diff --git a/network_process/src/connect_by_topo/pair_faces.cpp b/network_process/src/connect_by_topo/pair_faces.cpp
index c0305aa..bb0236c 100644
--- a/network_process/src/connect_by_topo/pair_faces.cpp
+++ b/network_process/src/connect_by_topo/pair_faces.cpp
@@ -1,4 +1,3 @@
-#include <functional>
 #include <numeric>
 #include <connect_by_topo.hpp>
 
@@ -254,18 +253,23 @@ void pair_patches_in_tets(const stl_vector_mp<uint32_t>                &containi
         uint32_t                                      vId1 = containing_simplex[0];
         uint32_t                                      vId2 = containing_simplex[1];
         flat_hash_map_mp<pod_key_t<3>, face_header_t> tet_plane_of_tri{};
-        uint32_t                                      vId;
-        pod_key_t<3>                                  tri;
+        static const std::array                       triangle_indices = {
+            std::array{1u, 2u, 3u}, // 0
+            std::array{0u, 2u, 3u}, // 1
+            std::array{0u, 1u, 3u}, // 2
+            std::array{0u, 1u, 2u}  // 3
+        };
         for (const auto tId : containing_tetIds) {
+            const auto &tet_vertices = tetrahedrons[tId];
             for (uint32_t i = 0; i < 4; ++i) {
-                vId = tetrahedrons[tId][i];
+                uint32_t vId = tet_vertices[i];
                 if (vId != vId1 && vId != vId2) {
-                    tri = {tetrahedrons[tId][(i + 1) % 4], tetrahedrons[tId][(i + 2) % 4], tetrahedrons[tId][(i + 3) % 4]};
-                    std::sort(tri.begin(), tri.end());
-                    auto iter_inserted = tet_plane_of_tri.try_emplace(tri, face_header_t{tId, i});
-                    if (!iter_inserted.second) {
-                        identical_tet_planes[{tId, i}]                    = iter_inserted.first->second;
-                        identical_tet_planes[iter_inserted.first->second] = {tId, i};
+                    face_header_t triangle_header{tId, i};
+                    auto [iter, is_new]               = tet_plane_of_tri.try_emplace(triangle_indices[i], triangle_header);
+                    const auto &other_triangle_header = iter->second;
+                    if (!is_new) {
+                        identical_tet_planes[triangle_header]       = other_triangle_header;
+                        identical_tet_planes[other_triangle_header] = triangle_header;
                     }
                 }
             }