Why are wireframes used?
Games don't really use wireframes much, but they might be useful for HUD items etc.
Asset creators, designers and engineers use wireframes to see whats inside objects. TO clarify the edged between elements or to preview unimportant aspects.
Image 1: Different 3D views (click to zoom)
Engineers and Architects also may have very ...
Regarding wireframes as an edge list.
Wireframe models are used in engineering and CAD they provide several benefits. The Wikipedia page you linked has some benefits, this AutoCAD page has some more. Wireframe are used less in games and movies since they are generally more concerned about the visuals and wireframes are more concerned about design (form over ...
Easiest is probably OBJ or PLY. But can not really dump material info like you want. But you could encode it in a per face value. Both formats use similar windup rules to yours.
Step (.STP) is out of question. Its a a few orders of magnitude more complex than what you have and does not deal with polygons, but rather a BREP model.*
Ascii STL might work. But ...