diff --git a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
index 7aee99816..dfe0cb790 100644
--- a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
@@ -187,9 +187,8 @@ mod tests {
         ];
 
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points(exterior)
-            .with_interior_polygon_from_points(interior)
+            .with_exterior_polygon_from_points(surface.clone(), exterior)
+            .with_interior_polygon_from_points(surface, interior)
             .build(&mut services.objects);
 
         let expected =
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_face.rs b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
index f7dd3549e..c9669e75d 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
@@ -95,8 +95,7 @@ mod tests {
         ]
         .map(|surface| {
             Face::partial()
-                .with_surface(surface)
-                .with_exterior_polygon_from_points(points)
+                .with_exterior_polygon_from_points(surface, points)
                 .build(&mut services.objects)
         });
 
@@ -123,8 +122,7 @@ mod tests {
         ];
         let [a, b] = surfaces.clone().map(|surface| {
             Face::partial()
-                .with_surface(surface)
-                .with_exterior_polygon_from_points(points)
+                .with_exterior_polygon_from_points(surface, points)
                 .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 90aea9fdc..021f18ae4 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_point.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
@@ -150,8 +150,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[0., 0.], [1., 1.], [0., 2.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [1., 1.], [0., 2.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([2., 1.]);
@@ -166,8 +168,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[0., 0.], [2., 1.], [0., 2.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [2., 1.], [0., 2.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([1., 1.]);
@@ -185,8 +189,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[4., 2.], [0., 4.], [0., 0.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[4., 2.], [0., 4.], [0., 0.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([1., 2.]);
@@ -204,13 +210,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [0., 0.],
-                [2., 1.],
-                [3., 0.],
-                [3., 4.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [2., 1.], [3., 0.], [3., 4.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([1., 1.]);
@@ -228,13 +231,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [0., 0.],
-                [2., 1.],
-                [3., 1.],
-                [0., 2.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [2., 1.], [3., 1.], [0., 2.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([1., 1.]);
@@ -252,14 +252,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [0., 0.],
-                [2., 1.],
-                [3., 1.],
-                [4., 0.],
-                [4., 5.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [2., 1.], [3., 1.], [4., 0.], [4., 5.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([1., 1.]);
@@ -277,8 +273,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[0., 0.], [2., 0.], [0., 1.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [2., 0.], [0., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([1., 0.]);
@@ -305,8 +303,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [1., 0.], [0., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let point = Point::from([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 5bc0273c1..bcb140734 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
@@ -168,13 +168,10 @@ mod tests {
 
         let surface = services.objects.surfaces.yz_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .translate([-1., 0., 0.], &mut services.objects);
@@ -190,13 +187,10 @@ mod tests {
 
         let surface = services.objects.surfaces.yz_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .translate([1., 0., 0.], &mut services.objects);
@@ -215,13 +209,10 @@ mod tests {
 
         let surface = services.objects.surfaces.yz_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .translate([0., 0., 2.], &mut services.objects);
@@ -237,13 +228,10 @@ mod tests {
 
         let surface = services.objects.surfaces.yz_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .translate([1., 1., 0.], &mut services.objects);
@@ -270,13 +258,10 @@ mod tests {
 
         let surface = services.objects.surfaces.yz_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .translate([1., 1., 1.], &mut services.objects);
@@ -301,13 +286,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
@@ -325,13 +307,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([
-                [-1., -1.],
-                [1., -1.],
-                [1., 1.],
-                [-1., 1.],
-            ])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[-1., -1.], [1., -1.], [1., 1.], [-1., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .translate([0., 0., 1.], &mut services.objects);
diff --git a/crates/fj-kernel/src/algorithms/sweep/face.rs b/crates/fj-kernel/src/algorithms/sweep/face.rs
index 0abe0d756..1b03318a7 100644
--- a/crates/fj-kernel/src/algorithms/sweep/face.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/face.rs
@@ -110,14 +110,15 @@ mod tests {
             .sweep(UP, &mut services.objects);
 
