public enum TinEdgeType : System.Enum, System.IComparable, System.IConvertible, System.IFormattable, System.ISpanFormattable  

// search all edges
using (ArcGIS.Core.Data.Analyst3D.TinEdgeCursor edgeCursor = tinDataset.SearchEdges(null))
{
  while (edgeCursor.MoveNext())
  {
    using (ArcGIS.Core.Data.Analyst3D.TinEdge edge = edgeCursor.Current)
    {

    }
  }
}

// search within an extent
ArcGIS.Core.Data.Analyst3D.TinEdgeFilter edgeFilter = new ArcGIS.Core.Data.Analyst3D.TinEdgeFilter();
edgeFilter.FilterEnvelope = envelope;
using (ArcGIS.Core.Data.Analyst3D.TinEdgeCursor edgeCursor = tinDataset.SearchEdges(edgeFilter))
{
  while (edgeCursor.MoveNext())
  {
    using (ArcGIS.Core.Data.Analyst3D.TinEdge edge = edgeCursor.Current)
    {

    }
  }
}

// search all "inside" edges
edgeFilter = new ArcGIS.Core.Data.Analyst3D.TinEdgeFilter();
edgeFilter.FilterType = ArcGIS.Core.Data.Analyst3D.TinFilterType.InsideDataArea;
using (ArcGIS.Core.Data.Analyst3D.TinEdgeCursor edgeCursor = tinDataset.SearchEdges(edgeFilter))
{
  while (edgeCursor.MoveNext())
  {
    using (ArcGIS.Core.Data.Analyst3D.TinEdge edge = edgeCursor.Current)
    {

    }
  }
}

// search for hard edges
edgeFilter = new ArcGIS.Core.Data.Analyst3D.TinEdgeFilter();
edgeFilter.FilterByEdgeType = true;
edgeFilter.EdgeType = ArcGIS.Core.Data.Analyst3D.TinEdgeType.HardEdge;
using (ArcGIS.Core.Data.Analyst3D.TinEdgeCursor edgeCursor = tinDataset.SearchEdges(edgeFilter))
{
  while (edgeCursor.MoveNext())
  {
    using (ArcGIS.Core.Data.Analyst3D.TinEdge edge = edgeCursor.Current)
    {

    }
  }
}

// nodes of the edge
var nodes = edge.Nodes;

// edge geometry
var polyline = edge.ToPolyline();
// edge length
var length = edge.Length;
// is the edge "inside"
var isInsideEdge = edge.IsInsideDataArea;
// edge type - regular/hard/soft
var edgeType = edge.EdgeType;

// get next (clockwise) edge in the triangle
var nextEdge = edge.GetNextEdgeInTriangle();
// get previous (anti-clockwise) edge in the triangle
var prevEdge = edge.GetPreviousEdgeInTriangle();

// get opposite edge
var oppEdge = edge.GeNeighbor();

// get left triangle
var leftTriangle = edge.LeftTriangle;
// get right triangle
var rightTriangle = edge.RightTriangle;