When inscribing polygons, most polygons require two arcs to be connected at some point.
For a dodecahedron, we at one point must bisect an angle, which requires connecting two arcs. For a square, you either bisect angles or draw a perpendicular bisector; both require connecting two arcs. For an octagon, you bisect quadrants, which requires connecting two arcs.
Doubling the number of sides of an inscribed polygon is done by bisecting the segments of the circle; again, this requires connecting two arcs.
The answer is "Connect two arcs together with a compass". You can inscribe different regular polygons by creating a circle and connecting two arcs together. There are different procedures and they depends on what kind of regular polygon you will be creating.
