diff --git a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
index de42b5e60..92677c73e 100644
--- a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
@@ -184,10 +184,9 @@ mod tests {
 
         let face = {
             let mut face = PartialFace {
-                surface: surface.clone(),
+                surface,
                 ..Default::default()
             };
-            face.exterior.write().surface = surface;
             face.exterior
                 .write()
                 .update_as_polygon_from_points(exterior);
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_face.rs b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
index 904f62630..30b9b2460 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
@@ -94,10 +94,9 @@ mod tests {
         ]
         .map(|surface| {
             let mut face = PartialFace {
-                surface: Partial::from(surface.clone()),
+                surface: Partial::from(surface),
                 ..Default::default()
             };
-            face.exterior.write().surface = Partial::from(surface);
             face.exterior.write().update_as_polygon_from_points(points);
 
             face.build(&mut services.objects)
@@ -126,10 +125,9 @@ mod tests {
         ];
         let [a, b] = surfaces.clone().map(|surface| {
             let mut face = PartialFace {
-                surface: Partial::from(surface.clone()),
+                surface: Partial::from(surface),
                 ..Default::default()
             };
-            face.exterior.write().surface = Partial::from(surface);
             face.exterior.write().update_as_polygon_from_points(points);
 
             face.build(&mut services.objects)
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_point.rs b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
index a44ca8c07..f5c94620e 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_point.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
@@ -151,10 +151,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [1., 1.],
@@ -176,10 +175,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [2., 1.],
@@ -204,10 +202,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [4., 2.],
             [0., 4.],
@@ -232,10 +229,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [2., 1.],
@@ -261,10 +257,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [2., 1.],
@@ -290,10 +285,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [2., 1.],
@@ -320,10 +314,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [2., 0.],
@@ -357,10 +350,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [0., 0.],
             [1., 0.],
diff --git a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
index 44269fbdf..2cfc93d03 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
@@ -166,10 +166,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.yz_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
@@ -193,10 +192,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.yz_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
@@ -223,10 +221,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.yz_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
@@ -250,10 +247,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.yz_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
@@ -288,10 +284,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.yz_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
@@ -326,10 +321,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
@@ -355,10 +349,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior.write().update_as_polygon_from_points([
             [-1., -1.],
             [1., -1.],
diff --git a/crates/fj-kernel/src/algorithms/reverse/cycle.rs b/crates/fj-kernel/src/algorithms/reverse/cycle.rs
index fd08da75a..23f517430 100644
--- a/crates/fj-kernel/src/algorithms/reverse/cycle.rs
+++ b/crates/fj-kernel/src/algorithms/reverse/cycle.rs
@@ -17,6 +17,6 @@ impl Reverse for Handle<Cycle> {
 
         edges.reverse();
 
-        Cycle::new(self.surface().clone(), edges).insert(objects)
+        Cycle::new(edges).insert(objects)
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index ca25066c7..a82c1a4f3 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -38,8 +38,7 @@ impl Sweep for (Handle<HalfEdge>, &Surface, Color) {
                 (edge.curve().clone(), surface)
                     .sweep_with_cache(path, cache, objects),
             );
-            face.surface = surface.clone();
-            face.exterior.write().surface = surface;
+            face.surface = surface;
         }
 
         // Now we're ready to create the edges.
@@ -270,7 +269,6 @@ mod tests {
             };
 
             let mut cycle = PartialCycle {
-                surface: Partial::from(surface.clone()),
                 ..Default::default()
             };
             cycle.half_edges.extend(
diff --git a/crates/fj-kernel/src/algorithms/sweep/face.rs b/crates/fj-kernel/src/algorithms/sweep/face.rs
index 51731cbc5..d55d0337a 100644
--- a/crates/fj-kernel/src/algorithms/sweep/face.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/face.rs
@@ -83,8 +83,6 @@ impl Sweep for Handle<Face> {
                 top_edges.push(Partial::from(top_edge));
             }
 
-            top_cycle.write().surface = Partial::from(top_surface.clone());
-
             top_cycle
                 .write()
                 .connect_to_closed_edges(top_edges, &top_surface.geometry());
@@ -165,8 +163,6 @@ mod tests {
 
             let mut face = sketch.add_face();
             face.write().surface = Partial::from(surface.clone());
-            face.write().exterior.write().surface =
-                Partial::from(surface.clone());
             face.write()
                 .exterior
                 .write()
@@ -185,7 +181,6 @@ mod tests {
                 ..Default::default()
             };
 
