diff --git a/crates/fj-kernel/src/algorithms/approx/edge.rs b/crates/fj-kernel/src/algorithms/approx/edge.rs
index dcab7cc147..27ee3c0e3e 100644
--- a/crates/fj-kernel/src/algorithms/approx/edge.rs
+++ b/crates/fj-kernel/src/algorithms/approx/edge.rs
@@ -22,14 +22,12 @@ impl Approx for &HalfEdge {
         tolerance: impl Into<Tolerance>,
         cache: &mut Self::Cache,
     ) -> Self::Approximation {
-        let [a, b] = self.vertices();
-        let boundary = [a, b].map(|vertex| vertex.position());
+        let boundary = self.boundary();
         let range = RangeOnPath { boundary };
 
-        let first = ApproxPoint::new(
-            a.surface_form().position(),
-            a.surface_form().global_form().position(),
-        );
+        let [first, _] = self.surface_vertices();
+        let first =
+            ApproxPoint::new(first.position(), first.global_form().position());
         let curve_approx =
             (self.curve(), range).approx_with_cache(tolerance, cache);
 
diff --git a/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs b/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs
index 0e667ee2b1..eaaca63b52 100644
--- a/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs
@@ -45,9 +45,9 @@ impl CurveEdgeIntersection {
                 }
             };
 
-            let edge_vertices = half_edge.vertices().clone().map(|vertex| {
-                edge_curve_as_line.point_from_line_coords(vertex.position())
-            });
+            let edge_vertices = half_edge
+                .boundary()
+                .map(|point| edge_curve_as_line.point_from_line_coords(point));
 
             Segment::from_points(edge_vertices)
         };
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_point.rs b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
index b32f10ae47..a4bf8aebee 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_point.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
@@ -309,9 +309,9 @@ mod tests {
             .exterior()
             .half_edges()
             .find(|edge| {
-                let [a, b] = edge.vertices();
-                a.surface_form().position() == Point::from([0., 0.])
-                    && b.surface_form().position() == Point::from([2., 0.])
+                let [a, b] = edge.surface_vertices();
+                a.position() == Point::from([0., 0.])
+                    && b.position() == Point::from([2., 0.])
             })
             .unwrap();
         assert_eq!(
diff --git a/crates/fj-kernel/src/algorithms/intersect/ray_edge.rs b/crates/fj-kernel/src/algorithms/intersect/ray_edge.rs
index 962fed93bd..15cfa6be75 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_edge.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_edge.rs
@@ -24,10 +24,9 @@ impl Intersect for (&HorizontalRayToTheRight<2>, &Handle<HalfEdge>) {
             }
         };
 
-        let points = edge.vertices().clone().map(|vertex| {
-            let point = vertex.position();
-            line.point_from_line_coords(point)
-        });
+        let points = edge
+            .boundary()
+            .map(|point| line.point_from_line_coords(point));
         let segment = Segment::from_points(points);
 
         (ray, &segment).intersect()
diff --git a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
index 08d4604482..d5f8aece92 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
@@ -253,9 +253,9 @@ mod tests {
             .exterior()
             .half_edges()
             .find(|edge| {
-                let [a, b] = edge.vertices();
-                a.surface_form().position() == Point::from([-1., 1.])
-                    && b.surface_form().position() == Point::from([-1., -1.])
+                let [a, b] = edge.surface_vertices();
+                a.position() == Point::from([-1., 1.])
+                    && b.position() == Point::from([-1., -1.])
             })
             .unwrap();
         assert_eq!(
diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index 4f884a24e0..29e69290de 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -36,11 +36,9 @@ impl Sweep for (Handle<HalfEdge>, Color) {
         // is not defined in the right surface. Let's create a new bottom edge,
         // by swapping the surface of the original.
         let bottom_edge = {
-            let vertices = edge.vertices();
-
-            let points_curve_and_surface = vertices.clone().map(|vertex| {
-                (vertex.position(), [vertex.position().t, Scalar::ZERO])
-            });
+            let points_curve_and_surface = edge
+                .boundary()
+                .map(|point| (point, [point.t, Scalar::ZERO]));
 
             let curve = {
                 // Please note that creating a line here is correct, even if the
@@ -63,7 +61,7 @@ impl Sweep for (Handle<HalfEdge>, Color) {
                 let points_surface = points_curve_and_surface
                     .map(|(_, point_surface)| point_surface);
 
