diff --git a/crates/fj-kernel/src/algorithms/sweep.rs b/crates/fj-kernel/src/algorithms/sweep.rs
index f1295ee24c..ab8839bb57 100644
--- a/crates/fj-kernel/src/algorithms/sweep.rs
+++ b/crates/fj-kernel/src/algorithms/sweep.rs
@@ -266,8 +266,7 @@ impl Relation {
         };
 
         exteriors
-            .0
-            .iter()
+            .as_handle()
             .map(|cycle| self.cycles.get(cycle).unwrap().clone())
             .collect()
     }
@@ -283,8 +282,7 @@ impl Relation {
         };
 
         interiors
-            .0
-            .iter()
+            .as_handle()
             .map(|cycle| self.cycles.get(cycle).unwrap().clone())
             .collect()
     }
diff --git a/crates/fj-kernel/src/shape/validate.rs b/crates/fj-kernel/src/shape/validate.rs
index deca757adb..823d335a97 100644
--- a/crates/fj-kernel/src/shape/validate.rs
+++ b/crates/fj-kernel/src/shape/validate.rs
@@ -149,7 +149,7 @@ impl Validate for Face {
             if !stores.surfaces.contains(surface) {
                 missing_surface = Some(surface.clone());
             }
-            for cycle in exteriors.0.iter().chain(&interiors.0) {
+            for cycle in exteriors.as_handle().chain(interiors.as_handle()) {
                 if !stores.cycles.contains(cycle) {
                     missing_cycles.insert(cycle.clone());
                 }
diff --git a/crates/fj-kernel/src/topology/faces.rs b/crates/fj-kernel/src/topology/faces.rs
index cff40c993d..c66231928a 100644
--- a/crates/fj-kernel/src/topology/faces.rs
+++ b/crates/fj-kernel/src/topology/faces.rs
@@ -171,6 +171,11 @@ impl CyclesInFace {
     }
 
     fn as_canonical(&self) -> impl Iterator<Item = Cycle<3>> + '_ {
-        self.0.iter().map(|edge| edge.get())
+        self.as_handle().map(|edge| edge.get())
+    }
+
+    /// Access an iterator over handles to the cycles
+    pub fn as_handle(&self) -> impl Iterator<Item = &'_ Handle<Cycle<3>>> + '_ {
+        self.0.iter()
     }
 }
diff --git a/crates/fj-operations/src/group.rs b/crates/fj-operations/src/group.rs
index a18f0d9229..5b4c21ba63 100644
--- a/crates/fj-operations/src/group.rs
+++ b/crates/fj-operations/src/group.rs
@@ -96,8 +96,12 @@ fn copy_shape(orig: Shape, target: &mut Shape) {
                 target
                     .insert(Face::new(
                         surfaces[&surface].clone(),
-                        exteriors.0.iter().map(|cycle| cycles[cycle].clone()),
-                        interiors.0.iter().map(|cycle| cycles[cycle].clone()),
+                        exteriors
+                            .as_handle()
+                            .map(|cycle| cycles[cycle].clone()),
+                        interiors
+                            .as_handle()
+                            .map(|cycle| cycles[cycle].clone()),
                         color,
                     ))
                     .unwrap();