diff --git a/src/output/VTKWriter.hpp b/src/output/VTKWriter.hpp
index d2459353e4bffa282eac8ff27e21c63d93273664..f3c202ffc51633d291d36150d662fe950023ef58 100644
--- a/src/output/VTKWriter.hpp
+++ b/src/output/VTKWriter.hpp
@@ -321,7 +321,9 @@ class VTKWriter
 
       {
         Array<int8_t> types(mesh->numberOfCells());
-        const auto& cell_type = mesh->connectivity().cellType();
+        const auto& cell_type           = mesh->connectivity().cellType();
+        const auto& cell_to_node_matrix = mesh->connectivity().cellToNodeMatrix();
+
         parallel_for(
           mesh->numberOfCells(), PUGS_LAMBDA(CellId j) {
             switch (cell_type[j]) {
@@ -342,7 +344,11 @@ class VTKWriter
               break;
             }
             case CellType::Pyramid: {
-              types[j] = 14;
+              if (cell_to_node_matrix[j].size() == 5) {
+                types[j] = 14;   // quadrangle basis
+              } else {
+                types[j] = 41;   // polygonal basis
+              }
               break;
             }
             case CellType::Prism: {
@@ -365,63 +371,72 @@ class VTKWriter
             }
           });
         _write_array(fout, "types", types);
-      }
-      if constexpr (MeshType::Dimension == 3) {
-        const auto& cell_to_face_matrix   = mesh->connectivity().cellToFaceMatrix();
-        const auto& cell_to_node_matrix   = mesh->connectivity().cellToNodeMatrix();
-        const auto& face_to_node_matrix   = mesh->connectivity().faceToNodeMatrix();
-        const auto& cell_face_is_reversed = mesh->connectivity().cellFaceIsReversed();
-
-        Array<size_t> faces_offsets(mesh->numberOfCells());
-        size_t next_offset = 0;
-        fout << "<DataArray type=\"Int64\" IdType=\"1\" Name=\"faces\">\n";
-        for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); ++cell_id) {
-          const auto& cell_nodes = cell_to_node_matrix[cell_id];
-          std::unordered_map<size_t, size_t> node_id_to_local_number_in_cell;
-          for (size_t i_cell_node = 0; i_cell_node < cell_nodes.size(); ++i_cell_node) {
-            node_id_to_local_number_in_cell[cell_nodes[i_cell_node]] = i_cell_node;
-          }
-
-          const auto& cell_faces = cell_to_face_matrix[cell_id];
-          fout << cell_faces.size() << '\n';
-          next_offset++;
-          for (size_t i_cell_face = 0; i_cell_face < cell_faces.size(); ++i_cell_face) {
-            const FaceId& face_id  = cell_faces[i_cell_face];
-            const auto& face_nodes = face_to_node_matrix[face_id];
-            fout << face_nodes.size();
-            next_offset++;
-            Array<size_t> face_node_in_cell(face_nodes.size());
-
-            for (size_t i_face_node = 0; i_face_node < face_nodes.size(); ++i_face_node) {
-              const NodeId& node_id                  = face_nodes[i_face_node];
-              auto i_node_id_to_local_number_in_cell = node_id_to_local_number_in_cell.find(node_id);
-              Assert(i_node_id_to_local_number_in_cell != node_id_to_local_number_in_cell.end());
-              face_node_in_cell[i_face_node] = i_node_id_to_local_number_in_cell->second;
+        if constexpr (MeshType::Dimension == 3) {
+          const bool has_general_polyhedron = [&] {
+            for (size_t i = 0; i < types.size(); ++i) {
+              if (types[i] == 41)
+                return true;
             }
-
-            if (cell_face_is_reversed(cell_id, i_cell_face)) {
-              for (size_t i = 0; i < face_node_in_cell.size(); ++i) {
-                fout << ' ' << face_node_in_cell[face_node_in_cell.size() - 1 - i];
+            return false;
+          }();
