diff --git a/cpp/test/CMakeLists.txt b/cpp/test/CMakeLists.txt
index a12aac898e4..e2a8e2a9b76 100644
--- a/cpp/test/CMakeLists.txt
+++ b/cpp/test/CMakeLists.txt
@@ -42,6 +42,7 @@ add_executable(
   common/sort.cpp
   fem/functionspace.cpp
   mesh/distributed_mesh.cpp
+  mesh/rectangle.cpp
   mesh/generation.cpp
   common/CIFailure.cpp
   refinement/interval.cpp
diff --git a/cpp/test/mesh/rectangle.cpp b/cpp/test/mesh/rectangle.cpp
new file mode 100644
index 00000000000..47a3835139c
--- /dev/null
+++ b/cpp/test/mesh/rectangle.cpp
@@ -0,0 +1,211 @@
+// Copyright (C) 2024 Paul T. Kühner
+//
+// This file is part of DOLFINX (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#include <mpi.h>
+
+#include <catch2/catch_template_test_macros.hpp>
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers.hpp>
+#include <catch2/matchers/catch_matchers_floating_point.hpp>
+#include <catch2/matchers/catch_matchers_range_equals.hpp>
+#include <catch2/matchers/catch_matchers_vector.hpp>
+
+#include <dolfinx/common/MPI.h>
+#include <dolfinx/graph/AdjacencyList.h>
+#include <dolfinx/mesh/Mesh.h>
+#include <dolfinx/mesh/generation.h>
+#include <dolfinx/mesh/utils.h>
+#include <dolfinx/refinement/interval.h>
+#include <dolfinx/refinement/refine.h>
+
+#include "util.h"
+
+using namespace dolfinx;
+using namespace Catch::Matchers;
+
+TEMPLATE_TEST_CASE("Rectangle quadrilateral mesh",
+                   "[mesh][rectangle][quadrilateral]", float, double)
+{
+  using T = TestType;
+
+  const std::array<double, 2> lower = {0, 0};
+  const std::array<double, 2> upper = {1, 1};
+
+  mesh::Mesh<T> mesh = dolfinx::mesh::create_rectangle<T>(
+      MPI_COMM_SELF, {lower, upper}, {1, 1}, mesh::CellType::quadrilateral);
+
+  // vertex layout:
+  // 1---3
+  // |   |
+  // |   |
+  // |   |
+  // 0---2
+  std::vector<T> expected_x = {
+      /* v_0 */ 0, 0, 0,
+      /* v_1 */ 0, 1, 0,
+      /* v_2 */ 1, 0, 0,
+      /* v_3 */ 1, 1, 0,
+  };
+
+  CHECK_THAT(mesh.geometry().x(),
+             RangeEquals(expected_x, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+
+  // edge layout:
+  // x-2-x
+  // |   |
+  // 0   3
+  // |   |
+  // x-1-x
+  mesh.topology()->create_connectivity(1, 0);
+  auto e_to_v = mesh.topology()->connectivity(1, 0);
+  REQUIRE(e_to_v);
+
+  CHECK_adjacency_list_equal(*e_to_v, {/* e_0 */ {0, 1},
+                                       /* e_1 */ {0, 2},
+                                       /* e_2 */ {1, 3},
+                                       /* e_3 */ {2, 3}});
+}
+
+TEMPLATE_TEST_CASE("Rectangle triangle mesh (right)",
+                   "[mesh][rectangle][triangle][right]", float, double)
+{
+  using T = TestType;
+
+  const std::array<double, 2> lower = {0, 0};
+  const std::array<double, 2> upper = {1, 1};
+
+  mesh::Mesh<T> mesh = dolfinx::mesh::create_rectangle<T>(
+      MPI_COMM_SELF, {lower, upper}, {1, 1}, mesh::CellType::triangle,
+      mesh::DiagonalType::right);
+
+  // vertex layout:
+  // 3---2
+  // |  /|
+  // | / |
+  // |/  |
+  // 0---1
+  std::vector<T> expected_x = {/* v_0 */ 0, 0, 0,
+                               /* v_1 */ 1, 0, 0,
+                               /* v_2 */ 1, 1, 0,
+                               /* v_3 */ 0, 1, 0};
+
+  CHECK_THAT(mesh.geometry().x(),
+             RangeEquals(expected_x, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+
+  // edge layout:
+  // x-4-x
+  // |  /|
+  // 2 1 3
+  // |/  |
+  // x-0-x
+  mesh.topology()->create_connectivity(1, 0);
+  auto e_to_v = mesh.topology()->connectivity(1, 0);
+  REQUIRE(e_to_v);
+
+  CHECK_adjacency_list_equal(*e_to_v, {/* e_0 */ {0, 1},
+                                       /* e_1 */ {0, 2},
+                                       /* e_2 */ {0, 3},
+                                       /* e_3 */ {1, 2},
