We explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?.
These devices also start with the monogon, a plane mirror, and include the bigon, a two-sided mirror, the trigon, quadrigon, and general n-gons.
An end-compressing monogon for F is a monogon properly embedded in the complimentarysic] region C which is not homotopic (rel. boundary) into \partial C.