diff --git a/crates/fj-core/src/algorithms/approx/curve.rs b/crates/fj-core/src/algorithms/approx/curve.rs
index f76043d484..6a5dc4bfa7 100644
--- a/crates/fj-core/src/algorithms/approx/curve.rs
+++ b/crates/fj-core/src/algorithms/approx/curve.rs
@@ -5,7 +5,10 @@ use std::collections::BTreeMap;
 use fj_math::Point;
 
 use crate::{
-    geometry::{CurveBoundary, GlobalPath, SurfaceGeometry, SurfacePath},
+    geometry::{
+        CurveBoundary, GlobalPath, HalfEdgeGeometry, SurfaceGeometry,
+        SurfacePath,
+    },
     objects::Curve,
     storage::Handle,
     Core,
@@ -13,14 +16,7 @@ use crate::{
 
 use super::{Approx, ApproxPoint, Tolerance};
 
-impl Approx
-    for (
-        &Handle<Curve>,
-        SurfacePath,
-        &SurfaceGeometry,
-        CurveBoundary<Point<1>>,
-    )
-{
+impl Approx for (&Handle<Curve>, &HalfEdgeGeometry, &SurfaceGeometry) {
     type Approximation = CurveApprox;
     type Cache = CurveApproxCache;
 
@@ -30,20 +26,20 @@ impl Approx
         cache: &mut Self::Cache,
         core: &mut Core,
     ) -> Self::Approximation {
-        let (curve, surface_path, surface, boundary) = self;
+        let (curve, half_edge, surface) = self;
 
-        match cache.get(curve, boundary) {
+        match cache.get(curve, half_edge.boundary) {
             Some(approx) => approx,
             None => {
                 let approx = approx_curve(
-                    &surface_path,
+                    &half_edge.path,
                     surface,
-                    boundary,
+                    half_edge.boundary,
                     tolerance,
                     core,
                 );
 
-                cache.insert(curve.clone(), boundary, approx)
+                cache.insert(curve.clone(), half_edge.boundary, approx)
             }
         }
     }
@@ -187,7 +183,10 @@ mod tests {
 
     use crate::{
         algorithms::approx::{Approx, ApproxPoint},
-        geometry::{CurveBoundary, GlobalPath, SurfaceGeometry, SurfacePath},
+        geometry::{
+            CurveBoundary, GlobalPath, HalfEdgeGeometry, SurfaceGeometry,
+            SurfacePath,
+        },
         objects::Curve,
         operations::insert::Insert,
         Core,
@@ -198,14 +197,15 @@ mod tests {
         let mut core = Core::new();
 
         let curve = Curve::new().insert(&mut core);
-        let (surface_path, boundary) =
+        let (path, boundary) =
             SurfacePath::line_from_points([[1., 1.], [2., 1.]]);
         let boundary = CurveBoundary::from(boundary);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = core.layers.geometry.xz_plane();
 
         let tolerance = 1.;
-        let approx = (&curve, surface_path, &surface, boundary)
-            .approx(tolerance, &mut core);
+        let approx =
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         assert_eq!(approx.points, vec![]);
     }
@@ -215,17 +215,18 @@ mod tests {
         let mut core = Core::new();
 
         let curve = Curve::new().insert(&mut core);
-        let (surface_path, boundary) =
+        let (path, boundary) =
             SurfacePath::line_from_points([[1., 1.], [2., 1.]]);
         let boundary = CurveBoundary::from(boundary);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = SurfaceGeometry {
             u: GlobalPath::circle_from_radius(1.),
             v: [0., 0., 1.].into(),
         };
 
         let tolerance = 1.;
-        let approx = (&curve, surface_path, &surface, boundary)
-            .approx(tolerance, &mut core);
+        let approx =
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         assert_eq!(approx.points, vec![]);
     }
@@ -236,26 +237,26 @@ mod tests {
 
         let global_path = GlobalPath::circle_from_radius(1.);
         let curve = Curve::new().insert(&mut core);
-        let surface_path = SurfacePath::line_from_points_with_coords([
+        let path = SurfacePath::line_from_points_with_coords([
             ([0.], [0., 1.]),
             ([TAU], [TAU, 1.]),
         ]);
         let boundary = CurveBoundary::from([[0.], [TAU]]);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = SurfaceGeometry {
             u: global_path,
             v: [0., 0., 1.].into(),
         };
 
