diff --git a/crates/fj-kernel/src/algorithms/approx/cycles.rs b/crates/fj-kernel/src/algorithms/approx/cycles.rs
index da1784063..ebf2e1f87 100644
--- a/crates/fj-kernel/src/algorithms/approx/cycles.rs
+++ b/crates/fj-kernel/src/algorithms/approx/cycles.rs
@@ -19,7 +19,7 @@ impl CycleApprox {
     pub fn new(cycle: &Cycle, tolerance: Tolerance) -> Self {
         let mut points = Vec::new();
 
-        for edge in &cycle.edges {
+        for edge in cycle.edges() {
             let mut edge_points = Vec::new();
             approx_curve(
                 edge.curve().global_form(),
diff --git a/crates/fj-kernel/src/algorithms/reverse.rs b/crates/fj-kernel/src/algorithms/reverse.rs
index ba391344c..ce7c6a86b 100644
--- a/crates/fj-kernel/src/algorithms/reverse.rs
+++ b/crates/fj-kernel/src/algorithms/reverse.rs
@@ -26,37 +26,33 @@ fn reverse_local_coordinates_in_cycle<'r>(
     cycles: impl IntoIterator<Item = &'r Cycle> + 'r,
 ) -> impl Iterator<Item = Cycle> + 'r {
     cycles.into_iter().map(|cycle| {
-        let edges = cycle
-            .edges
-            .iter()
-            .map(|edge| {
-                let curve = {
-                    let local = match edge.curve().local_form() {
-                        Curve::Circle(Circle { center, a, b }) => {
-                            let center = Point::from([center.u, -center.v]);
-
-                            let a = Vector::from([a.u, -a.v]);
-                            let b = Vector::from([b.u, -b.v]);
-
-                            Curve::Circle(Circle { center, a, b })
-                        }
-                        Curve::Line(Line { origin, direction }) => {
-                            let origin = Point::from([origin.u, -origin.v]);
-                            let direction =
-                                Vector::from([direction.u, -direction.v]);
-
-                            Curve::Line(Line { origin, direction })
-                        }
-                    };
-
-                    Local::new(local, *edge.curve().global_form())
+        let edges = cycle.edges().map(|edge| {
+            let curve = {
+                let local = match edge.curve().local_form() {
+                    Curve::Circle(Circle { center, a, b }) => {
+                        let center = Point::from([center.u, -center.v]);
+
+                        let a = Vector::from([a.u, -a.v]);
+                        let b = Vector::from([b.u, -b.v]);
+
+                        Curve::Circle(Circle { center, a, b })
+                    }
+                    Curve::Line(Line { origin, direction }) => {
+                        let origin = Point::from([origin.u, -origin.v]);
+                        let direction =
+                            Vector::from([direction.u, -direction.v]);
+
+                        Curve::Line(Line { origin, direction })
+                    }
                 };
 
-                Edge::new(curve, *edge.vertices())
-            })
-            .collect();
+                Local::new(local, *edge.curve().global_form())
+            };
 
-        Cycle { edges }
+            Edge::new(curve, *edge.vertices())
+        });
+
+        Cycle::new().with_edges(edges)
     })
 }
 
diff --git a/crates/fj-kernel/src/algorithms/sweep.rs b/crates/fj-kernel/src/algorithms/sweep.rs
index dc5bf8526..645930bb9 100644
--- a/crates/fj-kernel/src/algorithms/sweep.rs
+++ b/crates/fj-kernel/src/algorithms/sweep.rs
@@ -40,7 +40,7 @@ pub fn sweep(
         );
 
         for cycle in face.all_cycles() {
-            for edge in &cycle.edges {
+            for edge in cycle.edges() {
                 if let Some(vertices) = edge.vertices().get() {
                     create_non_continuous_side_face(
                         path,
@@ -158,7 +158,7 @@ fn create_non_continuous_side_face(
             edges.push(edge);
         }
 
-        Cycle { edges }
+        Cycle::new().with_edges(edges)
     };
 
     let face = Face::new(surface).with_exteriors([cycle]).with_color(color);
@@ -174,7 +174,7 @@ fn create_continuous_side_face(
 ) {
     let translation = Transform::translation(path);
 