-            bottom.exterior.write().surface = Partial::from(surface.clone());
             bottom
                 .exterior
                 .write()
@@ -200,11 +195,10 @@ mod tests {
             let surface = surface.clone().translate(UP, &mut services.objects);
 
             let mut top = PartialFace {
-                surface: Partial::from(surface.clone()),
+                surface: Partial::from(surface),
                 ..Default::default()
             };
 
-            top.exterior.write().surface = Partial::from(surface);
             top.exterior.write().update_as_polygon_from_points(TRIANGLE);
 
             top.build(&mut services.objects)
@@ -246,8 +240,6 @@ mod tests {
 
             let mut face = sketch.add_face();
             face.write().surface = Partial::from(surface.clone());
-            face.write().exterior.write().surface =
-                Partial::from(surface.clone());
             face.write()
                 .exterior
                 .write()
@@ -265,11 +257,10 @@ mod tests {
                 surface.clone().translate(DOWN, &mut services.objects);
 
             let mut bottom = PartialFace {
-                surface: Partial::from(surface.clone()),
+                surface: Partial::from(surface),
                 ..Default::default()
             };
 
-            bottom.exterior.write().surface = Partial::from(surface);
             bottom
                 .exterior
                 .write()
@@ -286,7 +277,6 @@ mod tests {
                 ..Default::default()
             };
 
-            top.exterior.write().surface = Partial::from(surface.clone());
             top.exterior.write().update_as_polygon_from_points(TRIANGLE);
 
             top.build(&mut services.objects)
diff --git a/crates/fj-kernel/src/algorithms/transform/cycle.rs b/crates/fj-kernel/src/algorithms/transform/cycle.rs
index e56793752..5fbc6eb32 100644
--- a/crates/fj-kernel/src/algorithms/transform/cycle.rs
+++ b/crates/fj-kernel/src/algorithms/transform/cycle.rs
@@ -14,16 +14,12 @@ impl TransformObject for Cycle {
         objects: &mut Service<Objects>,
         cache: &mut TransformCache,
     ) -> Self {
-        let surface = self
-            .surface()
-            .clone()
-            .transform_with_cache(transform, objects, cache);
         let half_edges = self.half_edges().map(|half_edge| {
             half_edge
                 .clone()
                 .transform_with_cache(transform, objects, cache)
         });
 
-        Self::new(surface, half_edges)
+        Self::new(half_edges)
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/triangulate/mod.rs b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
index 87d29de38..41b17b606 100644
--- a/crates/fj-kernel/src/algorithms/triangulate/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
@@ -99,10 +99,9 @@ mod tests {
         let surface = Partial::from(services.objects.surfaces.xy_plane());
 
         let mut face = PartialFace {
-            surface: surface.clone(),
+            surface,
             ..Default::default()
         };
-        face.exterior.write().surface = surface;
         face.exterior
             .write()
             .update_as_polygon_from_points([a, b, c, d]);
@@ -144,7 +143,6 @@ mod tests {
             surface: Partial::from(surface.clone()),
             ..Default::default()
         };
-        face.exterior.write().surface = Partial::from(surface.clone());
         face.exterior
             .write()
             .update_as_polygon_from_points([a, b, c, d]);
@@ -211,7 +209,6 @@ mod tests {
             surface: Partial::from(surface.clone()),
             ..Default::default()
         };
-        face.exterior.write().surface = Partial::from(surface.clone());
         face.exterior
             .write()
             .update_as_polygon_from_points([a, b, c, d, e]);
diff --git a/crates/fj-kernel/src/builder/face.rs b/crates/fj-kernel/src/builder/face.rs
index 173a45986..9514b6984 100644
--- a/crates/fj-kernel/src/builder/face.rs
+++ b/crates/fj-kernel/src/builder/face.rs
@@ -34,7 +34,6 @@ pub trait FaceBuilder {
 impl FaceBuilder for PartialFace {
     fn add_interior(&mut self) -> Partial<Cycle> {
         let cycle = Partial::from_partial(PartialCycle {
-            surface: self.exterior.read().surface.clone(),
             ..Default::default()
         });
         self.interiors.push(cycle.clone());
diff --git a/crates/fj-kernel/src/objects/full/cycle.rs b/crates/fj-kernel/src/objects/full/cycle.rs
index 5fdfb4a4a..a8f429553 100644
--- a/crates/fj-kernel/src/objects/full/cycle.rs
+++ b/crates/fj-kernel/src/objects/full/cycle.rs
@@ -3,16 +3,11 @@ use std::slice;
 use fj_interop::ext::SliceExt;
 use fj_math::{Scalar, Winding};
 
