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• A geodesic with multiple points contains at least one simple monogon.
• There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.
• 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?
• According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s+2 edges, and 4s+2 faces. Of these faces, 4s+1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.
• There is no monogon in M-int(N(B)), ie, no disk D⊂ M-int(N(B)) with ∂ D=D∩ N(B)=α∪β, where α⊂∂_vN(B) is in an interval fiber of ∂_vN(B) and β⊂∂_hN(B).
• An end-compressing monogon for F is a monogon properly embedded in the complimentary region C which is not homotopic (rel. boundary) into ∂ C.
• A new optical scanner is described which serves as a monogon or single-facet device, providing one scan per shaft rotation.
• 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.