         let bottom = Face::partial()
-            .with_surface(surface.clone())
-            .with_exterior_polygon_from_points(TRIANGLE)
+            .with_exterior_polygon_from_points(surface.clone(), TRIANGLE)
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .reverse(&mut services.objects);
         let top = Face::partial()
-            .with_surface(surface.translate(UP, &mut services.objects))
-            .with_exterior_polygon_from_points(TRIANGLE)
+            .with_exterior_polygon_from_points(
+                surface.translate(UP, &mut services.objects),
+                TRIANGLE,
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
@@ -153,16 +154,15 @@ mod tests {
             .sweep(DOWN, &mut services.objects);
 
         let bottom = Face::partial()
-            .with_surface(
+            .with_exterior_polygon_from_points(
                 surface.clone().translate(DOWN, &mut services.objects),
+                TRIANGLE,
             )
-            .with_exterior_polygon_from_points(TRIANGLE)
             .build(&mut services.objects)
             .insert(&mut services.objects)
             .reverse(&mut services.objects);
         let top = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points(TRIANGLE)
+            .with_exterior_polygon_from_points(surface, TRIANGLE)
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
diff --git a/crates/fj-kernel/src/algorithms/triangulate/mod.rs b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
index ac1e19022..3e83522f9 100644
--- a/crates/fj-kernel/src/algorithms/triangulate/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
@@ -98,8 +98,7 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([a, b, c, d])
+            .with_exterior_polygon_from_points(surface, [a, b, c, d])
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
@@ -134,9 +133,8 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface.clone())
-            .with_exterior_polygon_from_points([a, b, c, d])
-            .with_interior_polygon_from_points([e, f, g, h])
+            .with_exterior_polygon_from_points(surface.clone(), [a, b, c, d])
+            .with_interior_polygon_from_points(surface.clone(), [e, f, g, h])
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
@@ -193,8 +191,7 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface.clone())
-            .with_exterior_polygon_from_points([a, b, c, d, e])
+            .with_exterior_polygon_from_points(surface.clone(), [a, b, c, d, e])
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
diff --git a/crates/fj-kernel/src/builder/cycle.rs b/crates/fj-kernel/src/builder/cycle.rs
index 62e34b27a..1a44832e9 100644
--- a/crates/fj-kernel/src/builder/cycle.rs
+++ b/crates/fj-kernel/src/builder/cycle.rs
@@ -83,7 +83,6 @@ impl CycleBuilder for PartialCycle {
                 );
 
                 half_edges.push(PartialHalfEdge {
-                    curve: curve.into(),
                     vertices: vertices.map(Into::into),
                     ..Default::default()
                 });
diff --git a/crates/fj-kernel/src/builder/edge.rs b/crates/fj-kernel/src/builder/edge.rs
index 3381151d3..0f44ee1f6 100644
--- a/crates/fj-kernel/src/builder/edge.rs
+++ b/crates/fj-kernel/src/builder/edge.rs
@@ -73,7 +73,7 @@ impl HalfEdgeBuilder for PartialHalfEdge {
         radius: impl Into<Scalar>,
         objects: &mut Service<Objects>,
     ) -> Self {
-        let mut curve = self.curve.clone().into_partial();
+        let mut curve = self.curve().into_partial();
         curve.update_as_circle_from_radius(radius);
 
         let path = curve.path.expect("Expected path that was just created");
@@ -98,7 +98,6 @@ impl HalfEdgeBuilder for PartialHalfEdge {
                 surface_form: surface_vertex.clone().into(),
             });
 
