TITLE: Why are they called the dihedral groups?
QUESTION [5 upvotes]: Dihedron, two faced solid. It refers to the intersection of two planes. In what way are intersecting planes involved in these groups?

REPLY [6 votes]: The wiki page on this topic pretty much addresses this.
The polygon under examination has a "front" and a "back" which you can think of as being two different colors. They are basically two polygons back-to-back sharing edges and vertices. With vertices labeled by numbers, this allows you to see where vertices moved and if a flip occurred or not.
The linked page mentions thinking of this as a "degenerate prism" which has polygon ends, but no height, so that the two ends are back-to-back.
I can't find any reference to the "intersection of two planes" description. I can only guess it is an unclear explanation of this back-to-back description.