Hi.
Not sure what you are about to draw, what's the task in the project. As a general note, ask by the problem and not by asking directly how to achieve a *very* specific method.
Polygons offer the setting of variance and can be switched to stars, change the number of spikes, change the spoke ratio, roundness etc.
It is a parametric object as per se.
Paths are the basic elements in inkscape. They consists of segments connecting nodes.
The m, p, and the numbers indicate the node's coordinates and also the handles coordinates one after another, in the path's direction. In addition the path can have amongst the style attributes a sequence defining each nodes types -smooth or cusp, like csscccccscsssss etc.
The polygon tool draws a parametric object which needs to be converted to a path so then its nodes can be placed around.
Like, as you wrote, polygons don't have any indication of their "nodes" positions, since they are generated "on the fly".
All in all, illustrator probably describes the node editing relative to the parametric object. Cannot tell since I don't have illustrator, but I have serious doubts if you could simply change the side of the polygon after you modified one of the node's position.
Which, then all comes down you need a solution to your problem. The suggested development part would hardly happen since there is no real description of the desired feature to be implemented. Even if there was, you'd need to add it to the new bug tracker's as a feature request somewhere on github. Then it'd take quite some time even if it got attention to be worked on.
Soo, my guessing is you are trying to draw somekind of gear/cogs?
Probably a pattern along path effect could solve any problems yet, even better there is an extension somewhere to render gears with an evolvent tooth profile based on given parametres.
