Regular vs. Irregular Vertices in a Mesh

Question

Hi everybody,

Reading about Geometry Processing, I have realized that people in this area are very interested in regular vertices(degree=6) rather than irregular ones.

Can anybody give me reasons why this is an important property? Suppose that we can have a mesh with all regular vertices (genus 1) but with a very poor geometry positioning for the vertices.

So, is there any specific reason why connectivity is this much important regardless of the geometry?

Thanks