diff --git a/vtkm/CMakeLists.txt b/vtkm/CMakeLists.txt
index 3796750b8..758076c1c 100644
--- a/vtkm/CMakeLists.txt
+++ b/vtkm/CMakeLists.txt
@@ -29,6 +29,7 @@ set(headers
   Pair.h
   RegularConnectivity.h
   RegularStructure.h
+  TopologyElementTag.h
   TypeListTag.h
   Types.h
   TypeTraits.h
diff --git a/vtkm/RegularConnectivity.h b/vtkm/RegularConnectivity.h
index 1db911795..d99ea97b4 100644
--- a/vtkm/RegularConnectivity.h
+++ b/vtkm/RegularConnectivity.h
@@ -22,9 +22,9 @@
 #ifndef vtk_m_RegularConnectivity_h
 #define vtk_m_RegularConnectivity_h
 
-#include <vtkm/Types.h>
 #include <vtkm/RegularStructure.h>
-#include <vtkm/cont/TopologyType.h>
+#include <vtkm/Types.h>
+#include <vtkm/TopologyElementTag.h>
 #include <vtkm/cont/DeviceAdapterAlgorithm.h>
 
 VTKM_BOOST_PRE_INCLUDE
@@ -33,37 +33,38 @@ VTKM_BOOST_POST_INCLUDE
 
 namespace vtkm {
 
-template<vtkm::cont::TopologyType From, vtkm::cont::TopologyType To, vtkm::IdComponent Dimension>
+template<vtkm::IdComponent Dimension>
 struct SchedulingDimension
 {
   typedef vtkm::Id ValueType;
 };
 
-template<vtkm::cont::TopologyType From, vtkm::cont::TopologyType To>
-struct SchedulingDimension<From,To, 2>
+template<>
+struct SchedulingDimension<2>
 {
   typedef vtkm::Id2 ValueType;
 };
 
-template<vtkm::cont::TopologyType From, vtkm::cont::TopologyType To>
-struct SchedulingDimension<From,To, 3>
+template<>
+struct SchedulingDimension<3>
 {
   typedef vtkm::Id3 ValueType;
 };
 
-template<vtkm::cont::TopologyType From, vtkm::cont::TopologyType To, vtkm::IdComponent Dimension>
+template<typename From, typename To, vtkm::IdComponent Dimension>
 struct IndexLookupHelper
 {
   // We want an unconditional failure if this unspecialized class ever gets
   // instantiated, because it means someone missed a topology mapping type.
   // We need to create a test which depends on the templated types so
   // it doesn't get picked up without a concrete instantiation.
-  BOOST_STATIC_ASSERT_MSG(From != To && From == To,
+  BOOST_STATIC_ASSERT_MSG(sizeof(To) == static_cast<size_t>(-1),
                           "Missing Specialization for Topologies");
 };
 
 template<vtkm::IdComponent Dimension>
-struct IndexLookupHelper<vtkm::cont::NODE,vtkm::cont::CELL,Dimension>
+struct IndexLookupHelper<
+    vtkm::TopologyElementTagPoint, vtkm::TopologyElementTagCell, Dimension>
 {
   template <vtkm::IdComponent ItemTupleLength>
   VTKM_EXEC_CONT_EXPORT
@@ -75,7 +76,8 @@ struct IndexLookupHelper<vtkm::cont::NODE,vtkm::cont::CELL,Dimension>
 };
 
 template<vtkm::IdComponent Dimension>
-struct IndexLookupHelper<vtkm::cont::CELL,vtkm::cont::NODE,Dimension>
+struct IndexLookupHelper<
+    vtkm::TopologyElementTagCell, vtkm::TopologyElementTagPoint, Dimension>
 {
   template <vtkm::IdComponent ItemTupleLength>
   VTKM_EXEC_CONT_EXPORT
@@ -86,14 +88,16 @@ struct IndexLookupHelper<vtkm::cont::CELL,vtkm::cont::NODE,Dimension>
   }
 };
 