+                                       /* e_4 */ {2, 3}});
+}
+
+TEMPLATE_TEST_CASE("Rectangle triangle mesh (left)",
+                   "[mesh][rectangle][triangle][left]", float, double)
+{
+  using T = TestType;
+
+  const std::array<double, 2> lower = {0, 0};
+  const std::array<double, 2> upper = {1, 1};
+
+  mesh::Mesh<T> mesh = dolfinx::mesh::create_rectangle<T>(
+      MPI_COMM_SELF, {lower, upper}, {1, 1}, mesh::CellType::triangle,
+      mesh::DiagonalType::left);
+
+  // vertex layout:
+  // 2---3
+  // |\  |
+  // | \ |
+  // |  \|
+  // 0---1
+  std::vector<T> expected_x = {
+      /* v_0 */ 0, 0, 0,
+      /* v_1 */ 1, 0, 0,
+      /* v_2 */ 0, 1, 0,
+      /* v_3 */ 1, 1, 0,
+  };
+
+  CHECK_THAT(mesh.geometry().x(),
+             RangeEquals(expected_x, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+
+  // edge layout:
+  // x-4-x
+  // |\  |
+  // 1 2 3
+  // |  \|
+  // x-0-x
+  mesh.topology()->create_connectivity(1, 0);
+  auto e_to_v = mesh.topology()->connectivity(1, 0);
+  REQUIRE(e_to_v);
+
+  CHECK_adjacency_list_equal(*e_to_v, {/* e_0 */ {0, 1},
+                                       /* e_1 */ {0, 2},
+                                       /* e_2 */ {1, 2},
+                                       /* e_3 */ {1, 3},
+                                       /* e_4 */ {2, 3}});
+}
+
+TEMPLATE_TEST_CASE("Rectangle triangle mesh (crossed)",
+                   "[mesh][rectangle][triangle][crossed]", float, double)
+{
+  using T = TestType;
+
+  const std::array<double, 2> lower = {0, 0};
+  const std::array<double, 2> upper = {1, 1};
+
+  mesh::Mesh<T> mesh = dolfinx::mesh::create_rectangle<T>(
+      MPI_COMM_SELF, {lower, upper}, {1, 1}, mesh::CellType::triangle,
+      mesh::DiagonalType::crossed);
+
+  // vertex layout:
+  // 3---4
+  // |\ /|
+  // | 2 |
+  // |/ \|
+  // 0---1
+  std::vector<T> expected_x = {
+      /* v_0 */ 0,  0,  0,
+      /* v_1 */ 1,  0,  0,
+      /* v_2 */ .5, .5, 0,
+      /* v_3 */ 0,  1,  0,
+      /* v_4 */ 1,  1,  0,
+  };
+
+  CHECK_THAT(mesh.geometry().x(),
+             RangeEquals(expected_x, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+
+  // edge layout:
+  // x-7-x
+  // |5 6|
+  // 2 x 4
+  // |1 3|
+  // x-0-x
+  mesh.topology()->create_connectivity(1, 0);
+  auto e_to_v = mesh.topology()->connectivity(1, 0);
+  REQUIRE(e_to_v);
+
+  CHECK_adjacency_list_equal(*e_to_v, {/* e_0 */ {0, 1},
+                                       /* e_1 */ {0, 2},
+                                       /* e_2 */ {0, 3},
+                                       /* e_3 */ {1, 2},
+                                       /* e_4 */ {1, 4},
+                                       /* e_5 */ {2, 3},
+                                       /* e_6 */ {2, 4},
+                                       /* e_7 */ {3, 4}});
+}
diff --git a/cpp/test/mesh/util.h b/cpp/test/mesh/util.h
new file mode 100644
index 00000000000..5fe02779dc4
--- /dev/null
+++ b/cpp/test/mesh/util.h
@@ -0,0 +1,29 @@
+// Copyright (C) 2024 Paul T. Kühner
+//
+// This file is part of DOLFINX (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#pragma once
+
+#include <limits>
+#include <vector>
+
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers_range_equals.hpp>
+
+#include <dolfinx/graph/AdjacencyList.h>
+
+template <typename T>
+constexpr auto EPS = std::numeric_limits<T>::epsilon();
+
+template <typename T>
+void CHECK_adjacency_list_equal(
+    const dolfinx::graph::AdjacencyList<T>& adj_list,
+    const std::vector<std::vector<T>>& expected_list)
+{
+  REQUIRE(static_cast<std::size_t>(adj_list.num_nodes()) == expected_list.size());
+
+  for (T i = 0; i < adj_list.num_nodes(); i++)
+    CHECK_THAT(adj_list.links(i), Catch::Matchers::RangeEquals(expected_list[i]));
+}