+          if (has_general_polyhedron) {
+            const auto& cell_to_face_matrix   = mesh->connectivity().cellToFaceMatrix();
+            const auto& face_to_node_matrix   = mesh->connectivity().faceToNodeMatrix();
+            const auto& cell_face_is_reversed = mesh->connectivity().cellFaceIsReversed();
+
+            Array<size_t> faces_offsets(mesh->numberOfCells());
+            size_t next_offset = 0;
+            fout << "<DataArray type=\"Int64\" IdType=\"1\" Name=\"faces\">\n";
+            for (CellId cell_id = 0; cell_id < mesh->numberOfCells(); ++cell_id) {
+              const auto& cell_nodes = cell_to_node_matrix[cell_id];
+              std::unordered_map<size_t, size_t> node_id_to_local_number_in_cell;
+              for (size_t i_cell_node = 0; i_cell_node < cell_nodes.size(); ++i_cell_node) {
+                node_id_to_local_number_in_cell[cell_nodes[i_cell_node]] = i_cell_node;
               }
-            } else {
-              for (size_t i = 0; i < face_node_in_cell.size(); ++i) {
-                fout << ' ' << face_node_in_cell[i];
+
+              const auto& cell_faces = cell_to_face_matrix[cell_id];
+              fout << cell_faces.size() << '\n';
+              next_offset++;
+              for (size_t i_cell_face = 0; i_cell_face < cell_faces.size(); ++i_cell_face) {
+                const FaceId& face_id  = cell_faces[i_cell_face];
+                const auto& face_nodes = face_to_node_matrix[face_id];
+                fout << face_nodes.size();
+                next_offset++;
+                Array<size_t> face_node_in_cell(face_nodes.size());
+
+                for (size_t i_face_node = 0; i_face_node < face_nodes.size(); ++i_face_node) {
+                  const NodeId& node_id                  = face_nodes[i_face_node];
+                  auto i_node_id_to_local_number_in_cell = node_id_to_local_number_in_cell.find(node_id);
+                  Assert(i_node_id_to_local_number_in_cell != node_id_to_local_number_in_cell.end());
+                  face_node_in_cell[i_face_node] = i_node_id_to_local_number_in_cell->second;
+                }
+
+                if (cell_face_is_reversed(cell_id, i_cell_face)) {
+                  for (size_t i = 0; i < face_node_in_cell.size(); ++i) {
+                    fout << ' ' << face_node_in_cell[face_node_in_cell.size() - 1 - i];
+                  }
+                } else {
+                  for (size_t i = 0; i < face_node_in_cell.size(); ++i) {
+                    fout << ' ' << face_node_in_cell[i];
+                  }
+                }
+
+                next_offset += face_nodes.size();
+
+                fout << '\n';
               }
+              faces_offsets[cell_id] = next_offset;
             }
-
-            next_offset += face_nodes.size();
-
-            fout << '\n';
+            fout << "</DataArray>\n";
+            fout << "<DataArray type=\"Int64\" IdType=\"1\" Name=\"faceoffsets\">\n";
+            for (size_t i_face_offsets = 0; i_face_offsets < faces_offsets.size(); ++i_face_offsets) {
+              fout << faces_offsets[i_face_offsets] << '\n';
+            }
+            fout << "</DataArray>\n";
           }
-          faces_offsets[cell_id] = next_offset;
-        }
-        fout << "</DataArray>\n";
-        fout << "<DataArray type=\"Int64\" IdType=\"1\" Name=\"faceoffsets\">\n";
-        for (size_t i_face_offsets = 0; i_face_offsets < faces_offsets.size(); ++i_face_offsets) {
-          fout << faces_offsets[i_face_offsets] << '\n';
         }
-        fout << "</DataArray>\n";
       }
+
       fout << "</Cells>\n";
       fout << "</Piece>\n";
       fout << "</UnstructuredGrid>\n";