-template<vtkm::cont::TopologyType FromTopology, vtkm::cont::TopologyType ToTopoogy,
+template<typename FromTopology,
+         typename ToTopology,
          vtkm::IdComponent Dimension>
 class RegularConnectivity
 {
+  VTKM_IS_TOPOLOGY_ELEMENT_TAG(FromTopology);
+  VTKM_IS_TOPOLOGY_ELEMENT_TAG(ToTopology);
+
 public:
-  typedef typename SchedulingDimension< FromTopology,
-                                        ToTopoogy,
-                                        Dimension >::ValueType SchedulingDimension;
+  typedef typename SchedulingDimension<Dimension>::ValueType SchedulingDimension;
   RegularConnectivity():
     rs()
   {
@@ -124,14 +128,14 @@ public:
   VTKM_EXEC_CONT_EXPORT
   void GetIndices(vtkm::Id index, vtkm::Vec<vtkm::Id,ItemTupleLength> &ids)
   {
-    IndexLookupHelper<FromTopology,ToTopoogy,Dimension>::GetIndices(rs,index,ids);
+    IndexLookupHelper<FromTopology,ToTopology,Dimension>::GetIndices(rs,index,ids);
   }
 
   template <typename DeviceAdapterTag>
   struct ExecutionTypes
   { //Using this style so we can template the RegularConnecivity based on the
     //backend in the future without have to change the Transport logic
-    typedef vtkm::RegularConnectivity<FromTopology,ToTopoogy,Dimension> ExecObjectType;
+    typedef vtkm::RegularConnectivity<FromTopology,ToTopology,Dimension> ExecObjectType;
   };
 
   template<typename DeviceAdapterTag>
diff --git a/vtkm/TopologyElementTag.h b/vtkm/TopologyElementTag.h
new file mode 100644
index 000000000..4fd4221f1
--- /dev/null
+++ b/vtkm/TopologyElementTag.h
@@ -0,0 +1,109 @@
+//============================================================================
+//  Copyright (c) Kitware, Inc.
+//  All rights reserved.
+//  See LICENSE.txt for details.
+//  This software is distributed WITHOUT ANY WARRANTY; without even
+//  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+//  PURPOSE.  See the above copyright notice for more information.
+//
+//  Copyright 2015 Sandia Corporation.
+//  Copyright 2015 UT-Battelle, LLC.
+//  Copyright 2015 Los Alamos National Security.
+//
+//  Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
+//  the U.S. Government retains certain rights in this software.
+//
+//  Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
+//  Laboratory (LANL), the U.S. Government retains certain rights in
+//  this software.
+//============================================================================
+#ifndef vtk_m_TopologyElementTag_h
+#define vtk_m_TopologyElementTag_h
+
+#include <vtkm/Types.h>
+
+VTKM_BOOST_PRE_INCLUDE
+#include <boost/mpl/assert.hpp>
+VTKM_BOOST_POST_INCLUDE
+
+namespace vtkm {
+
+/// \brief A tag used to identify the cell elements in a topology.
+///
+/// A topology element refers to some type of substructure of a topology. For
+/// example, a 3D mesh has points, edges, faces, and cells. Each of these is an
+/// example of a topology element and has its own tag.
+///
+struct TopologyElementTagCell {  };
+
+/// \brief A tag used to identify the point elements in a topology.
+///
+/// A topology element refers to some type of substructure of a topology. For
+/// example, a 3D mesh has points, edges, faces, and cells. Each of these is an
+/// example of a topology element and has its own tag.
+///
+struct TopologyElementTagPoint {  };
+
+/// \brief A tag used to identify the edge elements in a topology.
+///
+/// A topology element refers to some type of substructure of a topology. For
+/// example, a 3D mesh has points, edges, faces, and cells. Each of these is an
+/// example of a topology element and has its own tag.
+///
+struct TopologyElementTagEdge {  };
+
+/// \brief A tag used to identify the face elements in a topology.
+///
+/// A topology element refers to some type of substructure of a topology. For
+/// example, a 3D mesh has points, edges, faces, and cells. Each of these is an
+/// example of a topology element and has its own tag.
+///
+struct TopologyElementTagFace {  };
+
+
+namespace internal {
+
+/// Checks to see if the given object is a topology element tag. This check is
+/// compatible with the Boost meta-template programing library (MPL). It
+/// contains a typedef named \c type that is either boost::mpl::true_ or
+/// boost::mpl::false_. Both of these have a typedef named value with the
+/// respective boolean value.
+///
+template<typename T>
+struct TopologyElementTagCheck
+{
+  typedef boost::mpl::false_ type;
+};
+
+template<>
+struct TopologyElementTagCheck<vtkm::TopologyElementTagCell>
+{
+  typedef boost::mpl::true_ type;
+};
+
+template<>
+struct TopologyElementTagCheck<vtkm::TopologyElementTagPoint>
+{
+  typedef boost::mpl::true_ type;
+};
+
+template<>
+struct TopologyElementTagCheck<vtkm::TopologyElementTagEdge>
+{
+  typedef boost::mpl::true_ type;
+};
+
+template<>
+struct TopologyElementTagCheck<vtkm::TopologyElementTagFace>
+{
+  typedef boost::mpl::true_ type;
+};
+
+#define VTKM_IS_TOPOLOGY_ELEMENT_TAG(type) \
+  BOOST_MPL_ASSERT(( ::vtkm::internal::TopologyElementTagCheck<type> ))
+
+} // namespace internal
+
+} // namespace vtkm
+
+#endif //vtk_m_TopologyElementTag_h
diff --git a/vtkm/cont/CMakeLists.txt b/vtkm/cont/CMakeLists.txt
index 515320692..b0588d1e1 100644
--- a/vtkm/cont/CMakeLists.txt
+++ b/vtkm/cont/CMakeLists.txt
@@ -64,7 +64,6 @@ set(headers
   StorageImplicit.h
   StorageListTag.h
   Timer.h
-  TopologyType.h
   )
 