-    let cycle = Cycle { edges: vec![edge] };
+    let cycle = Cycle::new().with_edges([edge]);
     let approx = CycleApprox::new(&cycle, tolerance);
 
     let mut quads = Vec::new();
diff --git a/crates/fj-kernel/src/algorithms/transform.rs b/crates/fj-kernel/src/algorithms/transform.rs
index e79583eea..7493b8944 100644
--- a/crates/fj-kernel/src/algorithms/transform.rs
+++ b/crates/fj-kernel/src/algorithms/transform.rs
@@ -46,12 +46,9 @@ impl TransformObject for Curve<3> {
 }
 
 impl TransformObject for Cycle {
-    fn transform(mut self, transform: &Transform) -> Self {
-        for edge in &mut self.edges {
-            *edge = edge.transform(transform);
-        }
-
-        self
+    fn transform(self, transform: &Transform) -> Self {
+        Self::new()
+            .with_edges(self.into_edges().map(|edge| edge.transform(transform)))
     }
 }
 
diff --git a/crates/fj-kernel/src/objects/cycle.rs b/crates/fj-kernel/src/objects/cycle.rs
index 9946d07d4..c25efdebf 100644
--- a/crates/fj-kernel/src/objects/cycle.rs
+++ b/crates/fj-kernel/src/objects/cycle.rs
@@ -9,11 +9,30 @@ use super::{Edge, Surface};
 /// one.
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Cycle {
-    /// The edges that make up the cycle
-    pub edges: Vec<Edge>,
+    edges: Vec<Edge>,
 }
 
 impl Cycle {
+    /// Create a new cycle
+    #[allow(clippy::new_without_default)]
+    pub fn new() -> Self {
+        // Implementation note:
+        // As I'm writing this, this constructor has no arguments. I expect it
+        // to take a `Surface` at some point. Remove the `#[allow(...)]`
+        // attribute then.
+        // - @hannobraun
+
+        Self { edges: Vec::new() }
+    }
+
+    /// Add edges to the cycle
+    ///
+    /// Consumes the cycle and returns the updated instance.
+    pub fn with_edges(mut self, edges: impl IntoIterator<Item = Edge>) -> Self {
+        self.edges.extend(edges);
+        self
+    }
+
     /// Create a polygon from a list of points
     pub fn polygon_from_points(
         surface: &Surface,
@@ -40,8 +59,13 @@ impl Cycle {
         Cycle { edges }
     }
 
-    /// Access this cycle's edges
+    /// Access edges that make up the cycle
     pub fn edges(&self) -> impl Iterator<Item = &Edge> + '_ {
         self.edges.iter()
     }
+
+    /// Consume the cycle and return its edges
+    pub fn into_edges(self) -> impl Iterator<Item = Edge> {
+        self.edges.into_iter()
+    }
 }
diff --git a/crates/fj-operations/src/difference_2d.rs b/crates/fj-operations/src/difference_2d.rs
index 307b0177b..b3fcf500f 100644
--- a/crates/fj-operations/src/difference_2d.rs
+++ b/crates/fj-operations/src/difference_2d.rs
@@ -92,7 +92,7 @@ impl Shape for fj::Difference2d {
 
 fn add_cycle(cycle: Cycle, reverse: bool) -> Cycle {
     let mut edges = Vec::new();
-    for edge in cycle.edges {
+    for edge in cycle.edges() {
         let curve_local = if reverse {
             edge.curve().local_form().reverse()
         } else {
@@ -120,5 +120,5 @@ fn add_cycle(cycle: Cycle, reverse: bool) -> Cycle {
         edges.reverse();
     }
 
-    Cycle { edges }
+    Cycle::new().with_edges(edges)
 }
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 0d0afc801..4fff1c49f 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -26,7 +26,7 @@ impl Shape for fj::Sketch {
 
                 let edge =
                     Edge::circle_from_radius(Scalar::from_f64(circle.radius()));
-                let cycle = Cycle { edges: vec![edge] };
+                let cycle = Cycle::new().with_edges([edge]);
 
                 Face::new(surface)
                     .with_exteriors([cycle])