-        self.curve = curve.into();
         self.vertices = [back, front].map(Into::into);
 
         self
@@ -133,7 +132,7 @@ impl HalfEdgeBuilder for PartialHalfEdge {
             [&from, &to].map(|vertex| vertex.surface_form());
 
         let surface = self
-            .curve
+            .curve()
             .surface()
             .merge_with(from_surface.surface())
             .merge_with(to_surface.surface())
@@ -144,7 +143,7 @@ impl HalfEdgeBuilder for PartialHalfEdge {
                 .expect("Can't infer line segment without surface position")
         });
 
-        let mut curve = self.curve.clone().into_partial();
+        let mut curve = self.curve().into_partial();
         curve.surface = Some(surface);
         curve.update_as_line_from_points(points);
 
@@ -201,7 +200,6 @@ impl HalfEdgeBuilder for PartialHalfEdge {
                 })
         };
 
-        self.curve = curve.into();
         self.vertices = [back, front];
 
         self
diff --git a/crates/fj-kernel/src/builder/face.rs b/crates/fj-kernel/src/builder/face.rs
index 41f6dc5b1..e3f1c7065 100644
--- a/crates/fj-kernel/src/builder/face.rs
+++ b/crates/fj-kernel/src/builder/face.rs
@@ -1,8 +1,9 @@
 use fj_math::Point;
 
 use crate::{
-    objects::Cycle,
+    objects::{Cycle, Surface},
     partial::{HasPartial, PartialFace},
+    storage::Handle,
 };
 
 use super::CycleBuilder;
@@ -12,12 +13,14 @@ pub trait FaceBuilder {
     /// Update the [`PartialFace`] with an exterior polygon
     fn with_exterior_polygon_from_points(
         self,
+        surface: Handle<Surface>,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Self;
 
     /// Update the [`PartialFace`] with an interior polygon
     fn with_interior_polygon_from_points(
         self,
+        surface: Handle<Surface>,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Self;
 }
@@ -25,10 +28,9 @@ pub trait FaceBuilder {
 impl FaceBuilder for PartialFace {
     fn with_exterior_polygon_from_points(
         self,
+        surface: Handle<Surface>,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Self {
-        let surface = self.surface().expect("Need surface to create polygon");
-
         self.with_exterior(
             Cycle::partial()
                 .with_poly_chain_from_points(surface, points)
@@ -38,10 +40,9 @@ impl FaceBuilder for PartialFace {
 
     fn with_interior_polygon_from_points(
         self,
+        surface: Handle<Surface>,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Self {
-        let surface = self.surface().expect("Need surface to build polygon.");
-
         self.with_interiors([Cycle::partial()
             .with_poly_chain_from_points(surface, points)
             .close_with_line_segment()])
diff --git a/crates/fj-kernel/src/builder/shell.rs b/crates/fj-kernel/src/builder/shell.rs
index ff18342a2..7b6b086a9 100644
--- a/crates/fj-kernel/src/builder/shell.rs
+++ b/crates/fj-kernel/src/builder/shell.rs
@@ -52,13 +52,10 @@ impl ShellBuilder {
                 objects.surfaces.xy_plane().translate([Z, Z, -h], objects);
 
             Face::partial()
-                .with_surface(surface)
-                .with_exterior_polygon_from_points([
-                    [-h, -h],
-                    [h, -h],
-                    [h, h],
-                    [-h, h],
-                ])
+                .with_exterior_polygon_from_points(
+                    surface,
+                    [[-h, -h], [h, -h], [h, h], [-h, h]],
+                )
                 .build(objects)
                 .insert(objects)
         };
@@ -162,13 +159,14 @@ impl ShellBuilder {
                         };
 
