diff --git a/crates/fj-kernel/src/algorithms/sweep/face.rs b/crates/fj-kernel/src/algorithms/sweep/face.rs
index 47441023a..5b59cc6d5 100644
--- a/crates/fj-kernel/src/algorithms/sweep/face.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/face.rs
@@ -5,10 +5,9 @@ use itertools::Itertools;
 
 use crate::{
     algorithms::{reverse::Reverse, transform::TransformObject},
-    builder::CycleBuilder,
     geometry::curve::GlobalPath,
-    objects::{Face, Shell},
-    operations::Insert,
+    objects::{Cycle, Face, Shell},
+    operations::{BuildCycle, Insert, JoinCycle},
     services::Services,
     storage::Handle,
 };
@@ -82,13 +81,14 @@ impl Sweep for Handle<Face> {
                 ));
             }
 
-            let top_cycle = CycleBuilder::connect_to_edges(top_edges, services)
-                .build(services);
+            let top_cycle = Cycle::empty()
+                .add_joined_edges(top_edges, services)
+                .insert(services);
 
             if i == 0 {
-                exterior = Some(top_cycle.insert(services));
+                exterior = Some(top_cycle);
             } else {
-                interiors.push(top_cycle.insert(services));
+                interiors.push(top_cycle);
             };
         }
 
diff --git a/crates/fj-kernel/src/builder/cycle.rs b/crates/fj-kernel/src/builder/cycle.rs
deleted file mode 100644
index c0a848daf..000000000
--- a/crates/fj-kernel/src/builder/cycle.rs
+++ /dev/null
@@ -1,76 +0,0 @@
-use fj_math::Point;
-use itertools::Itertools;
-
-use crate::{
-    geometry::curve::Curve,
-    objects::{Cycle, HalfEdge},
-    operations::{BuildHalfEdge, Insert, UpdateHalfEdge},
-    services::Services,
-    storage::Handle,
-};
-
-/// Builder API for [`Cycle`]
-#[derive(Default)]
-pub struct CycleBuilder {
-    half_edges: Vec<HalfEdge>,
-}
-
-impl CycleBuilder {
-    /// Create an instance of `CycleBuilder`
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Create a cycle whose half-edges are connected to the provided half-edges
-    ///
-    /// The half-edges of the new circle will be coincident with the provided
-    /// half-edges, but will point in the opposite direction.
-    ///
-    /// Assumes that the provided half-edges, once translated into local
-    /// equivalents of this cycle, form a cycle themselves.
-    pub fn connect_to_edges<Es>(edges: Es, services: &mut Services) -> Self
-    where
-        Es: IntoIterator<Item = (Handle<HalfEdge>, Curve, [Point<1>; 2])>,
-        Es::IntoIter: Clone + ExactSizeIterator,
-    {
-        let half_edges = edges
-            .into_iter()
-            .circular_tuple_windows()
-            .map(|((prev, _, _), (half_edge, curve, boundary))| {
-                HalfEdge::unjoined(curve, boundary, services)
-                    .replace_start_vertex(prev.start_vertex().clone())
-                    .replace_global_form(half_edge.global_form().clone())
-            })
-            .collect();
-
-        Self { half_edges }
-    }
-
-    /// Create a polygon
-    pub fn polygon<P, Ps>(points: Ps, services: &mut Services) -> Self
-    where
-        P: Into<Point<2>>,
-        Ps: IntoIterator<Item = P>,
-        Ps::IntoIter: Clone + ExactSizeIterator,
-    {
-        let half_edges = points
-            .into_iter()
-            .map(Into::into)
-            .circular_tuple_windows()
-            .map(|(start, end)| {
-                HalfEdge::line_segment([start, end], None, services)
-            })
-            .collect();
-
-        Self { half_edges }
-    }
-
-    /// Build the cycle
-    pub fn build(self, services: &mut Services) -> Cycle {
-        let half_edges = self
-            .half_edges
-            .into_iter()
-            .map(|half_edge| half_edge.insert(services));
-        Cycle::new(half_edges)
-    }
-}
diff --git a/crates/fj-kernel/src/builder/mod.rs b/crates/fj-kernel/src/builder/mod.rs
deleted file mode 100644
index 453523ff1..000000000
--- a/crates/fj-kernel/src/builder/mod.rs
+++ /dev/null
@@ -1,5 +0,0 @@
-//! API for building objects
-
-mod cycle;
-
-pub use self::cycle::CycleBuilder;
diff --git a/crates/fj-kernel/src/lib.rs b/crates/fj-kernel/src/lib.rs
index 952e0fb27..0996e6dd3 100644
--- a/crates/fj-kernel/src/lib.rs
+++ b/crates/fj-kernel/src/lib.rs
@@ -88,7 +88,6 @@
 #![warn(missing_docs)]
 
 pub mod algorithms;
-pub mod builder;
 pub mod geometry;
 pub mod objects;
 pub mod operations;
diff --git a/crates/fj-kernel/src/operations/join/cycle.rs b/crates/fj-kernel/src/operations/join/cycle.rs
index 52b6ddb4f..1b591a854 100644
--- a/crates/fj-kernel/src/operations/join/cycle.rs
+++ b/crates/fj-kernel/src/operations/join/cycle.rs
@@ -1,13 +1,24 @@
 use std::ops::RangeInclusive;
 
+use fj_math::Point;
+use itertools::Itertools;
+
 use crate::{
-    objects::Cycle,
-    operations::{Insert, UpdateCycle, UpdateHalfEdge},
+    geometry::curve::Curve,
+    objects::{Cycle, HalfEdge},
+    operations::{BuildHalfEdge, Insert, UpdateCycle, UpdateHalfEdge},
     services::Services,
+    storage::Handle,
 };
 
 /// Join a [`Cycle`] to another
 pub trait JoinCycle {
+    /// Create a cycle that is joined to the provided edges
+    fn add_joined_edges<Es>(&self, edges: Es, services: &mut Services) -> Self
+    where
+        Es: IntoIterator<Item = (Handle<HalfEdge>, Curve, [Point<1>; 2])>,
+        Es::IntoIter: Clone + ExactSizeIterator;
+
     /// Join the cycle to another
     ///
     /// Joins the cycle to the other at the provided ranges. The ranges specify
@@ -47,6 +58,21 @@ pub trait JoinCycle {
 }
 
 impl JoinCycle for Cycle {
+    fn add_joined_edges<Es>(&self, edges: Es, services: &mut Services) -> Self
+    where
+        Es: IntoIterator<Item = (Handle<HalfEdge>, Curve, [Point<1>; 2])>,
+        Es::IntoIter: Clone + ExactSizeIterator,
+    {
+        self.add_half_edges(edges.into_iter().circular_tuple_windows().map(
+            |((prev, _, _), (half_edge, curve, boundary))| {
+                HalfEdge::unjoined(curve, boundary, services)
+                    .replace_start_vertex(prev.start_vertex().clone())
+                    .replace_global_form(half_edge.global_form().clone())
+                    .insert(services)
+            },
+        ))
+    }
+
     fn join_to(
         &self,
         other: &Cycle,