diff --git a/meshmode/mesh/generation.py b/meshmode/mesh/generation.py
index ca5ddfb4f5d46f1b1a92c66983ca383129e572e1..4fa520bc4d7a62a4dfb27f55025ff9d906b52a0f 100644
--- a/meshmode/mesh/generation.py
+++ b/meshmode/mesh/generation.py
@@ -446,7 +446,7 @@ def generate_icosphere(r, order, uniform_refinement_rounds=0):
     mesh = generate_icosahedron(r, order)
 
     if uniform_refinement_rounds:
-        # These come out conformal, so we're OK to use the faster refiner.
+        # These come out conforming, so we're OK to use the faster refiner.
         from meshmode.mesh.refinement import RefinerWithoutAdjacency
         refiner = RefinerWithoutAdjacency(mesh)
         for i in range(uniform_refinement_rounds):
diff --git a/meshmode/mesh/refinement/no_adjacency.py b/meshmode/mesh/refinement/no_adjacency.py
index f37f66215ded63f530db8d5a2cb465d38771b5db..87f843d3ac052ebbb39b20d85deeb76445b2c5db 100644
--- a/meshmode/mesh/refinement/no_adjacency.py
+++ b/meshmode/mesh/refinement/no_adjacency.py
@@ -238,6 +238,8 @@ class RefinerWithoutAdjacency(object):
                             global_midpoint = inew_vertex
                             additional_vertices.append(
                                     midpoints[old_iel][:, imidpoint])
+                            self.global_vertex_pair_to_midpoint[
+                                    global_v1, global_v2] = global_midpoint
                             inew_vertex += 1
 
                         refining_vertices[iref_midpoint] = global_midpoint
diff --git a/test/test_refinement.py b/test/test_refinement.py
index 5e10a9462ae7b1aa195227a58950ec69482775ff..2bc29e89266f4e7a5ae824335d719cb259412ea6 100644
--- a/test/test_refinement.py
+++ b/test/test_refinement.py
@@ -294,7 +294,7 @@ def test_refinement_connection(
 
 
 @pytest.mark.parametrize("with_adjacency", [True, False])
-def test_uniform_refinement(ctx_factory, with_adjacency):
+def test_uniform_refinement(with_adjacency):
     make_mesh = partial(generate_box_mesh, (
             np.linspace(0.0, 1.0, 2),
             np.linspace(0.0, 1.0, 3),
@@ -305,6 +305,18 @@ def test_uniform_refinement(ctx_factory, with_adjacency):
     mesh = refine_uniformly(mesh, 1, with_adjacency=with_adjacency)
 
 
+@pytest.mark.parametrize("refinement_rounds", [0, 1, 2])
+def test_conformity_of_uniform_mesh(refinement_rounds):
+    from meshmode.mesh.generation import generate_icosphere
+    mesh = generate_icosphere(r=1.0, order=4,
+            uniform_refinement_rounds=refinement_rounds)
+
+    assert mesh.is_conforming
+
+    from meshmode.mesh import is_boundary_tag_empty, BTAG_ALL
+    assert is_boundary_tag_empty(mesh, BTAG_ALL)
+
+
 if __name__ == "__main__":
     import sys
     if len(sys.argv) > 1: