diff --git a/include/geom/cell_hex.h b/include/geom/cell_hex.h
index af98d0e0258..86477d82374 100644
--- a/include/geom/cell_hex.h
+++ b/include/geom/cell_hex.h
@@ -77,6 +77,11 @@ class Hex : public Cell
    */
   virtual unsigned int n_vertices() const override final { return 8; }
 
+  /**
+   * \returns 4. Every side has four vertices.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override final { return 4; }
+
   /**
    * \returns 12.  All hexahedra have 12 edges.
    */
diff --git a/include/geom/cell_inf_hex.h b/include/geom/cell_inf_hex.h
index afceea8dff6..5272dec4a76 100644
--- a/include/geom/cell_inf_hex.h
+++ b/include/geom/cell_inf_hex.h
@@ -90,6 +90,11 @@ class InfHex : public InfCell
    */
   virtual unsigned int n_vertices() const override final { return 8; }
 
+  /**
+   * \returns 4. Every side has four vertices.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override final { return 4; }
+
   /**
    * \returns \p true if the specified (local) node number is a
    * "mid-edge" node on an infinite element edge.
diff --git a/include/geom/cell_inf_prism.h b/include/geom/cell_inf_prism.h
index b5db41e285b..1e627f7e089 100644
--- a/include/geom/cell_inf_prism.h
+++ b/include/geom/cell_inf_prism.h
@@ -86,6 +86,9 @@ class InfPrism : public InfCell
    */
   virtual unsigned int n_vertices() const override final { return 6; }
 
+  virtual unsigned int n_vertices_on_side(const unsigned int side) const override final
+  { return 4 - (side == 0 || side == 4); }
+
   /**
    * \returns 6.  All infinite prisms have 6 edges,
    * 3 lying in the base, and 3 perpendicular to the base.
diff --git a/include/geom/cell_prism.h b/include/geom/cell_prism.h
index 78eb74efd88..b0cca8428dc 100644
--- a/include/geom/cell_prism.h
+++ b/include/geom/cell_prism.h
@@ -83,6 +83,9 @@ class Prism : public Cell
    */
   virtual unsigned int n_vertices() const override final { return 6; }
 
+  virtual unsigned int n_vertices_on_side(const unsigned int side) const override final
+  { return 4 - (side == 0 || side == 4); }
+
   /**
    * \returns 9.  All prisms have 9 edges.
    */
diff --git a/include/geom/cell_pyramid.h b/include/geom/cell_pyramid.h
index 96e6918f98a..ffb2cf03c8f 100644
--- a/include/geom/cell_pyramid.h
+++ b/include/geom/cell_pyramid.h
@@ -87,6 +87,9 @@ class Pyramid : public Cell
    */
   virtual unsigned int n_vertices() const override { return 5; }
 
+  virtual unsigned int n_vertices_on_side(const unsigned int side) const override final
+  { return 4 - (side != 4); }
+
   /**
    * \returns 8.  All pyramids have 8 edges.
    */
diff --git a/include/geom/cell_tet.h b/include/geom/cell_tet.h
index 6f310c6e9ce..6dd769a9793 100644
--- a/include/geom/cell_tet.h
+++ b/include/geom/cell_tet.h
@@ -78,6 +78,11 @@ class Tet : public Cell
    */
   virtual unsigned int n_vertices() const override final { return 4; }
 
+  /**
+   * \returns 3. Every side has three vertices.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override final { return 3; }
+
   /**
    * \returns 6.  All tetrahedra have 6 edges.
    */
diff --git a/include/geom/edge.h b/include/geom/edge.h
index 726e82e297c..d80dc9da8dd 100644
--- a/include/geom/edge.h
+++ b/include/geom/edge.h
@@ -78,6 +78,11 @@ class Edge : public Elem
    */
   virtual unsigned int n_vertices() const override final { return 2; }
 
+  /**
+   * \returns 1. Every side has one vertex.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override final { return 1; }
+
   /**
    * \returns 0.  All 1D elements have no edges.
    */
diff --git a/include/geom/elem.h b/include/geom/elem.h
index fd7a0fcc8b3..53de385efb5 100644
--- a/include/geom/elem.h
+++ b/include/geom/elem.h
@@ -659,6 +659,11 @@ class Elem : public ReferenceCountedObject<Elem>,
    */
   virtual unsigned int n_vertices () const = 0;
 
