diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index a03fc5e..c810ef6 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -7,6 +7,7 @@ set(CuberilleTests
   CuberilleTest02.cxx
   CuberilleTest03.cxx
   CuberilleTest04.cxx
+  CuberilleTest_Issue66.cxx
   )
 
 CreateTestDriver(Cuberille "${Cuberille-Test_LIBRARIES}" "${CuberilleTests}")
@@ -351,6 +352,9 @@ add_test(
 #  25      # Maximum number of steps
 #)
 
+add_test(NAME CuberilleIssue66
+  COMMAND ${itk-module}TestDriver CuberilleTest_Issue66 )
+
 itk_add_test(NAME CuberilleTestDirectionMatrix
   COMMAND ${itk-module}TestDriver CuberilleTest02 )
 
diff --git a/test/CuberilleTest_Issue66.cxx b/test/CuberilleTest_Issue66.cxx
new file mode 100644
index 0000000..14dd028
--- /dev/null
+++ b/test/CuberilleTest_Issue66.cxx
@@ -0,0 +1,150 @@
+/*=========================================================================
+ *
+ *  Copyright NumFOCUS
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License");
+ *  you may not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *         https://www.apache.org/licenses/LICENSE-2.0.txt
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS,
+ *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ *
+ *=========================================================================*/
+
+#include <itkImage.h>
+#include <itkQuadEdgeMesh.h>
+#include <itkCuberilleImageToMeshFilter.h>
+#include <itkMeshFileWriter.h>
+#include <itkImageFileWriter.h>
+
+const unsigned int Dimension = 3;
+using TPixel = unsigned char;
+using TImage = itk::Image<TPixel, Dimension>;
+using TMesh = itk::Mesh<double, 3>;
+// using TMesh = itk::QuadEdgeMesh<double, 3>;
+using TExtract = itk::CuberilleImageToMeshFilter<TImage, TMesh>;
+using TMeshWriter = itk::MeshFileWriter<TMesh>;
+
+/* This is description from https://github.com/InsightSoftwareConsortium/ITKCuberille/issues/66
+
+Imagine an image with only two foreground pixels, offset by {1, 1, 0}. When extracting the surface of this image as a
+mesh, it is necessary to duplicate the coincident edge, creating two disconnected cubes, in order to ensure that the
+result is manifold. A slice through the z plane would show:
+
+*---*---*
+| A |   |
+*---*---*
+|   | B |
+*---*---*
+Now imagine that these foreground pixels are still flanked by background pixels in the z plain, but are "connected" into
+the same connected component by foreground pixels in the two adjacent z plains:
+
+   Z-1          Z          Z+1
+*---*---*   *---*---*   *---*---*
+| X | X |   | A |   |   | X | X |
+*---*---*   *---*---*   *---*---*
+|   | X |   |   | B |   |   | X |
+*---*---*   *---*---*   *---*---*
+Here, the coincident edge of pixels A and B must again be duplicated; but unlike the first example, the two distinct
+edges actually connect the same two vertices. Quite reasonably, when asked to create a face which would require an edge
+between two vertices, itk::QuadEdgeMesh checks:
+https://github.com/InsightSoftwareConsortium/ITK/blob/v5.4.5/Modules/Core/QuadEdgeMesh/include/itkQuadEdgeMesh.hxx#L1212-L1221
+to see whether there is an existing edge, and refuses to create a new
+edge if one already exists.
+
+Most of the time, this is what we want--but in the case described above, it acts as a bug. It's not immediately obvious
+to me how to detect when this check is and is not necessary; as I work through this problem, I thought I would post it
+as an issue in case anyone else had any insight--pun intended. ;-D
+
+*/
+
+TImage::Pointer
+case1()
+{
+  const auto         image = TImage::New();
+  TImage::RegionType region({ { 0, 0, 0 } }, { { 5, 4, 4 } });
+  image->SetBufferedRegion(region);
+  image->AllocateInitialized(); // zero filled image
+
+  image->SetPixel({ { 1, 1, 1 } }, 1); // A
+  image->SetPixel({ { 2, 2, 1 } }, 1); // B
+
+  image->SetPixel({ { 1, 1, 0 } }, 1); // C
+  image->SetPixel({ { 1, 2, 0 } }, 1); // D
+  image->SetPixel({ { 2, 2, 0 } }, 1); // E
+
+  image->SetPixel({ { 1, 1, 2 } }, 1); // F
+  image->SetPixel({ { 1, 2, 2 } }, 1); // G
+  image->SetPixel({ { 2, 2, 2 } }, 1); // H
+
+  return image;
+}
+
+TImage::Pointer
+case2()
+{
+  const auto         image = TImage::New();
+  TImage::RegionType region({ { 0, 0, 0 } }, { { 5, 4, 4 } });
+  image->SetBufferedRegion(region);
+  image->AllocateInitialized(); // zero filled image
+
+  image->SetPixel({ { 1, 1, 1 } }, 1); // A
+  image->SetPixel({ { 2, 1, 1 } }, 1); // B
+
+  image->SetPixel({ { 3, 1, 1 } }, 1); // C
+  image->SetPixel({ { 1, 2, 1 } }, 1); // D
+  image->SetPixel({ { 3, 2, 1 } }, 1); // E
+
+  image->SetPixel({ { 1, 2, 2 } }, 1); // F
+  image->SetPixel({ { 2, 2, 2 } }, 1); // G
+  image->SetPixel({ { 3, 2, 2 } }, 1); // H
+
+  return image;
+}
+
+
+int
+CuberilleTest_Issue66(int argc, char * argv[])
+{
+  int countFailed = 0;
+  for (const auto image : { case1(), case2() })
+  {
+
+    const auto extract = TExtract::New();
+    extract->SetInput(image);
+    extract->SavePixelAsCellDataOn();
+    extract->GenerateTriangleFacesOff();
+    extract->ProjectVerticesToIsoSurfaceOff();
+
+    const auto m_writer = TMeshWriter::New();
+    m_writer->SetInput(extract->GetOutput());
+    m_writer->SetFileName("mesh.obj");
+    m_writer->Update();
+
+    const auto n_cell = extract->GetOutput()->GetNumberOfCells();
+    const auto n_data = extract->GetOutput()->GetCellData()->Size();
+
+    if (n_cell != n_data)
+    {
+      std::cout << "This fails if using itk::QuadEdgeMesh." << std::endl;
+      std::cout << "n_cell: " << n_cell << std::endl;
+      std::cout << "n_data: " << n_data << std::endl;
+      ++countFailed;
+    }
+    else
+    {
+      std::cout << "This succeeds if using itk::Mesh." << std::endl;
+    }
+  }
+
+  if (countFailed == 0)
+  {
+    return EXIT_SUCCESS;
+  }
+  return EXIT_FAILURE;
+}