diff --git a/crates/fj-kernel/src/shape/api.rs b/crates/fj-kernel/src/shape/api.rs
index 2608577fd..eb02f3242 100644
--- a/crates/fj-kernel/src/shape/api.rs
+++ b/crates/fj-kernel/src/shape/api.rs
@@ -319,7 +319,10 @@ mod tests {
         assert!(shape.get_handle(&surface.get()).as_ref() == Some(&surface));
 
         let vertex = Vertex { point };
-        let edge = Edge::new(curve, VerticesOfEdge::none());
+        let edge = Edge {
+            curve: LocalForm::canonical_only(curve),
+            vertices: VerticesOfEdge::none(),
+        };
 
         assert!(shape.get_handle(&vertex).is_none());
         assert!(shape.get_handle(&edge).is_none());
@@ -375,10 +378,10 @@ mod tests {
 
         // Shouldn't work. Nothing has been added to `shape`.
         let err = shape
-            .insert(Edge::new(
-                curve.clone(),
-                VerticesOfEdge::from_vertices([a.clone(), b.clone()]),
-            ))
+            .insert(Edge {
+                curve: LocalForm::canonical_only(curve.clone()),
+                vertices: VerticesOfEdge::from_vertices([a.clone(), b.clone()]),
+            })
             .unwrap_err();
         assert!(err.missing_curve(&curve));
         assert!(err.missing_vertex(&a.canonical()));
@@ -392,8 +395,10 @@ mod tests {
         let b = LocalForm::new(Point::from([2.]), b);
 
         // Everything has been added to `shape` now. Should work!
-        shape
-            .insert(Edge::new(curve, VerticesOfEdge::from_vertices([a, b])))?;
+        shape.insert(Edge {
+            curve: LocalForm::canonical_only(curve),
+            vertices: VerticesOfEdge::from_vertices([a, b]),
+        })?;
 
         Ok(())
     }
diff --git a/crates/fj-kernel/src/shape/object.rs b/crates/fj-kernel/src/shape/object.rs
index 265f7f416..29142939f 100644
--- a/crates/fj-kernel/src/shape/object.rs
+++ b/crates/fj-kernel/src/shape/object.rs
@@ -108,10 +108,10 @@ impl Object for Edge<3> {
                     Ok(LocalForm::new(*vertex.local(), canonical))
                 })?;
 
-        let merged = shape.get_handle_or_insert(Edge::new(
-            curve,
-            VerticesOfEdge::new(vertices),
-        ))?;
+        let merged = shape.get_handle_or_insert(Edge {
+            curve: LocalForm::canonical_only(curve),
+            vertices: VerticesOfEdge::new(vertices),
+        })?;
 
         if let Some(handle) = handle {
             mapping.edges.insert(handle, merged.clone());
diff --git a/crates/fj-kernel/src/topology/builder.rs b/crates/fj-kernel/src/topology/builder.rs
index 09b6d5bf8..d52832f31 100644
--- a/crates/fj-kernel/src/topology/builder.rs
+++ b/crates/fj-kernel/src/topology/builder.rs
@@ -66,9 +66,10 @@ impl<'r> EdgeBuilder<'r> {
             curve: LocalForm::new(curve_local, curve_canonical.clone()),
             vertices: VerticesOfEdge::none(),
         };
-        let edge_canonical = self
-            .shape
-            .insert(Edge::new(curve_canonical, VerticesOfEdge::none()))?;
+        let edge_canonical = self.shape.insert(Edge {
+            curve: LocalForm::canonical_only(curve_canonical),
+            vertices: VerticesOfEdge::none(),
+        })?;
 
         Ok(LocalForm::new(edge_local, edge_canonical))
     }
@@ -108,10 +109,10 @@ impl<'r> EdgeBuilder<'r> {
             LocalForm::new(Point::from([1.]), b),
         ];
 
-        let edge = self.shape.insert(Edge::new(
-            curve,
-            VerticesOfEdge::from_vertices(vertices),
-        ))?;
+        let edge = self.shape.insert(Edge {
+            curve: LocalForm::canonical_only(curve),
+            vertices: VerticesOfEdge::from_vertices(vertices),
+        })?;
 
         Ok(edge)
     }
diff --git a/crates/fj-kernel/src/topology/edge.rs b/crates/fj-kernel/src/topology/edge.rs
index 153a079a3..cf0446af8 100644
--- a/crates/fj-kernel/src/topology/edge.rs
+++ b/crates/fj-kernel/src/topology/edge.rs
@@ -4,7 +4,7 @@ use fj_math::Point;
 
 use crate::{
     geometry::Curve,
-    shape::{Handle, LocalForm, Shape},
+    shape::{LocalForm, Shape},
 };
 
 use super::{EdgeBuilder, Vertex};
@@ -37,19 +37,6 @@ pub struct Edge<const D: usize> {
     pub vertices: VerticesOfEdge,
 }
 
-impl Edge<3> {
-    /// Construct an instance of `Edge`
-    pub fn new(curve: Handle<Curve<3>>, vertices: VerticesOfEdge) -> Self {
-        let curve = LocalForm::canonical_only(curve);
-        Self { curve, vertices }
-    }
-
-    /// Build an edge using the [`EdgeBuilder`] API
-    pub fn builder(shape: &mut Shape) -> EdgeBuilder {
-        EdgeBuilder::new(shape)
-    }
-}
-
 impl<const D: usize> Edge<D> {
     /// Access the curve that the edge refers to
     ///
@@ -71,6 +58,13 @@ impl<const D: usize> Edge<D> {
     }
 }
 
+impl Edge<3> {
+    /// Build an edge using the [`EdgeBuilder`] API
+    pub fn builder(shape: &mut Shape) -> EdgeBuilder {
+        EdgeBuilder::new(shape)
+    }
+}
+
 impl<const D: usize> fmt::Display for Edge<D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         match self.vertices() {
diff --git a/crates/fj-operations/src/difference_2d.rs b/crates/fj-operations/src/difference_2d.rs
index a134441c1..5a36d1120 100644
--- a/crates/fj-operations/src/difference_2d.rs
+++ b/crates/fj-operations/src/difference_2d.rs
@@ -121,8 +121,10 @@ fn add_cycle(
             curve: LocalForm::new(curve_local, curve_canonical.clone()),
             vertices: vertices.clone(),
         };
-        let edge_canonical =
-            shape.merge(Edge::new(curve_canonical, vertices))?;
+        let edge_canonical = shape.merge(Edge {
+            curve: LocalForm::canonical_only(curve_canonical),
+            vertices,
+        })?;
 
         edges.push(LocalForm::new(edge_local, edge_canonical));
     }