diff --git a/crates/fj-core/src/operations/holes.rs b/crates/fj-core/src/operations/holes.rs
index 4c7f8abb8..d479ddc12 100644
--- a/crates/fj-core/src/operations/holes.rs
+++ b/crates/fj-core/src/operations/holes.rs
@@ -50,7 +50,7 @@ impl AddHole for Shell {
                 core,
             )
             .sweep_region(
-                location.face.surface(),
+                location.face.surface().clone(),
                 None,
                 path,
                 &mut SweepCache::default(),
@@ -113,7 +113,7 @@ impl AddHole for Shell {
                 core,
             )
             .sweep_region(
-                entry_location.face.surface(),
+                entry_location.face.surface().clone(),
                 None,
                 path,
                 &mut SweepCache::default(),
diff --git a/crates/fj-core/src/operations/sweep/cycle.rs b/crates/fj-core/src/operations/sweep/cycle.rs
index 7a9c4b91b..30fedb345 100644
--- a/crates/fj-core/src/operations/sweep/cycle.rs
+++ b/crates/fj-core/src/operations/sweep/cycle.rs
@@ -2,11 +2,11 @@ use fj_interop::Color;
 use fj_math::Vector;
 
 use crate::{
-    geometry::SurfaceGeometry,
     operations::{
         build::BuildCycle, join::JoinCycle, sweep::half_edge::SweepHalfEdge,
     },
-    topology::{Cycle, Face},
+    storage::Handle,
+    topology::{Cycle, Face, Surface},
     Core,
 };
 
@@ -38,7 +38,7 @@ pub trait SweepCycle {
     /// operation is called in, and therefore falls outside of its scope.
     fn sweep_cycle(
         &self,
-        surface: &SurfaceGeometry,
+        surface: Handle<Surface>,
         color: Option<Color>,
         path: impl Into<Vector<3>>,
         cache: &mut SweepCache,
@@ -49,7 +49,7 @@ pub trait SweepCycle {
 impl SweepCycle for Cycle {
     fn sweep_cycle(
         &self,
-        surface: &SurfaceGeometry,
+        surface: Handle<Surface>,
         color: Option<Color>,
         path: impl Into<Vector<3>>,
         cache: &mut SweepCache,
@@ -66,7 +66,7 @@ impl SweepCycle for Cycle {
 
             let (side_face, top_edge) = bottom_half_edge.sweep_half_edge(
                 bottom_half_edge_next.start_vertex().clone(),
-                surface,
+                surface.clone(),
                 color,
                 path,
                 cache,
diff --git a/crates/fj-core/src/operations/sweep/face.rs b/crates/fj-core/src/operations/sweep/face.rs
index d02376383..f06be7cc2 100644
--- a/crates/fj-core/src/operations/sweep/face.rs
+++ b/crates/fj-core/src/operations/sweep/face.rs
@@ -50,7 +50,7 @@ impl SweepFace for Handle<Face> {
         let other_faces = bottom_face
             .region()
             .sweep_region(
-                bottom_face.surface(),
+                bottom_face.surface().clone(),
                 bottom_face.region().get_color(core),
                 path,
                 cache,
diff --git a/crates/fj-core/src/operations/sweep/half_edge.rs b/crates/fj-core/src/operations/sweep/half_edge.rs
index 1aa8a30af..49f657c54 100644
--- a/crates/fj-core/src/operations/sweep/half_edge.rs
+++ b/crates/fj-core/src/operations/sweep/half_edge.rs
@@ -2,7 +2,6 @@ use fj_interop::{ext::ArrayExt, Color};
 use fj_math::{Point, Scalar, Vector};
 
 use crate::{
-    geometry::SurfaceGeometry,
     operations::{
         build::{BuildCycle, BuildHalfEdge},
         geometry::UpdateHalfEdgeGeometry,
@@ -11,7 +10,7 @@ use crate::{
         update::{UpdateCycle, UpdateHalfEdge},
     },
     storage::Handle,
-    topology::{Cycle, Face, HalfEdge, Region, Vertex},
+    topology::{Cycle, Face, HalfEdge, Region, Surface, Vertex},
     Core,
 };
 