 #-----------------------------------------------------------------------------
diff --git a/vtkm/cont/CellSet.h b/vtkm/cont/CellSet.h
index 11c9686ac..920fdaa0b 100644
--- a/vtkm/cont/CellSet.h
+++ b/vtkm/cont/CellSet.h
@@ -79,7 +79,7 @@ protected:
 namespace internal {
 
 /// Checks to see if the given object is a cell set. This check is compatible
-/// with the Boost meta-template programming library(MPL). It contains a
+/// with the Boost meta-template programming library (MPL). It contains a
 /// typedef named \c type that is either boost::mpl::true_ or
 /// boost::mpl::false_. Both of these have a typedef named value with the
 /// respective boolean value.
diff --git a/vtkm/cont/CellSetExplicit.h b/vtkm/cont/CellSetExplicit.h
index 1320d0998..acebd34ab 100644
--- a/vtkm/cont/CellSetExplicit.h
+++ b/vtkm/cont/CellSetExplicit.h
@@ -20,9 +20,9 @@
 #ifndef vtk_m_cont_CellSetExplicit_h
 #define vtk_m_cont_CellSetExplicit_h
 
+#include <vtkm/TopologyElementTag.h>
 #include <vtkm/cont/CellSet.h>
 #include <vtkm/cont/ExplicitConnectivity.h>
-#include <vtkm/cont/TopologyType.h>
 
 namespace vtkm {
 namespace cont {
@@ -56,8 +56,10 @@ public:
     return this->NodesOfCellsConnectivity.GetNumberOfElements();
   }
 
-  template<vtkm::cont::TopologyType FromTopology, vtkm::cont::TopologyType ToTopoogy>
+  template<typename FromTopology, typename ToTopology>
   struct ConnectivityType {
+    VTKM_IS_TOPOLOGY_ELEMENT_TAG(FromTopology);
+    VTKM_IS_TOPOLOGY_ELEMENT_TAG(ToTopology);
     // This type is really only valid for Point to Cell connectivity. When
     // other connectivity types are supported, these will need to be added.
     typedef ExplicitConnectivityType Type;
diff --git a/vtkm/cont/CellSetStructured.h b/vtkm/cont/CellSetStructured.h
index a5e98ff88..7a69da3bf 100644
--- a/vtkm/cont/CellSetStructured.h
+++ b/vtkm/cont/CellSetStructured.h
@@ -23,6 +23,7 @@
 #include <vtkm/cont/CellSet.h>
 #include <vtkm/RegularConnectivity.h>
 #include <vtkm/RegularStructure.h>
+#include <vtkm/TopologyElementTag.h>
 
 namespace vtkm {
 namespace cont {
@@ -47,28 +48,31 @@ public:
     return this->Structure.GetNumberOfCells();
   }
 
-  template<vtkm::cont::TopologyType FromTopology,
-           vtkm::cont::TopologyType ToTopology>
+  template<typename FromTopology, typename ToTopology>
   struct ConnectivityType {
+    VTKM_IS_TOPOLOGY_ELEMENT_TAG(FromTopology);
+    VTKM_IS_TOPOLOGY_ELEMENT_TAG(ToTopology);
     typedef vtkm::RegularConnectivity<FromTopology,ToTopology,Dimension> Type;
   };
 