+  /**
+   * \returns The number of verticies on the side with index \p s.
+   */
+  virtual unsigned int n_vertices_on_side (const unsigned int s) const = 0;
+
   /**
    * \returns The number of edges the element that has been derived
    * from this class has.
diff --git a/include/geom/face.h b/include/geom/face.h
index d3a818bf217..9e77cbd75cd 100644
--- a/include/geom/face.h
+++ b/include/geom/face.h
@@ -66,6 +66,11 @@ class Face : public Elem
    */
   virtual unsigned int n_faces() const override final { return 0; }
 
+  /**
+   * \returns 2. Every side has two vertices.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override final { return 2; }
+
   /**
    * build_side and build_edge are identical for faces.
    */
diff --git a/include/geom/face_inf_quad.h b/include/geom/face_inf_quad.h
index fba93f7c33f..09b951700db 100644
--- a/include/geom/face_inf_quad.h
+++ b/include/geom/face_inf_quad.h
@@ -106,6 +106,11 @@ class InfQuad : public Elem
    */
   virtual unsigned int n_vertices() const override final { return 4; }
 
+  /**
+   * \returns 2. Every side has two vertices.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override final { return 2; }
+
   /**
    * \returns 3.  All infinite quads have 1 edge in the
    * base, and 2 perpendicular to the base.
diff --git a/include/geom/node_elem.h b/include/geom/node_elem.h
index 312921a4fd6..20403950920 100644
--- a/include/geom/node_elem.h
+++ b/include/geom/node_elem.h
@@ -87,6 +87,12 @@ class NodeElem : public Elem
    */
   virtual unsigned int n_vertices() const override { return 1; }
 
+  /**
+   * The \p Elem::n_vertices_on_side makes no sense for nodes.
+   */
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override
+  { libmesh_not_implemented(); return 0; }
+
   /**
    * \returns 0.
    */
diff --git a/include/geom/remote_elem.h b/include/geom/remote_elem.h
index 49f1fa3a566..c891ab19c4b 100644
--- a/include/geom/remote_elem.h
+++ b/include/geom/remote_elem.h
@@ -125,6 +125,9 @@ class RemoteElem : public Elem,
   virtual unsigned int n_vertices () const override
   { libmesh_not_implemented(); return 0; }
 
+  virtual unsigned int n_vertices_on_side(const unsigned int) const override
+  { libmesh_not_implemented(); return 0; }
+
   virtual unsigned int n_edges () const override
   { libmesh_not_implemented(); return 0; }
 
diff --git a/tests/geom/elem_test.C b/tests/geom/elem_test.C
index c4c5161a915..99bbf2cf1ab 100644
--- a/tests/geom/elem_test.C
+++ b/tests/geom/elem_test.C
@@ -301,6 +301,21 @@ public:
         CPPUNIT_ASSERT_EQUAL(elem->build_side_ptr(s)->type(), elem->side_type(s));
   }
 
+  void test_n_vertices_on_side()
+  {
+    LOG_UNIT_TEST;
+
+    for (const auto & elem : _mesh->active_local_element_ptr_range())
+      for (const auto s : elem->side_index_range())
+      {
+        unsigned int n_vertices_on_side = 0;
+        for (const auto entry : elem_type::side_nodes_map[s])
+          if (entry >= elem->n_nodes())
+            ++n_vertices_on_side;
+        CPPUNIT_ASSERT_EQUAL(n_vertices_on_side, elem->n_vertices_on_side(s));
+      }
+  };
+
   void test_elem_side_builder()
   {
     LOG_UNIT_TEST;
@@ -331,6 +346,7 @@ public:
   CPPUNIT_TEST( test_contains_point_node );     \
   CPPUNIT_TEST( test_center_node_on_side );     \
   CPPUNIT_TEST( test_side_type );               \
+  CPPUNIT_TEST( test_n_vertices_on_side );      \
   CPPUNIT_TEST( test_elem_side_builder );
 
 #define INSTANTIATE_ELEMTEST(elemtype)                          \