         let tolerance = 1.;
-        let approx = (&curve, surface_path, &surface, boundary)
-            .approx(tolerance, &mut core);
+        let approx =
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
         let expected_approx = (global_path, boundary)
             .approx(tolerance, &mut core)
             .into_iter()
             .map(|(point_local, _)| {
-                let point_surface =
-                    surface_path.point_from_path_coords(point_local);
+                let point_surface = path.point_from_path_coords(point_local);
                 let point_global =
                     surface.point_from_surface_coords(point_surface);
                 ApproxPoint::new(point_local, point_global)
@@ -269,21 +270,20 @@ mod tests {
         let mut core = Core::new();
 
         let curve = Curve::new().insert(&mut core);
-        let surface_path =
-            SurfacePath::circle_from_center_and_radius([0., 0.], 1.);
+        let path = SurfacePath::circle_from_center_and_radius([0., 0.], 1.);
         let boundary = CurveBoundary::from([[0.], [TAU]]);
+        let half_edge = HalfEdgeGeometry { path, boundary };
         let surface = core.layers.geometry.xz_plane();
 
         let tolerance = 1.;
-        let approx = (&curve, surface_path, &surface, boundary)
-            .approx(tolerance, &mut core);
+        let approx =
+            (&curve, &half_edge, &surface).approx(tolerance, &mut core);
 
-        let expected_approx = (&surface_path, boundary)
+        let expected_approx = (&path, boundary)
             .approx(tolerance, &mut core)
             .into_iter()
             .map(|(point_local, _)| {
-                let point_surface =
-                    surface_path.point_from_path_coords(point_local);
+                let point_surface = path.point_from_path_coords(point_local);
                 let point_global =
                     surface.point_from_surface_coords(point_surface);
                 ApproxPoint::new(point_local, point_global)
diff --git a/crates/fj-core/src/algorithms/approx/edge.rs b/crates/fj-core/src/algorithms/approx/edge.rs
index 356cb193d0..5db47de993 100644
--- a/crates/fj-core/src/algorithms/approx/edge.rs
+++ b/crates/fj-core/src/algorithms/approx/edge.rs
@@ -50,9 +50,8 @@ impl Approx for (&Handle<HalfEdge>, &SurfaceGeometry) {
         let rest = {
             let approx = (
                 half_edge.curve(),
-                core.layers.geometry.of_half_edge(half_edge).path,
+                &core.layers.geometry.of_half_edge(half_edge),
                 surface,
-                half_edge.boundary(),
             )
                 .approx_with_cache(
                     tolerance,
diff --git a/crates/fj-core/src/algorithms/bounding_volume/edge.rs b/crates/fj-core/src/algorithms/bounding_volume/edge.rs
index ec7ed05f20..4e243d1581 100644
--- a/crates/fj-core/src/algorithms/bounding_volume/edge.rs
+++ b/crates/fj-core/src/algorithms/bounding_volume/edge.rs
@@ -22,11 +22,10 @@ impl super::BoundingVolume<2> for Handle<HalfEdge> {
                 })
             }
             SurfacePath::Line(_) => {
-                let points = self.boundary().inner.map(|point_curve| {
-                    geometry
-                        .of_half_edge(self)
-                        .path
-                        .point_from_path_coords(point_curve)
+                let geometry = geometry.of_half_edge(self);
+
+                let points = geometry.boundary.inner.map(|point_curve| {
+                    geometry.path.point_from_path_coords(point_curve)
                 });
 
                 Some(Aabb::<2>::from_points(points))
diff --git a/crates/fj-core/src/objects/kinds/cycle.rs b/crates/fj-core/src/objects/kinds/cycle.rs
index b1fc57b6a3..40e84b53a7 100644
--- a/crates/fj-core/src/objects/kinds/cycle.rs
+++ b/crates/fj-core/src/objects/kinds/cycle.rs
@@ -40,10 +40,12 @@ impl Cycle {
                 .next()
                 .expect("Invalid cycle: expected at least one edge");
 
-            let [a, b] = first.boundary().inner;
+            let geometry = geometry.of_half_edge(first);
+
+            let [a, b] = geometry.boundary.inner;
             let edge_direction_positive = a < b;
 
