Evolvent

An evolvent is a region in the plane that is isometric to a given region on a developable surface. Example: The evolvent of the side surface of a cone cut along a generator is a planar sector. The approximate construction of an evolvent can be achieved graphically by means of descriptive geometry.

The evolvent of a polyhedral surface is a set of polygons (the faces of the evolvent) with a rule for glueing their sides that defines a polyhedral metric isometric to the internal geometry of the polyhedral surface. The faces of the evolvent need not coincide with the real faces of the surface: when laid on the surface they may be folded.

References

[a1]	W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973)