Quote -Seems like a lot of tris in that cube. I thought Poser didn't handle tris well. What am I not getting?

For flat surfaces that aren't intended to deform, it's fine to use tris. Artifacts can start happening when the surface becomes less than flat. 

The example is simplistic for demonstration purposes. It could just as easily been done with all quads but would have taken a bit longer to construct. It could also have been done with fewer polys in the center ring. 

Quote -Topology is the mathematic study of forms that are unaffected by deformations (bends, twistes, morphs, but not breaks). In that sense, your cube+cylinder, both cubes, and Vicky 6 all have the same topology.

Topology is a perfectly valid word to use. In 3D modeling its important to differentiate between topology and morphology as they both represent different aspects. Topology is the specific pattern that makes up the overall surface of a geometric shape, which loosely conforms to the traditional mathematic definition (which is very generic to begin with). Morphforms are pulled from and dependant on the underlying topology. Many things can influence morphs, but they're all dependant on the underlying topology of the model. The only other word or phrase that could best describe topology is edgeflow, which is techincally two words. 

Topology also has other uses based on the field of study. Biology, for example, or geography. 

 

Quote -
In topology and related branches of mathematics, a topological space is a set of points, along with a set of neighbourhoods for each point, that satisfy a set of axioms relating points and neighbourhoods. The definition of a topological space relies only upon set theory and is the most general notion of a mathematical "space" that allows for the definition of concepts such as continuity, connectedness, and convergence. Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints. Being so general, topological spaces are a central unifying notion and appear in virtually every branch of modern mathematics. The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.

Source: http://en.wikipedia.org/wiki/Topological_space

Source: http://en.wikipedia.org/wiki/Topology_(disambiguation) (for other uses of the word topology)

 

~Shane