-            let circle = match geometry.of_half_edge(first).path {
+            let circle = match geometry.path {
                 SurfacePath::Circle(circle) => circle,
                 SurfacePath::Line(_) => unreachable!(
                     "Invalid cycle: less than 3 edges, but not all are circles"
diff --git a/crates/fj-core/src/objects/kinds/half_edge.rs b/crates/fj-core/src/objects/kinds/half_edge.rs
index 523def5dc8..6608d40d3c 100644
--- a/crates/fj-core/src/objects/kinds/half_edge.rs
+++ b/crates/fj-core/src/objects/kinds/half_edge.rs
@@ -1,7 +1,4 @@
-use fj_math::Point;
-
 use crate::{
-    geometry::CurveBoundary,
     objects::{Curve, Vertex},
     storage::Handle,
 };
@@ -35,30 +32,19 @@ use crate::{
 /// [`Shell`]: crate::objects::Shell
 #[derive(Clone, Debug)]
 pub struct HalfEdge {
-    boundary: CurveBoundary<Point<1>>,
     curve: Handle<Curve>,
     start_vertex: Handle<Vertex>,
 }
 
 impl HalfEdge {
     /// Create an instance of `Edge`
-    pub fn new(
-        boundary: impl Into<CurveBoundary<Point<1>>>,
-        curve: Handle<Curve>,
-        start_vertex: Handle<Vertex>,
-    ) -> Self {
+    pub fn new(curve: Handle<Curve>, start_vertex: Handle<Vertex>) -> Self {
         Self {
-            boundary: boundary.into(),
             curve,
             start_vertex,
         }
     }
 
-    /// Access the boundary points of the edge on the curve
-    pub fn boundary(&self) -> CurveBoundary<Point<1>> {
-        self.boundary
-    }
-
     /// Access the curve of the edge
     pub fn curve(&self) -> &Handle<Curve> {
         &self.curve
diff --git a/crates/fj-core/src/operations/build/half_edge.rs b/crates/fj-core/src/operations/build/half_edge.rs
index 0d0a3ce5aa..53c3abcd57 100644
--- a/crates/fj-core/src/operations/build/half_edge.rs
+++ b/crates/fj-core/src/operations/build/half_edge.rs
@@ -2,7 +2,7 @@ use fj_interop::ext::ArrayExt;
 use fj_math::{Arc, Point, Scalar};
 
 use crate::{
-    geometry::{CurveBoundary, HalfEdgeGeometry, SurfacePath},
+    geometry::{HalfEdgeGeometry, SurfacePath},
     objects::{Curve, HalfEdge, Vertex},
     operations::{geometry::UpdateHalfEdgeGeometry, insert::Insert},
     storage::Handle,
@@ -16,14 +16,11 @@ use crate::{
 /// [module-level documentation]: super
 pub trait BuildHalfEdge {
     /// Create a half-edge that is not joined to a sibling
-    fn unjoined(
-        boundary: impl Into<CurveBoundary<Point<1>>>,
-        core: &mut Core,
-    ) -> HalfEdge {
+    fn unjoined(core: &mut Core) -> HalfEdge {
         let curve = Curve::new().insert(core);
         let start_vertex = Vertex::new().insert(core);
 
-        HalfEdge::new(boundary, curve, start_vertex)
+        HalfEdge::new(curve, start_vertex)
     }
 
     /// Create a half-edge from its sibling
@@ -35,13 +32,9 @@ pub trait BuildHalfEdge {
         let mut geometry = core.layers.geometry.of_half_edge(sibling);
         geometry.boundary = geometry.boundary.reverse();
 
-        HalfEdge::new(
-            sibling.boundary().reverse(),
-            sibling.curve().clone(),
-            start_vertex,
-        )
-        .insert(core)
-        .set_geometry(geometry, &mut core.layers.geometry)
+        HalfEdge::new(sibling.curve().clone(), start_vertex)
+            .insert(core)
+            .set_geometry(geometry, &mut core.layers.geometry)
     }
 
     /// Create an arc
@@ -67,7 +60,7 @@ pub trait BuildHalfEdge {
         let boundary =
             [arc.start_angle, arc.end_angle].map(|coord| Point::from([coord]));
 
