I would like to plot an image of what I call a pentagonal spiral with Mathematica. A sample image of what I'd like to obtain is this (sorry for low-quality):
My initial idea was to get some kind of spiral and reduce the number of PlotPoints, but I just can't seem to get a decent accuracy using either an Archimedes sor a log spiral. The actual attempts are quite dissatisfying, as I am probably taking a wrong approach. I do not have any other ideas: even a reference to mathematical constructs that yield a similar spiral would be more than welcome. I do not know if this construction has a name, hence finding references has proven to be difficult.
What method cold I use to obtain a Plot similar to the one in the picture?