@@ -39,7 +38,7 @@ pub trait SweepHalfEdge {
     fn sweep_half_edge(
         &self,
         end_vertex: Handle<Vertex>,
-        surface: &SurfaceGeometry,
+        surface: Handle<Surface>,
         color: Option<Color>,
         path: impl Into<Vector<3>>,
         cache: &mut SweepCache,
@@ -51,7 +50,7 @@ impl SweepHalfEdge for Handle<HalfEdge> {
     fn sweep_half_edge(
         &self,
         end_vertex: Handle<Vertex>,
-        surface: &SurfaceGeometry,
+        surface: Handle<Surface>,
         color: Option<Color>,
         path: impl Into<Vector<3>>,
         cache: &mut SweepCache,
@@ -60,7 +59,11 @@ impl SweepHalfEdge for Handle<HalfEdge> {
         let path = path.into();
 
         let geometry = core.layers.geometry.of_half_edge(self);
-        let surface = geometry.path.sweep_surface_path(surface, path, core);
+        let surface = geometry.path.sweep_surface_path(
+            &core.layers.geometry.of_surface(&surface),
+            path,
+            core,
+        );
 
         // Next, we need to define the boundaries of the face. Let's start with
         // the global vertices and edges.
diff --git a/crates/fj-core/src/operations/sweep/region.rs b/crates/fj-core/src/operations/sweep/region.rs
index 4112b7e1c..05af614b7 100644
--- a/crates/fj-core/src/operations/sweep/region.rs
+++ b/crates/fj-core/src/operations/sweep/region.rs
@@ -2,7 +2,6 @@ use fj_interop::Color;
 use fj_math::Vector;
 
 use crate::{
-    geometry::SurfaceGeometry,
     operations::{
         insert::Insert, reverse::Reverse, transform::TransformObject,
     },
@@ -32,7 +31,7 @@ pub trait SweepRegion {
     /// operation's scope.
     fn sweep_region(
         &self,
-        surface: &Handle<Surface>,
+        surface: Handle<Surface>,
         color: Option<Color>,
         path: impl Into<Vector<3>>,
         cache: &mut SweepCache,
@@ -43,7 +42,7 @@ pub trait SweepRegion {
 impl SweepRegion for Region {
     fn sweep_region(
         &self,
-        surface: &Handle<Surface>,
+        surface: Handle<Surface>,
         color: Option<Color>,
         path: impl Into<Vector<3>>,
         cache: &mut SweepCache,
@@ -55,7 +54,7 @@ impl SweepRegion for Region {
 
         let top_exterior = sweep_cycle(
             self.exterior(),
-            &core.layers.geometry.of_surface(surface),
+            surface.clone(),
             color,
             &mut faces,
             path,
@@ -69,7 +68,7 @@ impl SweepRegion for Region {
             .map(|bottom_cycle| {
                 sweep_cycle(
                     bottom_cycle,
-                    &core.layers.geometry.of_surface(surface),
+                    surface.clone(),
                     color,
                     &mut faces,
                     path,
@@ -96,7 +95,7 @@ impl SweepRegion for Region {
 
 fn sweep_cycle(
     bottom_cycle: &Cycle,
-    bottom_surface: &SurfaceGeometry,
+    bottom_surface: Handle<Surface>,
     color: Option<Color>,
     faces: &mut Vec<Face>,
     path: Vector<3>,
diff --git a/crates/fj-core/src/operations/sweep/shell_face.rs b/crates/fj-core/src/operations/sweep/shell_face.rs
index 35c3a61dc..756544936 100644
--- a/crates/fj-core/src/operations/sweep/shell_face.rs
+++ b/crates/fj-core/src/operations/sweep/shell_face.rs
@@ -66,7 +66,7 @@ impl SweepFaceOfShell for Shell {
             .derive_from(face.region().exterior(), core);
         let region = Region::new(exterior, []);
         let swept_region = region.sweep_region(
-            face.surface(),
+            face.surface().clone(),
             face.region().get_color(core),
             path,
             &mut cache,