                         PartialHalfEdge {
-                            curve: curve.into(),
                             vertices: [
                                 PartialVertex {
+                                    curve: curve.clone().into(),
                                     surface_form: from.into(),
                                     ..Default::default()
                                 },
                                 PartialVertex {
+                                    curve: curve.into(),
                                     surface_form: to.into(),
                                     ..Default::default()
                                 },
@@ -288,7 +286,6 @@ impl ShellBuilder {
                     PartialHalfEdge {
                         vertices: vertices.map(Into::into),
                         global_form: edge.global_form().clone().into(),
-                        ..Default::default()
                     }
                     .update_as_line_segment()
                     .build(objects)
diff --git a/crates/fj-kernel/src/builder/sketch.rs b/crates/fj-kernel/src/builder/sketch.rs
index 5ce8e8470..afb649241 100644
--- a/crates/fj-kernel/src/builder/sketch.rs
+++ b/crates/fj-kernel/src/builder/sketch.rs
@@ -48,8 +48,7 @@ impl SketchBuilder {
             .as_ref()
             .expect("Can't build `Sketch` without `Surface`");
         self.faces.extend([Face::partial()
-            .with_surface(surface.clone())
-            .with_exterior_polygon_from_points(points)
+            .with_exterior_polygon_from_points(surface.clone(), points)
             .build(objects)
             .insert(objects)]);
         self
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index ee26673b3..2be2ac8c5 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -432,8 +432,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let object = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [1., 0.], [0., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
 
@@ -541,8 +543,10 @@ mod tests {
 
         let surface = services.objects.surfaces.xy_plane();
         let face = Face::partial()
-            .with_surface(surface)
-            .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
+            .with_exterior_polygon_from_points(
+                surface,
+                [[0., 0.], [1., 0.], [0., 1.]],
+            )
             .build(&mut services.objects)
             .insert(&mut services.objects);
         let object = Sketch::builder()
diff --git a/crates/fj-kernel/src/partial/maybe_partial.rs b/crates/fj-kernel/src/partial/maybe_partial.rs
index fd17431ca..6d8e370d2 100644
--- a/crates/fj-kernel/src/partial/maybe_partial.rs
+++ b/crates/fj-kernel/src/partial/maybe_partial.rs
@@ -5,7 +5,7 @@ use crate::{
     get::Get,
     insert::Insert,
     objects::{
-        Curve, GlobalCurve, GlobalEdge, GlobalVertex, HalfEdge, Objects,
+        Curve, Cycle, GlobalCurve, GlobalEdge, GlobalVertex, HalfEdge, Objects,
         Surface, SurfaceVertex, Vertex,
     },
     services::Service,
@@ -183,6 +183,16 @@ impl MaybePartial<Curve> {
     }
 }
 
+impl MaybePartial<Cycle> {
+    /// Access the surface
+    pub fn surface(&self) -> Option<Handle<Surface>> {
+        match self {
+            Self::Full(full) => full.surface().clone().into(),
+            Self::Partial(partial) => partial.surface(),
+        }
+    }
+}
+
 impl MaybePartial<GlobalEdge> {
     /// Access the curve
     pub fn curve(&self) -> MaybePartial<GlobalCurve> {
@@ -218,7 +228,7 @@ impl MaybePartial<HalfEdge> {
     pub fn curve(&self) -> MaybePartial<Curve> {
         match self {
             Self::Full(full) => full.curve().clone().into(),
-            Self::Partial(partial) => partial.curve.clone(),
+            Self::Partial(partial) => partial.curve(),
         }
     }
 
@@ -279,6 +289,14 @@ impl MaybePartial<SurfaceVertex> {
 }
 
 impl MaybePartial<Vertex> {
+    /// Access the curve
+    pub fn curve(&self) -> MaybePartial<Curve> {
+        match self {
+            Self::Full(full) => full.curve().clone().into(),
+            Self::Partial(partial) => partial.curve.clone(),
+        }
+    }
+
     /// Access the surface form
     pub fn surface_form(&self) -> MaybePartial<SurfaceVertex> {
         match self {
diff --git a/crates/fj-kernel/src/partial/objects/edge.rs b/crates/fj-kernel/src/partial/objects/edge.rs
index 4e19b627f..481ea8dee 100644
--- a/crates/fj-kernel/src/partial/objects/edge.rs
+++ b/crates/fj-kernel/src/partial/objects/edge.rs
@@ -14,9 +14,6 @@ use crate::{
 /// See [`crate::partial`] for more information.
 #[derive(Clone, Debug, Default)]
 pub struct PartialHalfEdge {
-    /// The curve that the [`HalfEdge`] is defined in
-    pub curve: MaybePartial<Curve>,
-
     /// The vertices that bound the [`HalfEdge`] in the curve
     pub vertices: [MaybePartial<Vertex>; 2],
 