-        let half_edge = HalfEdge::unjoined(boundary, core).insert(core);
+        let half_edge = HalfEdge::unjoined(core).insert(core);
         core.layers.geometry.define_half_edge(
             half_edge.clone(),
             HalfEdgeGeometry {
@@ -89,7 +82,7 @@ pub trait BuildHalfEdge {
         let boundary =
             [Scalar::ZERO, Scalar::TAU].map(|coord| Point::from([coord]));
 
-        let half_edge = HalfEdge::unjoined(boundary, core).insert(core);
+        let half_edge = HalfEdge::unjoined(core).insert(core);
         core.layers.geometry.define_half_edge(
             half_edge.clone(),
             HalfEdgeGeometry {
@@ -113,15 +106,13 @@ pub trait BuildHalfEdge {
             boundary.zip_ext(points_surface),
         );
 
-        HalfEdge::unjoined(boundary, core)
-            .insert(core)
-            .set_geometry(
-                HalfEdgeGeometry {
-                    path,
-                    boundary: boundary.into(),
-                },
-                &mut core.layers.geometry,
-            )
+        HalfEdge::unjoined(core).insert(core).set_geometry(
+            HalfEdgeGeometry {
+                path,
+                boundary: boundary.into(),
+            },
+            &mut core.layers.geometry,
+        )
     }
 }
 
diff --git a/crates/fj-core/src/operations/holes.rs b/crates/fj-core/src/operations/holes.rs
index 3017c09ef0..7b19b73478 100644
--- a/crates/fj-core/src/operations/holes.rs
+++ b/crates/fj-core/src/operations/holes.rs
@@ -68,11 +68,7 @@ impl AddHole for Shell {
                             [Cycle::empty().add_joined_edges(
                                 [(
                                     entry.clone(),
-                                    core.layers
-                                        .geometry
-                                        .of_half_edge(&entry)
-                                        .path,
-                                    entry.boundary(),
+                                    core.layers.geometry.of_half_edge(&entry),
                                 )],
                                 core,
                             )],
@@ -142,11 +138,7 @@ impl AddHole for Shell {
                             [Cycle::empty().add_joined_edges(
                                 [(
                                     entry.clone(),
-                                    core.layers
-                                        .geometry
-                                        .of_half_edge(&entry)
-                                        .path,
-                                    entry.boundary(),
+                                    core.layers.geometry.of_half_edge(&entry),
                                 )],
                                 core,
                             )],
@@ -167,11 +159,7 @@ impl AddHole for Shell {
                             [Cycle::empty().add_joined_edges(
                                 [(
                                     exit.clone(),
-                                    core.layers
-                                        .geometry
-                                        .of_half_edge(exit)
-                                        .path,
-                                    exit.boundary(),
+                                    core.layers.geometry.of_half_edge(exit),
                                 )],
                                 core,
                             )],
diff --git a/crates/fj-core/src/operations/join/cycle.rs b/crates/fj-core/src/operations/join/cycle.rs
index 82cd9bfc8c..5821a1d68f 100644
--- a/crates/fj-core/src/operations/join/cycle.rs
+++ b/crates/fj-core/src/operations/join/cycle.rs
@@ -1,10 +1,9 @@
 use std::ops::RangeInclusive;
 
-use fj_math::Point;
 use itertools::Itertools;
 
 use crate::{
-    geometry::{CurveBoundary, HalfEdgeGeometry, SurfacePath},
+    geometry::HalfEdgeGeometry,
     objects::{Cycle, HalfEdge},
     operations::{
         build::BuildHalfEdge,
@@ -22,9 +21,7 @@ pub trait JoinCycle {
     #[must_use]
     fn add_joined_edges<Es>(&self, edges: Es, core: &mut Core) -> Self
     where
-        Es: IntoIterator<
-            Item = (Handle<HalfEdge>, SurfacePath, CurveBoundary<Point<1>>),
-        >,
+        Es: IntoIterator<Item = (Handle<HalfEdge>, HalfEdgeGeometry)>,
         Es::IntoIter: Clone + ExactSizeIterator;
 