   VTKM_CONT_EXPORT
-  vtkm::RegularConnectivity<vtkm::cont::NODE,vtkm::cont::CELL,Dimension>
+  vtkm::RegularConnectivity<
+      vtkm::TopologyElementTagPoint,vtkm::TopologyElementTagCell,Dimension>
   GetNodeToCellConnectivity() const
   {
-    typedef vtkm::RegularConnectivity<vtkm::cont::NODE,
-                                      vtkm::cont::CELL,
+    typedef vtkm::RegularConnectivity<vtkm::TopologyElementTagPoint,
+                                      vtkm::TopologyElementTagCell,
                                       Dimension> NodeToCellConnectivity;
     return NodeToCellConnectivity(this->Structure);
   }
 
   VTKM_CONT_EXPORT
-  vtkm::RegularConnectivity<vtkm::cont::CELL,vtkm::cont::NODE,Dimension>
+  vtkm::RegularConnectivity<
+      vtkm::TopologyElementTagCell,vtkm::TopologyElementTagPoint,Dimension>
   GetCellToNodeConnectivity() const
   {
-    typedef vtkm::RegularConnectivity<vtkm::cont::CELL,
-                                      vtkm::cont::NODE,
+    typedef vtkm::RegularConnectivity<vtkm::TopologyElementTagCell,
+                                      vtkm::TopologyElementTagPoint,
                                       Dimension> CellToNodeConnectivity;
     return CellToNodeConnectivity(this->Structure);
   }
diff --git a/vtkm/cont/TopologyType.h b/vtkm/cont/TopologyType.h
deleted file mode 100644
index 83a86f91b..000000000
--- a/vtkm/cont/TopologyType.h
+++ /dev/null
@@ -1,37 +0,0 @@
-//============================================================================
-//  Copyright (c) Kitware, Inc.
-//  All rights reserved.
-//  See LICENSE.txt for details.
-//  This software is distributed WITHOUT ANY WARRANTY; without even
-//  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
-//  PURPOSE.  See the above copyright notice for more information.
-//
-//  Copyright 2015 Sandia Corporation.
-//  Copyright 2015 UT-Battelle, LLC.
-//  Copyright 2015 Los Alamos National Security.
-//
-//  Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
-//  the U.S. Government retains certain rights in this software.
-//
-//  Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
-//  Laboratory (LANL), the U.S. Government retains certain rights in
-//  this software.
-//============================================================================
-#ifndef vtk_m_cont_TopologyType_h
-#define vtk_m_cont_TopologyType_h
-
-namespace vtkm {
-namespace cont {
-
-enum TopologyType
-{
-  NODE,
-  CELL,
-  EDGE,
-  FACE
-};
-
-} // namespace cont
-} // namespace vtkm
-
-#endif //vtk_m_cont_TopologyType_h
diff --git a/vtkm/cont/arg/TransportTagTopologyIn.h b/vtkm/cont/arg/TransportTagTopologyIn.h
index cb3071497..8927ab767 100644
--- a/vtkm/cont/arg/TransportTagTopologyIn.h
+++ b/vtkm/cont/arg/TransportTagTopologyIn.h
@@ -20,10 +20,10 @@
 #ifndef vtk_m_cont_arg_TransportTagTopologyIn_h
 #define vtk_m_cont_arg_TransportTagTopologyIn_h
 
+#include <vtkm/TopologyElementTag.h>
 #include <vtkm/Types.h>
 
 #include <vtkm/cont/CellSet.h>
-#include <vtkm/cont/TopologyType.h>
 
 #include <vtkm/cont/arg/Transport.h>
 
@@ -44,7 +44,8 @@ struct Transport<vtkm::cont::arg::TransportTagTopologyIn, ContObjectType, Device
   VTKM_IS_CELL_SET(ContObjectType);
 
   typedef typename ContObjectType
-      ::template ConnectivityType<vtkm::cont::NODE,vtkm::cont::CELL>::Type
+      ::template ConnectivityType<
+          vtkm::TopologyElementTagPoint,vtkm::TopologyElementTagCell>::Type
       ::template ExecutionTypes<Device>
       ::ExecObjectType ExecObjectType;
 
diff --git a/vtkm/cont/testing/UnitTestDataSetRegular.cxx b/vtkm/cont/testing/UnitTestDataSetRegular.cxx
index df83fb068..cc2d6302a 100644
--- a/vtkm/cont/testing/UnitTestDataSetRegular.cxx
+++ b/vtkm/cont/testing/UnitTestDataSetRegular.cxx
@@ -18,14 +18,14 @@
 //  this software.
 //============================================================================
 
