public int ExteriorRingCount {get;}

public void GetExteriorRings(Polygon inputPolygon)
{
  if (inputPolygon == null || inputPolygon.IsEmpty)
    return;

  // polygon part count
  int partCount = inputPolygon.PartCount;
  // polygon exterior ring count
  int numExtRings = inputPolygon.ExteriorRingCount;
  // get set of exterior rings for the polygon
  IList<Polygon> extRings = inputPolygon.GetExteriorRings();

  // test each part for "exterior ring"
  for (int idx = 0; idx < partCount; idx++)
  {
    bool isExteriorRing = inputPolygon.IsExteriorRing(idx);
  }
}