diff --git a/crates/fj-core/src/geometry/geometry.rs b/crates/fj-core/src/geometry/geometry.rs
index 27e09c8d9..3c21b8554 100644
--- a/crates/fj-core/src/geometry/geometry.rs
+++ b/crates/fj-core/src/geometry/geometry.rs
@@ -11,7 +11,7 @@ use super::{GlobalPath, HalfEdgeGeometry, SurfaceGeometry};
 
 /// Geometric data that is associated with topological objects
 pub struct Geometry {
-    half_edge: BTreeMap<Handle<HalfEdge>, HalfEdgeGeometry>,
+    half_edge: BTreeMap<HandleWrapper<HalfEdge>, HalfEdgeGeometry>,
     surface: BTreeMap<HandleWrapper<Surface>, SurfaceGeometry>,
 
     xy_plane: Handle<Surface>,
@@ -61,7 +61,7 @@ impl Geometry {
         half_edge: Handle<HalfEdge>,
         geometry: HalfEdgeGeometry,
     ) {
-        self.half_edge.insert(half_edge, geometry);
+        self.half_edge.insert(half_edge.into(), geometry);
     }
 
     pub(crate) fn define_surface_inner(
@@ -82,7 +82,7 @@ impl Geometry {
         half_edge: &Handle<HalfEdge>,
     ) -> HalfEdgeGeometry {
         self.half_edge
-            .get(half_edge)
+            .get(&half_edge.clone().into())
             .copied()
             .expect("Expected geometry of half-edge to be defined")
     }
diff --git a/crates/fj-core/src/objects/kinds/half_edge.rs b/crates/fj-core/src/objects/kinds/half_edge.rs
index 24d9f4b18..e1bf01277 100644
--- a/crates/fj-core/src/objects/kinds/half_edge.rs
+++ b/crates/fj-core/src/objects/kinds/half_edge.rs
@@ -1,7 +1,7 @@
 use fj_math::Point;
 
 use crate::{
-    geometry::{CurveBoundary, SurfacePath},
+    geometry::CurveBoundary,
     objects::{Curve, Vertex},
     storage::{Handle, HandleWrapper},
 };
@@ -35,7 +35,6 @@ use crate::{
 /// [`Shell`]: crate::objects::Shell
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct HalfEdge {
-    path: SurfacePath,
     boundary: CurveBoundary<Point<1>>,
     curve: HandleWrapper<Curve>,
     start_vertex: HandleWrapper<Vertex>,
@@ -44,24 +43,17 @@ pub struct HalfEdge {
 impl HalfEdge {
     /// Create an instance of `Edge`
     pub fn new(
-        path: SurfacePath,
         boundary: impl Into<CurveBoundary<Point<1>>>,
         curve: Handle<Curve>,
         start_vertex: Handle<Vertex>,
     ) -> Self {
         Self {
-            path,
             boundary: boundary.into(),
             curve: curve.into(),
             start_vertex: start_vertex.into(),
         }
     }
 
-    /// Access the curve that defines the edge's geometry
-    pub fn path(&self) -> SurfacePath {
-        self.path
-    }
-
     /// Access the boundary points of the edge on the curve
     pub fn boundary(&self) -> CurveBoundary<Point<1>> {
         self.boundary
diff --git a/crates/fj-core/src/operations/build/half_edge.rs b/crates/fj-core/src/operations/build/half_edge.rs
index 4c07637ea..a02e9a0a1 100644
--- a/crates/fj-core/src/operations/build/half_edge.rs
+++ b/crates/fj-core/src/operations/build/half_edge.rs
@@ -17,14 +17,13 @@ use crate::{
 pub trait BuildHalfEdge {
     /// Create a half-edge that is not joined to a sibling
     fn unjoined(
-        path: SurfacePath,
         boundary: impl Into<CurveBoundary<Point<1>>>,
         core: &mut Core,
     ) -> HalfEdge {
         let curve = Curve::new().insert(core);
         let start_vertex = Vertex::new().insert(core);
 
-        HalfEdge::new(path, boundary, curve, start_vertex)
+        HalfEdge::new(boundary, curve, start_vertex)
     }
 
     /// Create a half-edge from its sibling
@@ -34,7 +33,6 @@ pub trait BuildHalfEdge {
         core: &mut Core,
     ) -> Handle<HalfEdge> {
         let half_edge = HalfEdge::new(
-            core.layers.geometry.of_half_edge(sibling).path,
             sibling.boundary().reverse(),
             sibling.curve().clone(),
             start_vertex,
@@ -74,7 +72,7 @@ pub trait BuildHalfEdge {
         let boundary =
             [arc.start_angle, arc.end_angle].map(|coord| Point::from([coord]));
 
-        let half_edge = HalfEdge::unjoined(path, boundary, core).insert(core);
+        let half_edge = HalfEdge::unjoined(boundary, core).insert(core);
         core.layers
             .geometry
             .define_half_edge(half_edge.clone(), HalfEdgeGeometry { path });
@@ -92,7 +90,7 @@ pub trait BuildHalfEdge {
         let boundary =
             [Scalar::ZERO, Scalar::TAU].map(|coord| Point::from([coord]));
 
