This .NET class wraps the AcBrEdge ObjectARX class. 

The Edge class is the interface class for brep edges. This class defines the functions that are pertinent to the edge level of a brep, and thus serves as a mapping between AutoCAD edge subentities and BREP items. 

Edges are primary brep elements and thus have associated geometry (that is, curves). This class provides an indirect link between Geometry classes, Solid3d, Region, and Body.

Autodesk.AutoCAD.BoundaryRepresentation.BrepEntity
    Autodesk.AutoCAD.BoundaryRepresentation.Edge

Public sealed Class Edge
Inherits BrepEntity

public sealed class Edge : BrepEntity;

The intended use of the Edge class is to create a BREP-contexted edge for dumping curve geometry and for accessing edge vertices. 

The subentity path should contain the object ID of an AutoCAD solid, region, or body; its chained transforms; and a valid edge subentity ID. 

Singularities show up properly as vertices in loop traversals, but their associated edge subentities in AutoCAD cannot be used to directly (re)set a Vertex due to type mismatch.