diff --git a/crates/fj-core/src/operations/build/shell.rs b/crates/fj-core/src/operations/build/shell.rs
index a40344324..2fdc55442 100644
--- a/crates/fj-core/src/operations/build/shell.rs
+++ b/crates/fj-core/src/operations/build/shell.rs
@@ -11,6 +11,11 @@ use crate::{
 
 /// Build a [`Shell`]
 pub trait BuildShell {
+    /// Build an empty shell
+    fn empty() -> Shell {
+        Shell::new([])
+    }
+
     /// Build a tetrahedron from the provided points
     ///
     /// Accepts 4 points, naturally. For the purposes of the following
diff --git a/crates/fj-core/src/operations/update/cycle.rs b/crates/fj-core/src/operations/update/cycle.rs
index 5315ea684..c2b47f488 100644
--- a/crates/fj-core/src/operations/update/cycle.rs
+++ b/crates/fj-core/src/operations/update/cycle.rs
@@ -9,7 +9,7 @@ pub trait UpdateCycle {
     fn add_half_edges(
         &self,
         half_edges: impl IntoIterator<Item = Handle<HalfEdge>>,
-    ) -> Cycle;
+    ) -> Self;
 
     /// Replace the provided half-edge
     ///
@@ -20,7 +20,7 @@ pub trait UpdateCycle {
         &self,
         original: &Handle<HalfEdge>,
         replacement: Handle<HalfEdge>,
-    ) -> Cycle;
+    ) -> Self;
 
     /// Update the half-edge at the given index
     ///
@@ -31,14 +31,14 @@ pub trait UpdateCycle {
         &self,
         index: usize,
         f: impl FnMut(&Handle<HalfEdge>) -> Handle<HalfEdge>,
-    ) -> Cycle;
+    ) -> Self;
 }
 
 impl UpdateCycle for Cycle {
     fn add_half_edges(
         &self,
         half_edges: impl IntoIterator<Item = Handle<HalfEdge>>,
-    ) -> Cycle {
+    ) -> Self {
         let half_edges = self.half_edges().cloned().chain(half_edges);
         Cycle::new(half_edges)
     }
@@ -47,7 +47,7 @@ impl UpdateCycle for Cycle {
         &self,
         original: &Handle<HalfEdge>,
         replacement: Handle<HalfEdge>,
-    ) -> Cycle {
+    ) -> Self {
         let mut num_replacements = 0;
 
         let half_edges = self.half_edges().map(|half_edge| {
@@ -73,7 +73,7 @@ impl UpdateCycle for Cycle {
         &self,
         index: usize,
         mut f: impl FnMut(&Handle<HalfEdge>) -> Handle<HalfEdge>,
-    ) -> Cycle {
+    ) -> Self {
         let mut num_replacements = 0;
 
         let half_edges = self.half_edges().enumerate().map(|(i, half_edge)| {
diff --git a/crates/fj-core/src/operations/update/edge.rs b/crates/fj-core/src/operations/update/edge.rs
index 758fd0293..c1def62b4 100644
--- a/crates/fj-core/src/operations/update/edge.rs
+++ b/crates/fj-core/src/operations/update/edge.rs
@@ -6,14 +6,14 @@ use crate::{
 /// Update a [`HalfEdge`]
 pub trait UpdateHalfEdge {
     /// Update the start vertex of the half-edge
-    fn replace_start_vertex(&self, start_vertex: Handle<Vertex>) -> HalfEdge;
+    fn replace_start_vertex(&self, start_vertex: Handle<Vertex>) -> Self;
 
     /// Update the global form of the half-edge
-    fn replace_global_form(&self, global_form: Handle<GlobalEdge>) -> HalfEdge;
+    fn replace_global_form(&self, global_form: Handle<GlobalEdge>) -> Self;
 }
 
 impl UpdateHalfEdge for HalfEdge {
-    fn replace_start_vertex(&self, start_vertex: Handle<Vertex>) -> HalfEdge {
+    fn replace_start_vertex(&self, start_vertex: Handle<Vertex>) -> Self {
         HalfEdge::new(
             self.curve(),
             self.boundary(),
@@ -22,7 +22,7 @@ impl UpdateHalfEdge for HalfEdge {
         )
     }
 
-    fn replace_global_form(&self, global_form: Handle<GlobalEdge>) -> HalfEdge {
+    fn replace_global_form(&self, global_form: Handle<GlobalEdge>) -> Self {
         HalfEdge::new(
             self.curve(),
             self.boundary(),
diff --git a/crates/fj-core/src/operations/update/shell.rs b/crates/fj-core/src/operations/update/shell.rs
index 3133b2d83..8d5291805 100644
--- a/crates/fj-core/src/operations/update/shell.rs
+++ b/crates/fj-core/src/operations/update/shell.rs
@@ -5,23 +5,31 @@ use crate::{
 
 /// Update a [`Shell`]
 pub trait UpdateShell {
+    /// Add faces to the shell
+    fn add_faces(&self, faces: impl IntoIterator<Item = Handle<Face>>) -> Self;
+
     /// Update a face of the shell
     fn replace_face(
         &self,
         original: &Handle<Face>,
         replacement: Handle<Face>,
-    ) -> Shell;
+    ) -> Self;
 
     /// Remove a face from the shell
-    fn remove_face(&self, handle: &Handle<Face>) -> Shell;
+    fn remove_face(&self, handle: &Handle<Face>) -> Self;
 }
 
 impl UpdateShell for Shell {
+    fn add_faces(&self, faces: impl IntoIterator<Item = Handle<Face>>) -> Self {
+        let faces = self.faces().into_iter().cloned().chain(faces);
+        Shell::new(faces)
+    }
+
     fn replace_face(
         &self,
         original: &Handle<Face>,
         replacement: Handle<Face>,
-    ) -> Shell {
+    ) -> Self {
         let faces = self.faces().into_iter().map(|face| {
             if face.id() == original.id() {
                 replacement.clone()
@@ -33,7 +41,7 @@ impl UpdateShell for Shell {
         Shell::new(faces)
     }
 
-    fn remove_face(&self, handle: &Handle<Face>) -> Shell {
+    fn remove_face(&self, handle: &Handle<Face>) -> Self {
         let faces = self
             .faces()
             .into_iter()
diff --git a/crates/fj-core/src/operations/update/solid.rs b/crates/fj-core/src/operations/update/solid.rs
index a6135207e..db2979a91 100644
--- a/crates/fj-core/src/operations/update/solid.rs
+++ b/crates/fj-core/src/operations/update/solid.rs
@@ -9,14 +9,14 @@ pub trait UpdateSolid {
     fn add_shells(
         &self,
         shells: impl IntoIterator<Item = Handle<Shell>>,
-    ) -> Solid;
+    ) -> Self;
 }
 
 impl UpdateSolid for Solid {
     fn add_shells(
         &self,
         shells: impl IntoIterator<Item = Handle<Shell>>,
-    ) -> Solid {
+    ) -> Self {
         let shells = self.shells().cloned().chain(shells);
         Solid::new(shells)
     }