-use crate::{
-    geometry::path::SurfacePath,
-    objects::{HalfEdge, Surface},
-    storage::Handle,
-};
+use crate::{geometry::path::SurfacePath, objects::HalfEdge, storage::Handle};
 
 /// A cycle of connected half-edges
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Cycle {
-    surface: Handle<Surface>,
     half_edges: Vec<Handle<HalfEdge>>,
 }
 
@@ -22,10 +17,7 @@ impl Cycle {
     /// # Panics
     ///
     /// Panics, if `half_edges` does not yield at least one half-edge.
-    pub fn new(
-        surface: Handle<Surface>,
-        half_edges: impl IntoIterator<Item = Handle<HalfEdge>>,
-    ) -> Self {
+    pub fn new(half_edges: impl IntoIterator<Item = Handle<HalfEdge>>) -> Self {
         let half_edges = half_edges.into_iter().collect::<Vec<_>>();
 
         // This is not a validation check, and thus not part of the validation
@@ -37,15 +29,7 @@ impl Cycle {
             "Cycle must contain at least one half-edge"
         );
 
-        Self {
-            surface,
-            half_edges,
-        }
-    }
-
-    /// Access the surface that the cycle is in
-    pub fn surface(&self) -> &Handle<Surface> {
-        &self.surface
+        Self { half_edges }
     }
 
     /// Access the half-edges that make up the cycle
diff --git a/crates/fj-kernel/src/partial/objects/cycle.rs b/crates/fj-kernel/src/partial/objects/cycle.rs
index b7ee51cf6..7718f52ad 100644
--- a/crates/fj-kernel/src/partial/objects/cycle.rs
+++ b/crates/fj-kernel/src/partial/objects/cycle.rs
@@ -1,5 +1,5 @@
 use crate::{
-    objects::{Cycle, HalfEdge, Objects, Surface},
+    objects::{Cycle, HalfEdge, Objects},
     partial::{FullToPartialCache, Partial, PartialObject},
     services::Service,
 };
@@ -7,9 +7,6 @@ use crate::{
 /// A partial [`Cycle`]
 #[derive(Clone, Debug, Default)]
 pub struct PartialCycle {
-    /// The surface that the cycle is defined in
-    pub surface: Partial<Surface>,
-
     /// The half-edges that make up the cycle
     pub half_edges: Vec<Partial<HalfEdge>>,
 }
@@ -19,7 +16,6 @@ impl PartialObject for PartialCycle {
 
     fn from_full(cycle: &Self::Full, cache: &mut FullToPartialCache) -> Self {
         Self {
-            surface: Partial::from_full(cycle.surface().clone(), cache),
             half_edges: cycle
                 .half_edges()
                 .cloned()
@@ -29,12 +25,11 @@ impl PartialObject for PartialCycle {
     }
 
     fn build(self, objects: &mut Service<Objects>) -> Self::Full {
-        let surface = self.surface.build(objects);
         let half_edges = self
             .half_edges
             .into_iter()
             .map(|half_edge| half_edge.build(objects));
 
-        Cycle::new(surface, half_edges)
+        Cycle::new(half_edges)
     }
 }
diff --git a/crates/fj-kernel/src/validate/cycle.rs b/crates/fj-kernel/src/validate/cycle.rs
index 48b36bb37..5d7c3c76d 100644
--- a/crates/fj-kernel/src/validate/cycle.rs
+++ b/crates/fj-kernel/src/validate/cycle.rs
@@ -148,7 +148,6 @@ mod tests {
             let surface = services.objects.surfaces.xy_plane();
 
             let mut cycle = PartialCycle {
-                surface: Partial::from(surface.clone()),
                 ..Default::default()
             };
             cycle.update_as_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]]);
@@ -175,7 +174,7 @@ mod tests {
                 .into_iter()
                 .map(|half_edge| half_edge.build(&mut services.objects));
 
