diff --git a/src/cellfunction/meshdata.jl b/src/cellfunction/meshdata.jl
index e557c9732..48dde0a00 100644
--- a/src/cellfunction/meshdata.jl
+++ b/src/cellfunction/meshdata.jl
@@ -32,6 +32,24 @@ function LazyOperators.materialize(data::MeshData{CellData}, cInfo::CellInfo)
     return _wrap_value(value)
 end
 
+function LazyOperators.materialize(
+    data::MeshData{CellData},
+    side::Side⁻{Nothing, <:Tuple{<:FaceInfo}},
+)
+    fInfo = get_args(side)[1]
+    cInfo_n = get_cellinfo_n(fInfo)
+    return materialize(data, cInfo_n)
+end
+
+function LazyOperators.materialize(
+    data::MeshData{CellData},
+    side::Side⁺{Nothing, <:Tuple{<:FaceInfo}},
+)
+    fInfo = get_args(side)[1]
+    cInfo_p = get_cellinfo_p(fInfo)
+    return materialize(data, cInfo_p)
+end
+
 function LazyOperators.materialize(
     data::MeshData{FaceData},
     side::AbstractSide{Nothing, <:Tuple{<:FaceInfo}},
diff --git a/src/function_space/function_space.jl b/src/function_space/function_space.jl
index 62fa6e6a4..e633fac2f 100644
--- a/src/function_space/function_space.jl
+++ b/src/function_space/function_space.jl
@@ -2,6 +2,16 @@
 """
 Abstract structure for the different types of function space, for
 instance the Lagrange function space, the Taylor function space etc.
+
+# Devs notes
+All subtypes should implement the following functions:
+* `ndofs(::AbstractFunctionSpace, ::AbstractShape)`
+* `_scalar_shape_functions(::AbstractFunctionSpace, ::AbstractShape, ξ)`
+* `idof_by_vertex(::AbstractFunctionSpace, ::AbstractShape)`
+* `idof_by_edge(::AbstractFunctionSpace, ::AbstractShape)`
+* `idof_by_edge_with_bounds(::AbstractFunctionSpace, ::AbstractShape)`
+* `idof_by_face(::AbstractFunctionSpace, ::AbstractShape)`
+* `idof_by_face_with_bounds(::AbstractFunctionSpace, ::AbstractShape)`
 """
 abstract type AbstractFunctionSpaceType end
 
diff --git a/src/function_space/lagrange.jl b/src/function_space/lagrange.jl
index bd134f926..6f809fc1d 100644
--- a/src/function_space/lagrange.jl
+++ b/src/function_space/lagrange.jl
@@ -771,6 +771,21 @@ function idof_by_face_with_bounds(::FunctionSpace{<:Lagrange, 1}, shape::Prism)
     (SA[1, 2, 5, 4], SA[2, 3, 6, 5], SA[3, 1, 4, 6], SA[1, 3, 2], SA[4, 5, 6])
 end
 
+# Pyramid
+function idof_by_edge(::FunctionSpace{<:Lagrange, 1}, shape::Pyramid)
+    ntuple(i -> SA[], nedges(shape))
+end
+function idof_by_edge_with_bounds(::FunctionSpace{<:Lagrange, 1}, shape::Pyramid)
+    (SA[1, 2], SA[2, 3], SA[3, 4], SA[4, 1], SA[1, 5], SA[2, 5], SA[3, 5], SA[4, 5])
+end
+
+function idof_by_face(::FunctionSpace{<:Lagrange, 1}, shape::Pyramid)
+    ntuple(i -> SA[], nfaces(shape))
+end
+function idof_by_face_with_bounds(::FunctionSpace{<:Lagrange, 1}, shape::Pyramid)
+    (SA[1, 4, 3, 2], SA[1, 2, 5], SA[2, 3, 5], SA[3, 4, 5], SA[4, 1, 5])
+end
+
 # Generic versions for Lagrange 0 and 1 (any shape)
 get_coords(::FunctionSpace{<:Lagrange, 0}, shape::AbstractShape) = (center(shape),)
 get_coords(::FunctionSpace{<:Lagrange, 1}, shape::AbstractShape) = get_coords(shape)
diff --git a/test/dof/test_meshdata.jl b/test/dof/test_meshdata.jl
index ecc9c0b23..da85ed7d4 100644
--- a/test/dof/test_meshdata.jl
+++ b/test/dof/test_meshdata.jl
@@ -35,6 +35,13 @@
             _cellFuncs = Bcube.materialize(cellFuncs, cInfo)
             @test Bcube.materialize(_cellFuncs, cPointRef) == funcs[i](cPointPhy)
         end
+
+        #--- Test 3, MeshCellData in face integration
+        mesh = rectangle_mesh(2, 2; xmin = 0, xmax = 3, ymin = -1, ymax = 1)
+        data = MeshCellData(ones(ncells(mesh)))
+        dΓ = Measure(BoundaryFaceDomain(mesh), 1)
+        values = nonzeros(Bcube.compute(∫(side_n(data))dΓ))
+        @test isapprox_arrays(values, [3.0, 2.0, 3.0, 2.0])
     end
 
     @testset "FaceData" begin