     /// Join the cycle to another
@@ -81,26 +78,21 @@ pub trait JoinCycle {
 impl JoinCycle for Cycle {
     fn add_joined_edges<Es>(&self, edges: Es, core: &mut Core) -> Self
     where
-        Es: IntoIterator<
-            Item = (Handle<HalfEdge>, SurfacePath, CurveBoundary<Point<1>>),
-        >,
+        Es: IntoIterator<Item = (Handle<HalfEdge>, HalfEdgeGeometry)>,
         Es::IntoIter: Clone + ExactSizeIterator,
     {
         let half_edges = edges
             .into_iter()
             .circular_tuple_windows()
-            .map(|((prev_half_edge, _, _), (half_edge, path, boundary))| {
-                HalfEdge::unjoined(boundary, core)
+            .map(|((prev_half_edge, _), (half_edge, geometry))| {
+                HalfEdge::unjoined(core)
                     .update_curve(|_, _| half_edge.curve().clone(), core)
                     .update_start_vertex(
                         |_, _| prev_half_edge.start_vertex().clone(),
                         core,
                     )
                     .insert(core)
-                    .set_geometry(
-                        HalfEdgeGeometry { path, boundary },
-                        &mut core.layers.geometry,
-                    )
+                    .set_geometry(geometry, &mut core.layers.geometry)
             })
             .collect::<Vec<_>>();
         self.add_half_edges(half_edges, core)
diff --git a/crates/fj-core/src/operations/reverse/cycle.rs b/crates/fj-core/src/operations/reverse/cycle.rs
index a3dd7b3cb9..f3d3f341d4 100644
--- a/crates/fj-core/src/operations/reverse/cycle.rs
+++ b/crates/fj-core/src/operations/reverse/cycle.rs
@@ -18,7 +18,6 @@ impl Reverse for Cycle {
                 geometry.boundary = geometry.boundary.reverse();
 
                 HalfEdge::new(
-                    current.boundary().reverse(),
                     current.curve().clone(),
                     next.start_vertex().clone(),
                 )
diff --git a/crates/fj-core/src/operations/reverse/edge.rs b/crates/fj-core/src/operations/reverse/edge.rs
index 4508a25e76..e42ae6a98a 100644
--- a/crates/fj-core/src/operations/reverse/edge.rs
+++ b/crates/fj-core/src/operations/reverse/edge.rs
@@ -13,13 +13,10 @@ impl ReverseCurveCoordinateSystems for Handle<HalfEdge> {
         geometry.path = geometry.path.reverse();
         geometry.boundary = geometry.boundary.reverse();
 
-        let half_edge = HalfEdge::new(
-            geometry.boundary,
-            self.curve().clone(),
-            self.start_vertex().clone(),
-        )
-        .insert(core)
-        .derive_from(self, core);
+        let half_edge =
+            HalfEdge::new(self.curve().clone(), self.start_vertex().clone())
+                .insert(core)
+                .derive_from(self, core);
 
         core.layers
             .geometry
diff --git a/crates/fj-core/src/operations/split/edge.rs b/crates/fj-core/src/operations/split/edge.rs
index 84496ca443..b85893a4f5 100644
--- a/crates/fj-core/src/operations/split/edge.rs
+++ b/crates/fj-core/src/operations/split/edge.rs
@@ -37,7 +37,7 @@ impl SplitEdge for Shell {
         let point = point.into();
 
         let sibling = self
-            .get_sibling_of(half_edge)
+            .get_sibling_of(half_edge, &core.layers.geometry)
             .expect("Expected half-edge and its sibling to be part of shell");
 
         let [half_edge_a, half_edge_b] = half_edge.split_half_edge(point, core);
diff --git a/crates/fj-core/src/operations/split/half_edge.rs b/crates/fj-core/src/operations/split/half_edge.rs
index 9279599a81..92621b7fa4 100644
--- a/crates/fj-core/src/operations/split/half_edge.rs
+++ b/crates/fj-core/src/operations/split/half_edge.rs
@@ -42,36 +42,24 @@ impl SplitHalfEdge for Handle<HalfEdge> {
     ) -> [Handle<HalfEdge>; 2] {
         let point = point.into();
 
-        let [start, end] = self.boundary().inner;
+        let geometry = core.layers.geometry.of_half_edge(self);
+        let [start, end] = geometry.boundary.inner;
 