-#include <vtkm/cont/testing/Testing.h>
-#include <vtkm/cont/testing/MakeTestDataSet.h>
-
 #include <vtkm/cont/DataSet.h>
 #include <vtkm/cont/DeviceAdapterAlgorithm.h>
 #include <vtkm/CellType.h>
 #include <vtkm/RegularConnectivity.h>
 
+#include <vtkm/cont/testing/Testing.h>
+#include <vtkm/cont/testing/MakeTestDataSet.h>
+
 static void TwoDimRegularTest();
 static void ThreeDimRegularTest();
 
@@ -67,10 +67,14 @@ TwoDimRegularTest()
       VTKM_TEST_ASSERT(shape == vtkm::VTKM_PIXEL, "Incorrect element type.");
     }
 
-    vtkm::RegularConnectivity<vtkm::cont::NODE, vtkm::cont::CELL,2> nodeToCell =
-        cellSet.GetNodeToCellConnectivity();
-    vtkm::RegularConnectivity<vtkm::cont::CELL, vtkm::cont::NODE,2> cellToNode =
-        cellSet.GetCellToNodeConnectivity();
+    vtkm::RegularConnectivity<
+        vtkm::TopologyElementTagPoint,
+        vtkm::TopologyElementTagCell,
+        2> nodeToCell = cellSet.GetNodeToCellConnectivity();
+    vtkm::RegularConnectivity<
+        vtkm::TopologyElementTagCell,
+        vtkm::TopologyElementTagPoint,
+        2> cellToNode = cellSet.GetCellToNodeConnectivity();
 
     vtkm::Id cells[2][4] = {{0,1,3,4}, {1,2,4,5}};
     vtkm::Vec<vtkm::Id,4> nodeIds;
@@ -135,8 +139,10 @@ ThreeDimRegularTest()
     }
 
     //Test regular connectivity.
-    vtkm::RegularConnectivity<vtkm::cont::NODE, vtkm::cont::CELL,3> nodeToCell =
-        cellSet.GetNodeToCellConnectivity();
+    vtkm::RegularConnectivity<
+        vtkm::TopologyElementTagPoint,
+        vtkm::TopologyElementTagCell,
+        3> nodeToCell = cellSet.GetNodeToCellConnectivity();
     vtkm::Id expectedPointIds[8] = {0,1,3,4,6,7,9,10};
     vtkm::Vec<vtkm::Id,8> retrievedPointIds;
     nodeToCell.GetIndices(0, retrievedPointIds);
@@ -147,8 +153,10 @@ ThreeDimRegularTest()
             "Incorrect node ID for cell");
     }
 
-    vtkm::RegularConnectivity<vtkm::cont::CELL, vtkm::cont::NODE,3> cellToNode =
-        cellSet.GetCellToNodeConnectivity();
+    vtkm::RegularConnectivity<
+        vtkm::TopologyElementTagCell,
+        vtkm::TopologyElementTagPoint,
+        3> cellToNode = cellSet.GetCellToNodeConnectivity();
     vtkm::Vec<vtkm::Id,8> expectedCellIds;
     vtkm::Id retrievedCellIds[8] = {0,-1,-1,-1,-1,-1,-1,-1};
     cellToNode.GetIndices(0, expectedCellIds);
diff --git a/vtkm/worklet/DispatcherMapTopology.h b/vtkm/worklet/DispatcherMapTopology.h
index fbd83e81b..bdd8cb8f7 100644
--- a/vtkm/worklet/DispatcherMapTopology.h
+++ b/vtkm/worklet/DispatcherMapTopology.h
@@ -114,12 +114,13 @@ public:
   }
 
   template<typename Invocation,
-           vtkm::cont::TopologyType From,
-           vtkm::cont::TopologyType To,
+           typename From,
+           typename To,
            vtkm::IdComponent Domain>
   VTKM_CONT_EXPORT
-  void InvokeBasedOnDomainType(const Invocation &invocation,
-                               const vtkm::RegularConnectivity<From,To,Domain>& domain) const
+  void InvokeBasedOnDomainType(
+      const Invocation &invocation,
+      const vtkm::RegularConnectivity<From,To,Domain>& domain) const
   {
 
     // For a DispatcherMapTopology, the inputDomain is some for of connectivity