-                vertices
+                edge.vertices()
                     .each_ref_ext()
                     .into_iter_fixed()
                     .zip(points_surface)
@@ -89,17 +87,14 @@ impl Sweep for (Handle<HalfEdge>, Color) {
         });
 
         let top_edge = {
-            let bottom_vertices = bottom_edge.vertices();
-
             let surface_vertices = side_edges.clone().map(|edge| {
                 let [_, vertex] = edge.vertices();
                 vertex.surface_form().clone()
             });
 
-            let points_curve_and_surface =
-                bottom_vertices.clone().map(|vertex| {
-                    (vertex.position(), [vertex.position().t, Scalar::ONE])
-                });
+            let points_curve_and_surface = bottom_edge
+                .boundary()
+                .map(|point| (point, [point.t, Scalar::ONE]));
 
             let curve = {
                 let global = bottom_edge
@@ -127,14 +122,12 @@ impl Sweep for (Handle<HalfEdge>, Color) {
             )
             .insert(objects);
 
-            let vertices = bottom_vertices
-                .each_ref_ext()
+            let vertices = bottom_edge
+                .boundary()
                 .into_iter_fixed()
                 .zip(surface_vertices)
                 .collect::<[_; 2]>()
-                .map(|(vertex, surface_form)| {
-                    Vertex::new(vertex.position(), surface_form)
-                });
+                .map(|(point, surface_form)| Vertex::new(point, surface_form));
 
             HalfEdge::new(curve, vertices, global).insert(objects)
         };
diff --git a/crates/fj-kernel/src/objects/full/cycle.rs b/crates/fj-kernel/src/objects/full/cycle.rs
index 3104a7c1fd..dc9f8b1927 100644
--- a/crates/fj-kernel/src/objects/full/cycle.rs
+++ b/crates/fj-kernel/src/objects/full/cycle.rs
@@ -39,7 +39,7 @@ impl Cycle {
     /// Access the surface that the cycle is in
     pub fn surface(&self) -> &Handle<Surface> {
         if let Some(half_edge) = self.half_edges.first() {
-            return half_edge.surface();
+            return half_edge.curve().surface();
         }
 
         unreachable!(
@@ -67,8 +67,8 @@ impl Cycle {
                 .next()
                 .expect("Invalid cycle: expected at least one half-edge");
 
-            let [a, b] = first.vertices();
-            let edge_direction_positive = a.position() < b.position();
+            let [a, b] = first.boundary();
+            let edge_direction_positive = a < b;
 
             let circle = match first.curve().path() {
                 SurfacePath::Circle(circle) => circle,
@@ -93,8 +93,8 @@ impl Cycle {
 
         for [a, b] in self.half_edges.as_slice().array_windows_ext() {
             let [a, b] = [a, b].map(|half_edge| {
-                let [vertex, _] = half_edge.vertices();
-                vertex.surface_form().position()
+                let [surface_vertex, _] = half_edge.surface_vertices();
+                surface_vertex.position()
             });
 
             sum += (b.u - a.u) * (b.v + a.v);
diff --git a/crates/fj-kernel/src/objects/full/edge.rs b/crates/fj-kernel/src/objects/full/edge.rs
index 93a82f63c1..1372c09006 100644
--- a/crates/fj-kernel/src/objects/full/edge.rs
+++ b/crates/fj-kernel/src/objects/full/edge.rs
@@ -1,7 +1,10 @@
 use std::fmt;
 
+use fj_interop::ext::ArrayExt;
+use fj_math::Point;
+
 use crate::{
-    objects::{Curve, GlobalCurve, GlobalVertex, Surface, Vertex},
+    objects::{Curve, GlobalCurve, GlobalVertex, SurfaceVertex, Vertex},
     storage::{Handle, HandleWrapper},
 };
 