-        let a = HalfEdge::new(
-            [start, point],
-            self.curve().clone(),
-            self.start_vertex().clone(),
-        )
-        .insert(core)
-        .derive_from(self, core)
-        .set_geometry(
-            core.layers
-                .geometry
-                .of_half_edge(self)
-                .with_boundary([start, point]),
-            &mut core.layers.geometry,
-        );
-        let b = HalfEdge::new(
-            [point, end],
-            self.curve().clone(),
-            Vertex::new().insert(core),
-        )
-        .insert(core)
-        .derive_from(self, core)
-        .set_geometry(
-            core.layers
-                .geometry
-                .of_half_edge(self)
-                .with_boundary([point, end]),
-            &mut core.layers.geometry,
-        );
+        let a =
+            HalfEdge::new(self.curve().clone(), self.start_vertex().clone())
+                .insert(core)
+                .derive_from(self, core)
+                .set_geometry(
+                    geometry.with_boundary([start, point]),
+                    &mut core.layers.geometry,
+                );
+        let b = HalfEdge::new(self.curve().clone(), Vertex::new().insert(core))
+            .insert(core)
+            .derive_from(self, core)
+            .set_geometry(
+                geometry.with_boundary([point, end]),
+                &mut core.layers.geometry,
+            );
 
         [a, b]
     }
diff --git a/crates/fj-core/src/operations/sweep/cycle.rs b/crates/fj-core/src/operations/sweep/cycle.rs
index 23f04051cd..313c71efc8 100644
--- a/crates/fj-core/src/operations/sweep/cycle.rs
+++ b/crates/fj-core/src/operations/sweep/cycle.rs
@@ -77,8 +77,7 @@ impl SweepCycle for Cycle {
 
             top_edges.push((
                 top_edge,
-                core.layers.geometry.of_half_edge(bottom_half_edge).path,
-                bottom_half_edge.boundary(),
+                core.layers.geometry.of_half_edge(bottom_half_edge),
             ));
         }
 
diff --git a/crates/fj-core/src/operations/sweep/half_edge.rs b/crates/fj-core/src/operations/sweep/half_edge.rs
index 3014c16b2f..4fbb1f711d 100644
--- a/crates/fj-core/src/operations/sweep/half_edge.rs
+++ b/crates/fj-core/src/operations/sweep/half_edge.rs
@@ -59,12 +59,8 @@ impl SweepHalfEdge for Handle<HalfEdge> {
     ) -> (Face, Handle<HalfEdge>) {
         let path = path.into();
 
-        let surface = core
-            .layers
-            .geometry
-            .of_half_edge(self)
-            .path
-            .sweep_surface_path(surface, path, core);
+        let geometry = core.layers.geometry.of_half_edge(self);
+        let surface = geometry.path.sweep_surface_path(surface, path, core);
 
         // Next, we need to define the boundaries of the face. Let's start with
         // the global vertices and edges.
@@ -86,7 +82,7 @@ impl SweepHalfEdge for Handle<HalfEdge> {
 
         // Let's figure out the surface coordinates of the edge vertices.
         let surface_points = {
-            let [a, b] = self.boundary().inner;
+            let [a, b] = geometry.boundary.inner;
 
             [
                 [a.t, Scalar::ZERO],
@@ -104,7 +100,7 @@ impl SweepHalfEdge for Handle<HalfEdge> {
 
         // Now, the boundaries of each edge.
         let boundaries = {
-            let [a, b] = self.boundary().inner;
+            let [a, b] = geometry.boundary.inner;
             let [c, d] = [0., 1.].map(|coord| Point::from([coord]));
 
             [[a, b], [c, d], [b, a], [d, c]]
diff --git a/crates/fj-core/src/operations/transform/edge.rs b/crates/fj-core/src/operations/transform/edge.rs
index 9e1a708adc..6baf3fcc9f 100644
--- a/crates/fj-core/src/operations/transform/edge.rs
+++ b/crates/fj-core/src/operations/transform/edge.rs
@@ -13,7 +13,6 @@ impl TransformObject for Handle<HalfEdge> {
         core: &mut Core,
         cache: &mut TransformCache,
     ) -> Self {
-        let boundary = self.boundary();
         let curve = self
             .curve()
             .clone()
@@ -23,8 +22,7 @@ impl TransformObject for Handle<HalfEdge> {
             .clone()
             .transform_with_cache(transform, core, cache);
 
