearer one, with other pages reditrecting to it. Let's go with vertex-transitive. Steelpillow 18:30, 10 February 2007 (UTC)

Whoa! Just found that Vertex-transitive is a disambiguation page. We can't call ours that. 'Vertex-transitive polyhedron or tiling' is a bit of a mouthful. Best ideas, anyone? Steelpillow 19:12, 10 February 2007 (UTC)

What I'd propose is:

1. Take over Vertex-transitive
2. Add two sections, one for graphs, one for polytopes
3. Put the graph one first with a short summary and a "For more information see: Vertex-transitive graph.
4. Then move this content there. If the polytope content got large enough, a Vertex-transitive polytope article could be created with more detail, and return Vertex-transitive to a short version.

Tom Ruen 21:23, 10 February 2007 (UTC)

Hopefuly a fair job, I moved them all, and relinked to new names. Tom Ruen 02:45, 11 February 2007 (UTC)

Archimedean

No mention of Archimedean solids? --ReyHahn (talk) 11:52, 19 November 2021 (UTC)

Poll: split off polytopes and rename to vertex-transitive tilings

I think it is time to reconsider a change from isogonal to vertex-transitive. The term isogonal is basically absent from research literature, in contrast to vertex-transitive (check arXiv search). The term vertex-transitive is (to a degree) self-explanatory or at least quickly understood and immediately relates to edge-transitive, face-transitive etc (by the way, I also suggest to rename isotoxal and isohedral). As suggested by Tom Ruen, we create a separate page for vertex-transitive polytopes (I plan to write a lot more about them). I then suggest to rename this page to vertex-transitive tilings as the term figure seems to have no clear meaning in contemporary research and has no definition on Wikipedia either. I suggest to create a page titled vertex-transitive that gives a more general definition of what this term means and then links to the different objects that can be vertex-transitive: polytopes, tilings, graphs, complexes, etc. Note that I am new here and have no idea (yet) how to execute this in detail, but think it would be the right thing to move towards. Any thoughts? MWinter4 (talk) 19:36, 31 August 2023 (UTC)

Too unspecific redirects

The following redirects to this page are too unspecific.

• Vertex-transitivity
• Vertex-uniform
• Vertex transitive
• Vertex-transitive

Many more mathematical objects than just polytopes can be vertex-transitive, such as graphs, simplicial complexes etc. There is no evidence that polytopes are the primary use of this term, in fact, I would argue that the primary use is graph.

I cannot delete redirects, but maybe someone can? MWinter4 (talk) 11:26, 20 May 2025 (UTC)