Talk:Isogonal figure

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)

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: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:

::# Take over Vertex-transitive

::# Add two sections, one for graphs, one for polytopes

::# Put the graph one first with a short summary and a "For more information see: Vertex-transitive graph.

::# 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)

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

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)

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)