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What is the general approach for maintaining good, quads-only topology when encountering an arbitrary polygon with more than four sides?

No matter how hard I try to keep a good topology, sometimes I still find pentagons or hexagons in my meshes. This happens especially when cutting/extruding organic shapes in a box-modeled mesh.

For example, this model has a clean topology with only quads: Clean topology

But when I cut a triangle into the mesh, it's still mostly quads, except for a few pentagons and hexagons: Pentagons, oh no! Hexagons, oh no!

My initial reaction is to cut the hexagons in half to make two quads. But the new quads aren't square at all anymore. I have no idea what to do with the pentagons.

Here's an example of a "real" model where a decagon was created in the topology and shoulderblade of this dog: More pentagons!

I also encounter eccentric polygons when connecting a highly detailed part of an organic model to a less-finely detailed part. For example, this dog's face has more detail than the back of the head. I tried to convert this heptagon to quads with no success: enter image description here

Many Stack Exchange questions address this question for specific examples of meshes:

Most of these answers work under the premise that the number of sides is even or that the large polygon has an even number of faces.

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  • $\begingroup$ The dog topology looks just fine. What’s the problem? $\endgroup$
    – TheLabCat
    Jul 11 at 0:04
  • $\begingroup$ Thanks! For this model, I'm primarily concerned about the face, especially the lower cheeks. When I see other models, they usually comprise a nice grid of mostly square quads, and those deform well during animation. The cheeks here seem to lack that grid pattern. Also, the little triangle at the top corner of the mouth might be problematic post-rigging. $\endgroup$ Jul 11 at 1:53
  • $\begingroup$ This is more of a general question though, I care much more about learning how to make good models than rescuing/improving this one. $\endgroup$ Jul 11 at 1:54
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    $\begingroup$ You dont' always need to use quads, if you have tris and ngons and it doesn't create artefacts and doesn't bother your topology flow, you dont't have to care. About the file you share, it really depends on your goal, you could leave the topology as it is and even dissolve some edges, you could make it only quads (actually you can divide a triangle with 3 quads) but I'm not sure it's really useful? It 's really case by case, and I'm not sure that it has a sense to create a topology with only quads for your shared file, unless you explain a bit more. $\endgroup$
    – moonboots
    Jul 11 at 7:17
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    $\begingroup$ For your dog topology, it could be better, maybe share it if you want people to try to improve. I would make the topology turn around the mouth $\endgroup$
    – moonboots
    Jul 11 at 7:20
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Topology depends of what type of model you're creating, since every model is different...

When u want to extrude something in a certain face, but also preserve quads, u can click "i" or "Ctrl i" (can't remember the correct key), and it will make an inside extrusion that u can scale with the mouse. This can be made in a single face, or multiple faces.

Now, a "lazy" way to fix bad topology on a model that has tris and n-gons, is to use Subdivision Modifier, which smoothes your mesh, and converts the tris and n-gons into quads by making a bunch of loops... However, this might not be a good method for any kind of model, since your mesh could lose the original shape, and become more mid/high poly.

Here are a few tutorials about topology that could help (u can search for more in YouTube if u need):

https://youtu.be/rwW6HpOcAuw

https://youtu.be/xo9JRPhGi68

Hope it helps!

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