-        let half_edge =
-            HalfEdge::new(boundary, curve, start_vertex).insert(core);
+        let half_edge = HalfEdge::new(curve, start_vertex).insert(core);
 
         core.layers.geometry.define_half_edge(
             half_edge.clone(),
diff --git a/crates/fj-core/src/operations/update/half_edge.rs b/crates/fj-core/src/operations/update/half_edge.rs
index 003a6a2244..b1f782d1d6 100644
--- a/crates/fj-core/src/operations/update/half_edge.rs
+++ b/crates/fj-core/src/operations/update/half_edge.rs
@@ -38,7 +38,6 @@ impl UpdateHalfEdge for HalfEdge {
         T: Insert<Inserted = Handle<Curve>>,
     {
         HalfEdge::new(
-            self.boundary(),
             update(self.curve(), core)
                 .insert(core)
                 .derive_from(self.curve(), core),
@@ -55,7 +54,6 @@ impl UpdateHalfEdge for HalfEdge {
         T: Insert<Inserted = Handle<Vertex>>,
     {
         HalfEdge::new(
-            self.boundary(),
             self.curve().clone(),
             update(self.start_vertex(), core)
                 .insert(core)
diff --git a/crates/fj-core/src/queries/sibling_of_half_edge.rs b/crates/fj-core/src/queries/sibling_of_half_edge.rs
index 5c5dd2314c..07583f548e 100644
--- a/crates/fj-core/src/queries/sibling_of_half_edge.rs
+++ b/crates/fj-core/src/queries/sibling_of_half_edge.rs
@@ -1,4 +1,5 @@
 use crate::{
+    geometry::Geometry,
     objects::{HalfEdge, Shell},
     storage::Handle,
 };
@@ -8,7 +9,12 @@ use super::BoundingVerticesOfHalfEdge;
 /// Queries related to the sibling of a [`HalfEdge`]
 pub trait SiblingOfHalfEdge {
     /// Indicate whether the provided half-edges are siblings
-    fn are_siblings(&self, a: &Handle<HalfEdge>, b: &Handle<HalfEdge>) -> bool;
+    fn are_siblings(
+        &self,
+        a: &Handle<HalfEdge>,
+        b: &Handle<HalfEdge>,
+        geometry: &Geometry,
+    ) -> bool;
 
     /// Retrieve the sibling of this half-edge
     ///
@@ -18,13 +24,20 @@ pub trait SiblingOfHalfEdge {
     fn get_sibling_of(
         &self,
         half_edge: &Handle<HalfEdge>,
+        geometry: &Geometry,
     ) -> Option<Handle<HalfEdge>>;
 }
 
 impl SiblingOfHalfEdge for Shell {
-    fn are_siblings(&self, a: &Handle<HalfEdge>, b: &Handle<HalfEdge>) -> bool {
+    fn are_siblings(
+        &self,
+        a: &Handle<HalfEdge>,
+        b: &Handle<HalfEdge>,
+        geometry: &Geometry,
+    ) -> bool {
         let same_curve = a.curve().id() == b.curve().id();
-        let same_boundary = a.boundary() == b.boundary().reverse();
+        let same_boundary = geometry.of_half_edge(a).boundary
+            == geometry.of_half_edge(b).boundary.reverse();
         let same_vertices = {
             let Some(a_vertices) = self.bounding_vertices_of_half_edge(a)
             else {
@@ -44,11 +57,12 @@ impl SiblingOfHalfEdge for Shell {
     fn get_sibling_of(
         &self,
         half_edge: &Handle<HalfEdge>,
+        geometry: &Geometry,
     ) -> Option<Handle<HalfEdge>> {
         for face in self.faces() {
             for cycle in face.region().all_cycles() {
                 for h in cycle.half_edges() {
-                    if self.are_siblings(half_edge, h) {
+                    if self.are_siblings(half_edge, h, geometry) {
                         return Some(h.clone());
                     }
                 }
diff --git a/crates/fj-core/src/validate/shell.rs b/crates/fj-core/src/validate/shell.rs
index 237d743c16..83d85a258c 100644
--- a/crates/fj-core/src/validate/shell.rs
+++ b/crates/fj-core/src/validate/shell.rs
@@ -23,7 +23,7 @@ impl Validate for Shell {
         ShellValidationError::check_curve_coordinates(
             self, geometry, config, errors,
         );
-        ShellValidationError::check_half_edge_pairs(self, errors);
+        ShellValidationError::check_half_edge_pairs(self, geometry, errors);
         ShellValidationError::check_half_edge_coincidence(
             self, geometry, config, errors,
         );
@@ -112,7 +112,7 @@ impl ShellValidationError {
                     // we have right now are circles, 3 would be enough to check
                     // for coincidence. But the first and last might be
                     // identical, so let's add an extra one.
-                    let [a, d] = edge_a.boundary().inner;
+                    let [a, d] = geometry.of_half_edge(edge_a).boundary.inner;
                     let b = a + (d - a) * 1. / 3.;
                     let c = a + (d - a) * 2. / 3.;
 