@@ -25,21 +22,26 @@ pub struct PartialHalfEdge {
 }
 
 impl PartialHalfEdge {
+    /// Access the partial half-edge's curve
+    pub fn curve(&self) -> MaybePartial<Curve> {
+        let [a, b] = &self.vertices;
+        a.curve().merge_with(b.curve())
+    }
+
     /// Build a full [`HalfEdge`] from the partial half-edge
-    pub fn build(mut self, objects: &mut Service<Objects>) -> HalfEdge {
+    pub fn build(self, objects: &mut Service<Objects>) -> HalfEdge {
         let global_curve = self
-            .curve
+            .curve()
             .global_form()
             .merge_with(self.global_form.curve());
 
-        let curve = {
-            self.curve = self.curve.merge_with(PartialCurve {
+        let curve = self
+            .curve()
+            .merge_with(PartialCurve {
                 global_form: global_curve,
                 ..Default::default()
-            });
-
-            self.curve.into_full(objects)
-        };
+            })
+            .into_full(objects);
         let vertices = self.vertices.map(|vertex| {
             vertex
                 .merge_with(PartialVertex {
@@ -65,7 +67,6 @@ impl MergeWith for PartialHalfEdge {
         let other = other.into();
 
         Self {
-            curve: self.curve.merge_with(other.curve),
             vertices: self.vertices.merge_with(other.vertices),
             global_form: self.global_form.merge_with(other.global_form),
         }
@@ -74,8 +75,6 @@ impl MergeWith for PartialHalfEdge {
 
 impl Replace<Surface> for PartialHalfEdge {
     fn replace(&mut self, surface: Handle<Surface>) -> &mut Self {
-        self.curve.replace(surface.clone());
-
         for vertex in &mut self.vertices {
             vertex.replace(surface.clone());
         }
@@ -90,7 +89,6 @@ impl From<&HalfEdge> for PartialHalfEdge {
             half_edge.vertices().clone().map(Into::into);
 
         Self {
-            curve: half_edge.curve().clone().into(),
             vertices: [back_vertex, front_vertex],
             global_form: half_edge.global_form().clone().into(),
         }
diff --git a/crates/fj-kernel/src/partial/objects/face.rs b/crates/fj-kernel/src/partial/objects/face.rs
index a2383ed91..85e044d37 100644
--- a/crates/fj-kernel/src/partial/objects/face.rs
+++ b/crates/fj-kernel/src/partial/objects/face.rs
@@ -12,7 +12,6 @@ use crate::{
 /// See [`crate::partial`] for more information.
 #[derive(Clone, Debug, Default)]
 pub struct PartialFace {
-    surface: Option<Handle<Surface>>,
     exterior: MaybePartial<Cycle>,
     interiors: Vec<MaybePartial<Cycle>>,
     color: Option<Color>,
@@ -21,7 +20,7 @@ pub struct PartialFace {
 impl PartialFace {
     /// Access th surface that the [`Face`] is defined in
     pub fn surface(&self) -> Option<Handle<Surface>> {
-        self.surface.clone()
+        self.exterior.surface()
     }
 
     /// Access the [`Face`]'s exterior cycle
@@ -39,12 +38,6 @@ impl PartialFace {
         self.color
     }
 