@@ -32,26 +35,21 @@ impl HalfEdge {
         &self.curve
     }
 
+    /// Access the boundary points of the half-edge on the curve
+    pub fn boundary(&self) -> [Point<1>; 2] {
+        self.vertices.each_ref_ext().map(|vertex| vertex.position())
+    }
+
     /// Access the vertices that bound the half-edge on the curve
     pub fn vertices(&self) -> &[Vertex; 2] {
         &self.vertices
     }
 
-    /// Access the vertex at the back of the half-edge
-    pub fn back(&self) -> &Vertex {
-        let [back, _] = self.vertices();
-        back
-    }
-
-    /// Access the vertex at the front of the half-edge
-    pub fn front(&self) -> &Vertex {
-        let [_, front] = self.vertices();
-        front
-    }
-
-    /// Access the surface that the half-edge's curve is defined in
-    pub fn surface(&self) -> &Handle<Surface> {
-        self.curve().surface()
+    /// Access the surface vertices that bound the half-edge
+    pub fn surface_vertices(&self) -> [&Handle<SurfaceVertex>; 2] {
+        self.vertices
+            .each_ref_ext()
+            .map(|vertex| vertex.surface_form())
     }
 
     /// Access the global form of the half-edge
@@ -62,7 +60,7 @@ impl HalfEdge {
 
 impl fmt::Display for HalfEdge {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        let [a, b] = self.vertices().clone().map(|vertex| vertex.position());
+        let [a, b] = self.boundary();
         write!(f, "edge from {a:?} to {b:?}")?;
         write!(f, " on {:?}", self.curve().global_form())?;
 
diff --git a/crates/fj-kernel/src/validate/cycle.rs b/crates/fj-kernel/src/validate/cycle.rs
index 41b3e23733..b3fb9bde80 100644
--- a/crates/fj-kernel/src/validate/cycle.rs
+++ b/crates/fj-kernel/src/validate/cycle.rs
@@ -45,11 +45,8 @@ impl CycleValidationError {
         errors: &mut Vec<ValidationError>,
     ) {
         for (a, b) in cycle.half_edges().circular_tuple_windows() {
-            let [_, prev] = a.vertices();
-            let [next, _] = b.vertices();
-
-            let prev = prev.surface_form();
-            let next = next.surface_form();
+            let [_, prev] = a.surface_vertices();
+            let [next, _] = b.surface_vertices();
 
             if prev.id() != next.id() {
                 errors.push(
diff --git a/crates/fj-kernel/src/validate/edge.rs b/crates/fj-kernel/src/validate/edge.rs
index 09a711d04c..6f5f127787 100644
--- a/crates/fj-kernel/src/validate/edge.rs
+++ b/crates/fj-kernel/src/validate/edge.rs
@@ -163,9 +163,9 @@ impl HalfEdgeValidationError {
         let global_vertices_from_vertices = {
             let (global_vertices_from_vertices, _) =
                 VerticesInNormalizedOrder::new(
-                    half_edge.vertices().each_ref_ext().map(|vertex| {
-                        vertex.surface_form().global_form().clone()
-                    }),
+                    half_edge.surface_vertices().each_ref_ext().map(
+                        |surface_vertex| surface_vertex.global_form().clone(),
+                    ),
                 );
 
             global_vertices_from_vertices.access_in_normalized_order()
@@ -200,8 +200,8 @@ impl HalfEdgeValidationError {
     ) {
         let curve_surface = half_edge.curve().surface();
 
-        for vertex in half_edge.vertices() {
-            let surface_form_surface = vertex.surface_form().surface();
+        for surface_vertex in half_edge.surface_vertices() {
+            let surface_form_surface = surface_vertex.surface();
 
             if curve_surface.id() != surface_form_surface.id() {
                 errors.push(
@@ -220,9 +220,7 @@ impl HalfEdgeValidationError {
         config: &ValidationConfig,
         errors: &mut Vec<ValidationError>,
     ) {
-        let back_position = half_edge.back().position();
-        let front_position = half_edge.front().position();
-
+        let [back_position, front_position] = half_edge.boundary();
         let distance = (back_position - front_position).magnitude();
 
         if distance < config.distinct_min_distance {