@@ -177,14 +177,18 @@ impl ShellValidationError {
     }
 
     /// Check that each half-edge is part of a pair
-    fn check_half_edge_pairs(shell: &Shell, errors: &mut Vec<ValidationError>) {
+    fn check_half_edge_pairs(
+        shell: &Shell,
+        geometry: &Geometry,
+        errors: &mut Vec<ValidationError>,
+    ) {
         let mut unmatched_half_edges = BTreeMap::new();
 
         for face in shell.faces() {
             for cycle in face.region().all_cycles() {
                 for half_edge in cycle.half_edges() {
                     let curve = half_edge.curve().clone();
-                    let boundary = half_edge.boundary();
+                    let boundary = geometry.of_half_edge(half_edge).boundary;
                     let vertices =
                         cycle.bounding_vertices_of_half_edge(half_edge).expect(
                             "`half_edge` came from `cycle`, must exist there",
@@ -200,7 +204,8 @@ impl ShellValidationError {
                             // currently looking at. Let's make sure the logic
                             // we use here to determine that matches the
                             // "official" definition.
-                            assert!(shell.are_siblings(half_edge, sibling));
+                            assert!(shell
+                                .are_siblings(half_edge, sibling, geometry));
                         }
                         None => {
                             // If this half-edge has a sibling, we haven't seen
@@ -238,7 +243,7 @@ impl ShellValidationError {
                     continue;
                 }
 
-                if shell.are_siblings(half_edge_a, half_edge_b) {
+                if shell.are_siblings(half_edge_a, half_edge_b, geometry) {
                     // If the half-edges are siblings, they are allowed to be
                     // coincident. Must be, in fact. There's another validation
                     // check that takes care of that.
@@ -257,8 +262,11 @@ impl ShellValidationError {
                 .all(|d| d < config.distinct_min_distance)
                 {
                     let boundaries = Box::new(CoincidentHalfEdgeBoundaries {
-                        boundaries: [half_edge_a, half_edge_b]
-                            .map(|half_edge| half_edge.boundary()),
+                        boundaries: [half_edge_a, half_edge_b].map(
+                            |half_edge| {
+                                geometry.of_half_edge(half_edge).boundary
+                            },
+                        ),
                     });
                     let curves = Box::new(CoincidentHalfEdgeCurves {
                         curves: [half_edge_a, half_edge_b]
@@ -384,7 +392,7 @@ fn distances(
         (edge, surface): (&Handle<HalfEdge>, &SurfaceGeometry),
         geometry: &Geometry,
     ) -> Point<3> {
-        let [start, end] = edge.boundary().inner;
+        let [start, end] = geometry.of_half_edge(edge).boundary.inner;
         let path_coords = start + (end - start) * percent;
         let surface_coords = geometry
             .of_half_edge(edge)
@@ -454,7 +462,6 @@ mod tests {
                                             geometry.boundary.reverse();
 
                                         [HalfEdge::new(
-                                            half_edge.boundary().reverse(),
                                             half_edge.curve().clone(),
                                             half_edge.start_vertex().clone(),
                                         )
diff --git a/crates/fj-core/src/validation/checks/half_edge_connection.rs b/crates/fj-core/src/validation/checks/half_edge_connection.rs
index 0cad2daa8e..7fefc9560e 100644
--- a/crates/fj-core/src/validation/checks/half_edge_connection.rs
+++ b/crates/fj-core/src/validation/checks/half_edge_connection.rs
@@ -46,7 +46,7 @@ impl ValidationCheck<Cycle> for AdjacentHalfEdgesNotConnected {
     ) -> impl Iterator<Item = Self> {
         object.half_edges().pairs().filter_map(|(first, second)| {
             let end_pos_of_first_half_edge = {
-                let [_, end] = first.boundary().inner;
+                let [_, end] = geometry.of_half_edge(first).boundary.inner;
                 geometry
                     .of_half_edge(first)
                     .path