diff --git a/crates/fj-kernel/src/partial/maybe_partial.rs b/crates/fj-kernel/src/partial/maybe_partial.rs
index 973f0ccb6..dc8edd741 100644
--- a/crates/fj-kernel/src/partial/maybe_partial.rs
+++ b/crates/fj-kernel/src/partial/maybe_partial.rs
@@ -105,6 +105,28 @@ impl MaybePartial<GlobalEdge> {
 }
 
 impl MaybePartial<HalfEdge> {
+    /// Access the back vertex
+    pub fn back(&self) -> Option<MaybePartial<Vertex>> {
+        match self {
+            Self::Full(full) => Some(full.back().clone().into()),
+            Self::Partial(partial) => {
+                let [back, _] = &partial.vertices;
+                back.clone()
+            }
+        }
+    }
+
+    /// Access the front vertex
+    pub fn front(&self) -> Option<MaybePartial<Vertex>> {
+        match self {
+            Self::Full(full) => Some(full.front().clone().into()),
+            Self::Partial(partial) => {
+                let [_, front] = &partial.vertices;
+                front.clone()
+            }
+        }
+    }
+
     /// Access the vertices
     pub fn vertices(&self) -> [Option<MaybePartial<Vertex>>; 2] {
         match self {
diff --git a/crates/fj-kernel/src/partial/objects/cycle.rs b/crates/fj-kernel/src/partial/objects/cycle.rs
index 3b3167b70..f4df40e7c 100644
--- a/crates/fj-kernel/src/partial/objects/cycle.rs
+++ b/crates/fj-kernel/src/partial/objects/cycle.rs
@@ -160,21 +160,46 @@ impl PartialCycle {
     }
 
     /// Build a full [`Cycle`] from the partial cycle
-    pub fn build(self, objects: &Objects) -> Cycle {
+    pub fn build(mut self, objects: &Objects) -> Cycle {
         let surface = self.surface.expect("Need surface to build `Cycle`");
         let surface_for_edges = surface.clone();
         let half_edges = {
+            let last_vertex = self
+                .half_edges
+                .last_mut()
+                .and_then(|half_edge| {
+                    half_edge.front().map(|vertex| (half_edge, vertex))
+                })
+                .and_then(|(half_edge, vertex)| {
+                    vertex.surface_form().map(|surface_vertex| {
+                        (half_edge, vertex, surface_vertex)
+                    })
+                })
+                .map(|(half_edge, vertex, surface_vertex)| {
+                    let surface_vertex = surface_vertex
+                        .update_partial(|surface_vertex| {
+                            surface_vertex.with_surface(Some(surface.clone()))
+                        })
+                        .into_full(objects);
+
+                    *half_edge =
+                        half_edge.clone().update_partial(|half_edge| {
+                            half_edge.with_front_vertex(Some(
+                                vertex.update_partial(|vertex| {
+                                    vertex.with_surface_form(Some(
+                                        surface_vertex.clone(),
+                                    ))
+                                }),
+                            ))
+                        });
+
+                    surface_vertex
+                });
+
             let (half_edges, _) = self.half_edges.into_iter().fold(
-                (Vec::new(), None),
-                |(mut half_edges, previous), next| {
-                    let previous_half_edge: Option<HalfEdge> = previous;
-
-                    let previous_vertex = previous_half_edge.map(|half_edge| {
-                        let [_, vertex] = half_edge.vertices().clone();
-                        vertex.surface_form().clone()
-                    });
-
-                    let next = next
+                (Vec::new(), last_vertex),
+                |(mut half_edges, previous_vertex), half_edge| {
+                    let half_edge = half_edge
                         .update_partial(|half_edge| {
                             let [from, _] = half_edge.vertices.clone();
                             let from = from.map(|vertex| {
@@ -189,9 +214,10 @@ impl PartialCycle {
                         })
                         .into_full(objects);
 
-                    half_edges.push(next.clone());
+                    let front = half_edge.front().surface_form().clone();
+                    half_edges.push(half_edge);
 
-                    (half_edges, Some(next))
+                    (half_edges, Some(front))
                 },
             );