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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|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.



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  W. Blaschke,   K. Leichtweiss,   "Elementare Differentialgeometrie" , Springer  (1973)</TD></TR></table>