Maintaining Good Topology When Part of a Mesh Becomes Non-Quad

Question

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:

But when I cut a triangle into the mesh, it's still mostly quads, except for a few pentagons and hexagons:

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:

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:

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

• Problem faced while doing re-topology - can't maintain quads
• maintaining quads when cutting circles into mesh
• How would you cut a shape out of an object using another object?
• How to party add geoetry while keeping good topology (Cat nose)
• Apply complex hole pattern to simple face while maintaining good topology
• How to Remove these Ngon's with good topology?

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.

Answer 1

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!