-            Cycle::new(valid.surface().clone(), half_edges)
+            Cycle::new(half_edges)
         };
 
         valid.validate_and_return_first_error()?;
@@ -192,7 +191,6 @@ mod tests {
             let surface = services.objects.surfaces.xy_plane();
 
             let mut cycle = PartialCycle {
-                surface: Partial::from(surface.clone()),
                 ..Default::default()
             };
             cycle.update_as_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]]);
@@ -214,7 +212,7 @@ mod tests {
                 .into_iter()
                 .map(|half_edge| half_edge.build(&mut services.objects));
 
-            Cycle::new(valid.surface().clone(), half_edges)
+            Cycle::new(half_edges)
         };
 
         valid.validate_and_return_first_error()?;
diff --git a/crates/fj-kernel/src/validate/face.rs b/crates/fj-kernel/src/validate/face.rs
index 24f193338..883d9d6c5 100644
--- a/crates/fj-kernel/src/validate/face.rs
+++ b/crates/fj-kernel/src/validate/face.rs
@@ -13,7 +13,6 @@ impl Validate for Face {
         config: &ValidationConfig,
         errors: &mut Vec<ValidationError>,
     ) {
-        FaceValidationError::check_surface_identity(self, errors);
         FaceValidationError::check_interior_winding(self, errors);
         FaceValidationError::check_vertex_positions(self, config, errors);
     }
@@ -87,23 +86,6 @@ pub enum FaceValidationError {
 }
 
 impl FaceValidationError {
-    fn check_surface_identity(face: &Face, errors: &mut Vec<ValidationError>) {
-        let surface = face.surface();
-
-        for interior in face.interiors() {
-            if surface.id() != interior.surface().id() {
-                errors.push(
-                    Box::new(Self::SurfaceMismatch {
-                        surface: surface.clone(),
-                        interior: interior.clone(),
-                        face: face.clone(),
-                    })
-                    .into(),
-                );
-            }
-        }
-    }
-
     fn check_interior_winding(face: &Face, errors: &mut Vec<ValidationError>) {
         let exterior_winding = face.exterior().winding();
 
@@ -182,10 +164,9 @@ mod tests {
             let surface = services.objects.surfaces.xy_plane();
 
             let mut face = PartialFace {
-                surface: Partial::from(surface.clone()),
+                surface: Partial::from(surface),
                 ..Default::default()
             };
-            face.exterior.write().surface = Partial::from(surface);
             face.exterior.write().update_as_polygon_from_points([
                 [0., 0.],
                 [3., 0.],
@@ -203,7 +184,6 @@ mod tests {
             let surface = services.objects.surfaces.xz_plane();
 
             let mut cycle = PartialCycle {
-                surface: Partial::from(surface.clone()),
                 ..Default::default()
             };
             cycle.update_as_polygon_from_points([[1., 1.], [1., 2.], [2., 1.]]);
@@ -235,10 +215,9 @@ mod tests {
             let surface = services.objects.surfaces.xy_plane();
 
             let mut face = PartialFace {
-                surface: Partial::from(surface.clone()),
+                surface: Partial::from(surface),
                 ..Default::default()
             };
-            face.exterior.write().surface = Partial::from(surface);
             face.exterior.write().update_as_polygon_from_points([
                 [0., 0.],
                 [3., 0.],
@@ -283,7 +262,6 @@ mod tests {
                 surface: Partial::from(surface.clone()),
                 ..Default::default()
             };
-            face.exterior.write().surface = Partial::from(surface.clone());
 
             let mut half_edge = face.exterior.write().add_half_edge();
             half_edge.write().update_as_circle_from_radius(1.);
@@ -326,8 +304,8 @@ mod tests {
                 .insert(&mut services.objects)
             };
 
-            let exterior = Cycle::new(valid.surface().clone(), [half_edge])
-                .insert(&mut services.objects);
+            let exterior =
+                Cycle::new([half_edge]).insert(&mut services.objects);
 
             Face::new(
                 valid.surface().clone(),
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 83dec0e28..1e223a917 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -37,7 +37,6 @@ impl Shape for fj::Sketch {
                 };
                 let exterior = {
                     let mut cycle = PartialCycle {
-                        surface: surface.clone(),
                         ..Default::default()
                     };
                     cycle.half_edges.push(half_edge);
@@ -60,7 +59,6 @@ impl Shape for fj::Sketch {
 
                 let exterior = {
                     let mut cycle = PartialCycle {
-                        surface: Partial::from(surface.clone()),
                         ..Default::default()
                     };
                     let mut line_segments = vec![];