diff --git a/crates/fj-kernel/src/builder/cycle.rs b/crates/fj-kernel/src/builder/cycle.rs
index e35c95eb4..158b057bb 100644
--- a/crates/fj-kernel/src/builder/cycle.rs
+++ b/crates/fj-kernel/src/builder/cycle.rs
@@ -1,3 +1,5 @@
+use std::collections::VecDeque;
+
 use fj_interop::ext::ArrayExt;
 use fj_math::Point;
 
@@ -76,6 +78,33 @@ pub trait CycleBuilder {
         &mut self,
         points: [impl Into<Point<3>>; 3],
     ) -> [Partial<HalfEdge>; 3];
+
+    /// Connect the cycle to the provided half-edges
+    ///
+    /// Assumes that the provided half-edges, once translated into local
+    /// equivalents of this cycle, will not form a cycle themselves.
+    ///
+    /// Returns the local equivalents of the provided half-edges and, as the
+    /// last entry, an additional half-edge that closes the cycle.
+    fn connect_to_open_edges<O>(
+        &mut self,
+        edges: O,
+    ) -> O::SizePlusOne<Partial<HalfEdge>>
+    where
+        O: ObjectArgument<Partial<HalfEdge>>;
+
+    /// Connect the cycles to the provided half-edges
+    ///
+    /// Assumes that the provided half-edges, once translated into local
+    /// equivalents of this cycle, form a cycle themselves.
+    ///
+    /// Returns the local equivalents of the provided half-edges.
+    fn connect_to_closed_edges<O>(
+        &mut self,
+        edges: O,
+    ) -> O::SameSize<Partial<HalfEdge>>
+    where
+        O: ObjectArgument<Partial<HalfEdge>>;
 }
 
 impl CycleBuilder for PartialCycle {
@@ -197,4 +226,43 @@ impl CycleBuilder for PartialCycle {
 
         half_edges
     }
+
+    fn connect_to_open_edges<O>(
+        &mut self,
+        edges: O,
+    ) -> O::SizePlusOne<Partial<HalfEdge>>
+    where
+        O: ObjectArgument<Partial<HalfEdge>>,
+    {
+        // We need to create the additional half-edge last, but at the same time
+        // need to provide it to the `map_plus_one` method first. Really no
+        // choice but to create them all in one go, as we do here.
+        let mut half_edges = VecDeque::new();
+        for _ in 0..edges.num_objects() {
+            half_edges.push_back(self.add_half_edge());
+        }
+        let additional_half_edge = self.add_half_edge();
+
+        edges.map_plus_one(additional_half_edge, |other| {
+            let mut this = half_edges.pop_front().expect(
+                "Pushed correct number of half-edges; should be able to pop",
+            );
+            this.write().update_from_other_edge(&other);
+            this
+        })
+    }
+
+    fn connect_to_closed_edges<O>(
+        &mut self,
+        edges: O,
+    ) -> O::SameSize<Partial<HalfEdge>>
+    where
+        O: ObjectArgument<Partial<HalfEdge>>,
+    {
+        edges.map(|other| {
+            let mut this = self.add_half_edge();
+            this.write().update_from_other_edge(&other);
+            this
+        })
+    }
 }
diff --git a/crates/fj-kernel/src/builder/face.rs b/crates/fj-kernel/src/builder/face.rs
index 75d336cee..34bde9efc 100644
--- a/crates/fj-kernel/src/builder/face.rs
+++ b/crates/fj-kernel/src/builder/face.rs
@@ -4,41 +4,14 @@ use fj_interop::ext::ArrayExt;
 
 use crate::{
     geometry::path::SurfacePath,
-    objects::{Cycle, HalfEdge, Surface},
+    objects::{Cycle, Surface},
     partial::{MaybeSurfacePath, Partial, PartialCycle, PartialFace},
 };
 
-use super::{CycleBuilder, HalfEdgeBuilder, ObjectArgument, SurfaceBuilder};
+use super::SurfaceBuilder;
 
 /// Builder API for [`PartialFace`]
 pub trait FaceBuilder {
-    /// Connect the face to other faces at the provided half-edges
-    ///
-    /// Assumes that the provided half-edges, once translated into local
-    /// equivalents of this face, will not form a cycle.
-    ///
-    /// Returns the local equivalents of the provided half-edges and, as the
-    /// last entry, an additional half-edge that closes the cycle.
-    fn connect_to_open_edges<O>(
-        &mut self,
-        edges: O,
-    ) -> O::SizePlusOne<Partial<HalfEdge>>
-    where
-        O: ObjectArgument<Partial<HalfEdge>>;
-
-    /// Connect the face to other faces at the provided half-edges
-    ///
-    /// Assumes that the provided half-edges, once translated into local
-    /// equivalents of this face, form a cycle.
-    ///
-    /// Returns the local equivalents of the provided half-edges.
-    fn connect_to_closed_edges<O>(
-        &mut self,
-        edges: O,
-    ) -> O::SameSize<Partial<HalfEdge>>
-    where
-        O: ObjectArgument<Partial<HalfEdge>>;
-
     /// Add an interior cycle
     fn add_interior(&mut self) -> Partial<Cycle>;
 
@@ -59,45 +32,6 @@ pub trait FaceBuilder {
 }
 
 impl FaceBuilder for PartialFace {
-    fn connect_to_open_edges<O>(
-        &mut self,
-        edges: O,
-    ) -> O::SizePlusOne<Partial<HalfEdge>>
-    where
-        O: ObjectArgument<Partial<HalfEdge>>,
-    {
-        // We need to create the additional half-edge last, but at the same time
-        // need to provide it to the `map_plus_one` method first. Really no
-        // choice but to create them all in one go, as we do here.
-        let mut half_edges = VecDeque::new();
-        for _ in 0..edges.num_objects() {
-            half_edges.push_back(self.exterior.write().add_half_edge());
-        }
-        let additional_half_edge = self.exterior.write().add_half_edge();
-
-        edges.map_plus_one(additional_half_edge, |other| {
-            let mut this = half_edges.pop_front().expect(
-                "Pushed correct number of half-edges; should be able to pop",
-            );
-            this.write().update_from_other_edge(&other);
-            this
-        })
-    }
-
-    fn connect_to_closed_edges<O>(
-        &mut self,
-        edges: O,
-    ) -> O::SameSize<Partial<HalfEdge>>
-    where
-        O: ObjectArgument<Partial<HalfEdge>>,
-    {
-        edges.map(|other| {
-            let mut this = self.exterior.write().add_half_edge();
-            this.write().update_from_other_edge(&other);
-            this
-        })
-    }
-
     fn add_interior(&mut self) -> Partial<Cycle> {
         let cycle = Partial::from_partial(PartialCycle {
             surface: self.exterior.read().surface.clone(),