-        let half_edge = HalfEdge::unjoined(path, boundary, core).insert(core);
+        let half_edge = HalfEdge::unjoined(boundary, core).insert(core);
         core.layers
             .geometry
             .define_half_edge(half_edge.clone(), HalfEdgeGeometry { path });
@@ -112,7 +110,7 @@ pub trait BuildHalfEdge {
             boundary.zip_ext(points_surface),
         );
 
-        HalfEdge::unjoined(path, boundary, core)
+        HalfEdge::unjoined(boundary, core)
             .insert(core)
             .set_path(path, &mut core.layers.geometry)
     }
diff --git a/crates/fj-core/src/operations/join/cycle.rs b/crates/fj-core/src/operations/join/cycle.rs
index b58b1506d..c66ae593c 100644
--- a/crates/fj-core/src/operations/join/cycle.rs
+++ b/crates/fj-core/src/operations/join/cycle.rs
@@ -90,7 +90,7 @@ impl JoinCycle for Cycle {
             .into_iter()
             .circular_tuple_windows()
             .map(|((prev_half_edge, _, _), (half_edge, path, boundary))| {
-                HalfEdge::unjoined(path, boundary, core)
+                HalfEdge::unjoined(boundary, core)
                     .update_curve(|_, _| half_edge.curve().clone(), core)
                     .update_start_vertex(
                         |_, _| prev_half_edge.start_vertex().clone(),
diff --git a/crates/fj-core/src/operations/reverse/cycle.rs b/crates/fj-core/src/operations/reverse/cycle.rs
index 36a6fa2ea..8ed73a81a 100644
--- a/crates/fj-core/src/operations/reverse/cycle.rs
+++ b/crates/fj-core/src/operations/reverse/cycle.rs
@@ -17,7 +17,6 @@ impl Reverse for Cycle {
                 let path = core.layers.geometry.of_half_edge(current).path;
 
                 HalfEdge::new(
-                    path,
                     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 bba0b773a..65eecd191 100644
--- a/crates/fj-core/src/operations/reverse/edge.rs
+++ b/crates/fj-core/src/operations/reverse/edge.rs
@@ -14,7 +14,6 @@ impl ReverseCurveCoordinateSystems for Handle<HalfEdge> {
         let boundary = self.boundary().reverse();
 
         let half_edge = HalfEdge::new(
-            path,
             boundary,
             self.curve().clone(),
             self.start_vertex().clone(),
diff --git a/crates/fj-core/src/operations/split/half_edge.rs b/crates/fj-core/src/operations/split/half_edge.rs
index efc170571..c899e3222 100644
--- a/crates/fj-core/src/operations/split/half_edge.rs
+++ b/crates/fj-core/src/operations/split/half_edge.rs
@@ -44,14 +44,12 @@ impl SplitHalfEdge for Handle<HalfEdge> {
         let [start, end] = self.boundary().inner;
 
         let a = HalfEdge::new(
-            core.layers.geometry.of_half_edge(self).path,
             [start, point],
             self.curve().clone(),
             self.start_vertex().clone(),
         )
         .insert(core);
         let b = HalfEdge::new(
-            core.layers.geometry.of_half_edge(self).path,
             [point, end],
             self.curve().clone(),
             Vertex::new().insert(core),
diff --git a/crates/fj-core/src/operations/transform/edge.rs b/crates/fj-core/src/operations/transform/edge.rs
index 933ac520e..0ba22b374 100644
--- a/crates/fj-core/src/operations/transform/edge.rs
+++ b/crates/fj-core/src/operations/transform/edge.rs
@@ -28,7 +28,7 @@ impl TransformObject for Handle<HalfEdge> {
             .transform_with_cache(transform, core, cache);
 
         let half_edge =
-            HalfEdge::new(path, boundary, curve, start_vertex).insert(core);
+            HalfEdge::new(boundary, curve, start_vertex).insert(core);
 
         core.layers
             .geometry
diff --git a/crates/fj-core/src/operations/update/half_edge.rs b/crates/fj-core/src/operations/update/half_edge.rs
index f10ace4d6..003a6a224 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.path(),
             self.boundary(),
             update(self.curve(), core)
                 .insert(core)
@@ -56,7 +55,6 @@ impl UpdateHalfEdge for HalfEdge {
         T: Insert<Inserted = Handle<Vertex>>,
     {
         HalfEdge::new(
-            self.path(),
             self.boundary(),
             self.curve().clone(),
             update(self.start_vertex(), core)
diff --git a/crates/fj-core/src/validate/shell.rs b/crates/fj-core/src/validate/shell.rs
index 2f5597857..707f4be70 100644
--- a/crates/fj-core/src/validate/shell.rs
+++ b/crates/fj-core/src/validate/shell.rs
@@ -446,7 +446,6 @@ mod tests {
                                     cycle.half_edges().nth_circular(0),
                                     |half_edge, core| {
                                         [HalfEdge::new(
-                                            half_edge.path().reverse(),
                                             half_edge.boundary().reverse(),
                                             half_edge.curve().clone(),
                                             half_edge.start_vertex().clone(),