diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index f1f2005f6..36f745545 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -71,7 +71,6 @@ impl Sweep for (HalfEdge, Color) {
                         vertex.position(),
                         curve.clone(),
                         surface_vertex,
-                        *vertex.global_form(),
                     )
                 })
             };
@@ -134,18 +133,13 @@ impl Sweep for (HalfEdge, Color) {
                     (b_vertex, b_surface, b_global),
                 ];
 
-                vertices.map(|(vertex, point_surface, vertex_global)| {
-                    let vertex_surface = SurfaceVertex::new(
+                vertices.map(|(vertex, point_surface, global_form)| {
+                    let surface_form = SurfaceVertex::new(
                         point_surface,
                         surface.clone(),
-                        vertex_global,
+                        global_form,
                     );
-                    Vertex::new(
-                        vertex.position(),
-                        curve.clone(),
-                        vertex_surface,
-                        vertex_global,
-                    )
+                    Vertex::new(vertex.position(), curve.clone(), surface_form)
                 })
             };
 
diff --git a/crates/fj-kernel/src/algorithms/sweep/vertex.rs b/crates/fj-kernel/src/algorithms/sweep/vertex.rs
index 2f9eb4df2..04835a3ac 100644
--- a/crates/fj-kernel/src/algorithms/sweep/vertex.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/vertex.rs
@@ -104,18 +104,11 @@ impl Sweep for (Vertex, Handle<Surface>) {
                     },
                 );
 
-            // Can be cleaned up, once `zip` is stable:
-            // https://doc.rust-lang.org/std/primitive.array.html#method.zip
-            let [a_surface, b_surface] = vertices_surface;
-            let [a_global, b_global] = vertices_global;
-            let vertices = [(a_surface, a_global), (b_surface, b_global)];
-
-            vertices.map(|(vertex_surface, vertex_global)| {
+            vertices_surface.map(|surface_form| {
                 Vertex::new(
-                    [vertex_surface.position().v],
+                    [surface_form.position().v],
                     curve.clone(),
-                    vertex_surface,
-                    vertex_global,
+                    surface_form,
                 )
             })
         };
diff --git a/crates/fj-kernel/src/algorithms/validate/mod.rs b/crates/fj-kernel/src/algorithms/validate/mod.rs
index c6901c89d..bc294e214 100644
--- a/crates/fj-kernel/src/algorithms/validate/mod.rs
+++ b/crates/fj-kernel/src/algorithms/validate/mod.rs
@@ -205,14 +205,9 @@ mod tests {
             Point::from([Scalar::ZERO + deviation]),
             curve.clone(),
             a_surface,
-            a_global,
-        );
-        let b = Vertex::new(
-            Point::from([Scalar::ONE]),
-            curve.clone(),
-            b_surface,
-            b_global,
         );
+        let b =
+            Vertex::new(Point::from([Scalar::ONE]), curve.clone(), b_surface);
         let vertices = [a, b];
 
         let global_edge = GlobalEdge::partial()
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index 51a11b1c0..2c3ba1047 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -589,7 +589,7 @@ mod tests {
         let global_vertex = GlobalVertex::from_position([0., 0., 0.]);
         let surface_vertex =
             SurfaceVertex::new([0., 0.], surface, global_vertex);
-        let object = Vertex::new([0.], curve, surface_vertex, global_vertex);
+        let object = Vertex::new([0.], curve, surface_vertex);
 
         assert_eq!(1, object.curve_iter().count());
         assert_eq!(0, object.cycle_iter().count());
diff --git a/crates/fj-kernel/src/objects/vertex.rs b/crates/fj-kernel/src/objects/vertex.rs
index 1751cbac2..88f35dee8 100644
--- a/crates/fj-kernel/src/objects/vertex.rs
+++ b/crates/fj-kernel/src/objects/vertex.rs
@@ -15,7 +15,6 @@ pub struct Vertex {
     position: Point<1>,
     curve: Handle<Curve>,
     surface_form: SurfaceVertex,
-    global_form: GlobalVertex,
 }
 
 impl Vertex {
@@ -27,7 +26,6 @@ impl Vertex {
         position: impl Into<Point<1>>,
         curve: Handle<Curve>,
         surface_form: SurfaceVertex,
-        global_form: GlobalVertex,
     ) -> Self {
         let position = position.into();
 
@@ -36,17 +34,11 @@ impl Vertex {
             surface_form.surface().id(),
             "Surface form of vertex must be defined on same surface as curve",
         );
-        assert_eq!(
-            surface_form.global_form(),
-            &global_form,
-            "Vertex and its surface form must have same global form",
-        );
 
         Self {
             position,
             curve,
             surface_form,
-            global_form,
         }
     }
 
@@ -67,7 +59,7 @@ impl Vertex {
 
     /// Access the global form of this vertex
     pub fn global_form(&self) -> &GlobalVertex {
-        &self.global_form
+        self.surface_form.global_form()
     }
 }
 
diff --git a/crates/fj-kernel/src/partial/objects/vertex.rs b/crates/fj-kernel/src/partial/objects/vertex.rs
index 25b6d551c..0c020e390 100644
--- a/crates/fj-kernel/src/partial/objects/vertex.rs
+++ b/crates/fj-kernel/src/partial/objects/vertex.rs
@@ -110,9 +110,7 @@ impl PartialVertex {
             })
             .into_full(stores);
 
-        let global_form = *surface_form.global_form();
-
-        Vertex::new(position, curve, surface_form, global_form)
+        Vertex::new(position, curve, surface_form)
     }
 }