diff --git a/crates/fj-core/src/queries/all_half_edges_with_surface.rs b/crates/fj-core/src/queries/all_half_edges_with_surface.rs
index 55fa85d9f..d368bf230 100644
--- a/crates/fj-core/src/queries/all_half_edges_with_surface.rs
+++ b/crates/fj-core/src/queries/all_half_edges_with_surface.rs
@@ -8,34 +8,29 @@ pub trait AllHalfEdgesWithSurface {
     /// Access all half-edges of the object, and the surface they're on
     fn all_half_edges_with_surface(
         &self,
-        result: &mut Vec<(Handle<HalfEdge>, Handle<Surface>)>,
-    );
+    ) -> impl Iterator<Item = (Handle<HalfEdge>, Handle<Surface>)>;
 }
 
 impl AllHalfEdgesWithSurface for Face {
     fn all_half_edges_with_surface(
         &self,
-        result: &mut Vec<(Handle<HalfEdge>, Handle<Surface>)>,
-    ) {
-        for cycle in self.region().all_cycles() {
-            result.extend(
-                cycle
-                    .half_edges()
-                    .iter()
-                    .cloned()
-                    .map(|half_edge| (half_edge, self.surface().clone())),
-            );
-        }
+    ) -> impl Iterator<Item = (Handle<HalfEdge>, Handle<Surface>)> {
+        self.region().all_cycles().flat_map(|cycle| {
+            cycle
+                .half_edges()
+                .iter()
+                .cloned()
+                .map(|half_edge| (half_edge, self.surface().clone()))
+        })
     }
 }
 
 impl AllHalfEdgesWithSurface for Shell {
     fn all_half_edges_with_surface(
         &self,
-        result: &mut Vec<(Handle<HalfEdge>, Handle<Surface>)>,
-    ) {
-        for face in self.faces() {
-            face.all_half_edges_with_surface(result);
-        }
+    ) -> impl Iterator<Item = (Handle<HalfEdge>, Handle<Surface>)> {
+        self.faces()
+            .into_iter()
+            .flat_map(|face| face.all_half_edges_with_surface())
     }
 }
diff --git a/crates/fj-core/src/validate/shell.rs b/crates/fj-core/src/validate/shell.rs
index f06fb6054..7c7f73654 100644
--- a/crates/fj-core/src/validate/shell.rs
+++ b/crates/fj-core/src/validate/shell.rs
@@ -84,8 +84,8 @@ impl ShellValidationError {
         config: &ValidationConfig,
         errors: &mut Vec<ValidationError>,
     ) {
-        let mut edges_and_surfaces = Vec::new();
-        shell.all_half_edges_with_surface(&mut edges_and_surfaces);
+        let edges_and_surfaces =
+            shell.all_half_edges_with_surface().collect::<Vec<_>>();
 
         for (edge_a, surface_a) in &edges_and_surfaces {
             for (edge_b, surface_b) in &edges_and_surfaces {
@@ -230,8 +230,8 @@ impl ShellValidationError {
         config: &ValidationConfig,
         errors: &mut Vec<ValidationError>,
     ) {
-        let mut edges_and_surfaces = Vec::new();
-        shell.all_half_edges_with_surface(&mut edges_and_surfaces);
+        let edges_and_surfaces =
+            shell.all_half_edges_with_surface().collect::<Vec<_>>();
 
         // This is O(N^2) which isn't great, but we can't use a HashMap since we
         // need to deal with float inaccuracies. Maybe we could use some smarter