-    /// Build the [`Face`] with the provided surface
-    pub fn with_surface(mut self, surface: Handle<Surface>) -> Self {
-        self.surface = Some(surface);
-        self
-    }
-
     /// Build the [`Face`] with the provided exterior
     pub fn with_exterior(
         mut self,
@@ -89,7 +82,6 @@ impl MergeWith for PartialFace {
         let other = other.into();
 
         Self {
-            surface: self.surface.merge_with(other.surface),
             exterior: self.exterior.merge_with(other.exterior),
             interiors: Mergeable(self.interiors)
                 .merge_with(Mergeable(other.interiors))
@@ -102,7 +94,6 @@ impl MergeWith for PartialFace {
 impl From<&Face> for PartialFace {
     fn from(face: &Face) -> Self {
         Self {
-            surface: Some(face.surface().clone()),
             exterior: face.exterior().clone().into(),
             interiors: face.interiors().cloned().map(Into::into).collect(),
             color: Some(face.color()),
diff --git a/crates/fj-kernel/src/partial/objects/vertex.rs b/crates/fj-kernel/src/partial/objects/vertex.rs
index 9ebab2aca..ecb4a49d7 100644
--- a/crates/fj-kernel/src/partial/objects/vertex.rs
+++ b/crates/fj-kernel/src/partial/objects/vertex.rs
@@ -69,6 +69,7 @@ impl MergeWith for PartialVertex {
 
 impl Replace<Surface> for PartialVertex {
     fn replace(&mut self, surface: Handle<Surface>) -> &mut Self {
+        self.curve.replace(surface.clone());
         self.surface_form.replace(surface);
         self
     }
diff --git a/crates/fj-kernel/src/validate/face.rs b/crates/fj-kernel/src/validate/face.rs
index db9a082ec..67208e1ea 100644
--- a/crates/fj-kernel/src/validate/face.rs
+++ b/crates/fj-kernel/src/validate/face.rs
@@ -117,10 +117,17 @@ mod tests {
     fn face_surface_mismatch() {
         let mut services = Services::new();
 
+        let surface = services.objects.surfaces.xy_plane();
+
         let valid = Face::partial()
-            .with_surface(services.objects.surfaces.xy_plane())
-            .with_exterior_polygon_from_points([[0., 0.], [3., 0.], [0., 3.]])
-            .with_interior_polygon_from_points([[1., 1.], [1., 2.], [2., 1.]])
+            .with_exterior_polygon_from_points(
+                surface.clone(),
+                [[0., 0.], [3., 0.], [0., 3.]],
+            )
+            .with_interior_polygon_from_points(
+                surface,
+                [[1., 1.], [1., 2.], [2., 1.]],
+            )
             .build(&mut services.objects);
         let invalid = {
             let interiors = [Cycle::partial()
@@ -143,10 +150,17 @@ mod tests {
     fn face_invalid_interior_winding() {
         let mut services = Services::new();
 
+        let surface = services.objects.surfaces.xy_plane();
+
         let valid = Face::partial()
-            .with_surface(services.objects.surfaces.xy_plane())
-            .with_exterior_polygon_from_points([[0., 0.], [3., 0.], [0., 3.]])
-            .with_interior_polygon_from_points([[1., 1.], [1., 2.], [2., 1.]])
+            .with_exterior_polygon_from_points(
+                surface.clone(),
+                [[0., 0.], [3., 0.], [0., 3.]],
+            )
+            .with_interior_polygon_from_points(
+                surface,
+                [[1., 1.], [1., 2.], [2., 1.]],
+            )
             .build(&mut services.objects);
         let invalid = {
             let interiors = valid
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 375409366..69c24790d 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -51,8 +51,7 @@ impl Shape for fj::Sketch {
                     .map(Point::from);
 
                 Face::partial()
-                    .with_surface(surface)
-                    .with_exterior_polygon_from_points(points)
+                    .with_exterior_polygon_from_points(surface, points)
                     .with_color(Color(self.color()))
                     .build(objects)
                     .insert(objects)