diff --git a/crates/fj-core/src/operations/reverse/cycle.rs b/crates/fj-core/src/operations/reverse/cycle.rs
index 7d2fdc3af..e998dde11 100644
--- a/crates/fj-core/src/operations/reverse/cycle.rs
+++ b/crates/fj-core/src/operations/reverse/cycle.rs
@@ -4,7 +4,7 @@ use crate::{
     services::Services,
 };
 
-use super::Reverse;
+use super::{Reverse, ReverseCurveCoordinateSystems};
 
 impl Reverse for Cycle {
     fn reverse(&self, services: &mut Services) -> Self {
@@ -27,3 +27,17 @@ impl Reverse for Cycle {
         Cycle::new(edges)
     }
 }
+
+impl ReverseCurveCoordinateSystems for Cycle {
+    fn reverse_curve_coordinate_systems(
+        &self,
+        services: &mut Services,
+    ) -> Self {
+        let edges = self.half_edges().map(|edge| {
+            edge.reverse_curve_coordinate_systems(services)
+                .insert(services)
+        });
+
+        Cycle::new(edges)
+    }
+}
diff --git a/crates/fj-core/src/operations/reverse/edge.rs b/crates/fj-core/src/operations/reverse/edge.rs
new file mode 100644
index 000000000..7d53ee4c9
--- /dev/null
+++ b/crates/fj-core/src/operations/reverse/edge.rs
@@ -0,0 +1,18 @@
+use crate::{objects::HalfEdge, services::Services};
+
+use super::ReverseCurveCoordinateSystems;
+
+impl ReverseCurveCoordinateSystems for HalfEdge {
+    fn reverse_curve_coordinate_systems(&self, _: &mut Services) -> Self {
+        let path = self.path().reverse();
+        let boundary = self.boundary().reverse();
+
+        HalfEdge::new(
+            path,
+            boundary,
+            self.curve().clone(),
+            self.start_vertex().clone(),
+            self.global_form().clone(),
+        )
+    }
+}
diff --git a/crates/fj-core/src/operations/reverse/face.rs b/crates/fj-core/src/operations/reverse/face.rs
index 801acafa6..12abfa420 100644
--- a/crates/fj-core/src/operations/reverse/face.rs
+++ b/crates/fj-core/src/operations/reverse/face.rs
@@ -6,7 +6,7 @@ use crate::{
     services::Services,
 };
 
-use super::Reverse;
+use super::{Reverse, ReverseCurveCoordinateSystems};
 
 impl Reverse for Face {
     fn reverse(&self, services: &mut Services) -> Self {
@@ -30,3 +30,47 @@ impl<const D: usize> Reverse for Polygon<D, IsInsertedYes> {
         self.replace_face(face)
     }
 }
+
+impl ReverseCurveCoordinateSystems for Face {
+    fn reverse_curve_coordinate_systems(
+        &self,
+        services: &mut Services,
+    ) -> Self {
+        let region = self
+            .region()
+            .reverse_curve_coordinate_systems(services)
+            .insert(services);
+        Face::new(self.surface().clone(), region)
+    }
+}
+
+impl<const D: usize> ReverseCurveCoordinateSystems
+    for Polygon<D, IsInsertedNo>
+{
+    fn reverse_curve_coordinate_systems(
+        &self,
+        services: &mut Services,
+    ) -> Self {
+        let face = self
+            .face
+            .borrow()
+            .reverse_curve_coordinate_systems(services);
+        self.replace_face(face)
+    }
+}
+
+impl<const D: usize> ReverseCurveCoordinateSystems
+    for Polygon<D, IsInsertedYes>
+{
+    fn reverse_curve_coordinate_systems(
+        &self,
+        services: &mut Services,
+    ) -> Self {
+        let face: &Face = self.face.borrow();
+        let face = face
+            .reverse_curve_coordinate_systems(services)
+            .insert(services);
+
+        self.replace_face(face)
+    }
+}
diff --git a/crates/fj-core/src/operations/reverse/mod.rs b/crates/fj-core/src/operations/reverse/mod.rs
index 235ac707c..b705492b3 100644
--- a/crates/fj-core/src/operations/reverse/mod.rs
+++ b/crates/fj-core/src/operations/reverse/mod.rs
@@ -3,6 +3,7 @@
 use crate::services::Services;
 
 mod cycle;
+mod edge;
 mod face;
 mod region;
 
@@ -12,3 +13,13 @@ pub trait Reverse {
     #[must_use]
     fn reverse(&self, services: &mut Services) -> Self;
 }
+
+/// Reverse the direction of the curve coordinate systems within an object
+pub trait ReverseCurveCoordinateSystems {
+    /// Reverse the direction of the curve coordinate systems within an object
+    ///
+    /// This will not have any effect on object positions in global coordinates.
+    #[must_use]
+    fn reverse_curve_coordinate_systems(&self, services: &mut Services)
+        -> Self;
+}
diff --git a/crates/fj-core/src/operations/reverse/region.rs b/crates/fj-core/src/operations/reverse/region.rs
index cb1b0c09a..9c1c3026f 100644
--- a/crates/fj-core/src/operations/reverse/region.rs
+++ b/crates/fj-core/src/operations/reverse/region.rs
@@ -1,6 +1,6 @@
 use crate::{objects::Region, operations::Insert, services::Services};
 
-use super::Reverse;
+use super::{Reverse, ReverseCurveCoordinateSystems};
 
 impl Reverse for Region {
     fn reverse(&self, services: &mut Services) -> Self {
@@ -12,3 +12,22 @@ impl Reverse for Region {
         Region::new(exterior, interiors, self.color())
     }
 }
+
+impl ReverseCurveCoordinateSystems for Region {
+    fn reverse_curve_coordinate_systems(
+        &self,
+        services: &mut Services,
+    ) -> Self {
+        let exterior = self
+            .exterior()
+            .reverse_curve_coordinate_systems(services)
+            .insert(services);
+        let interiors = self.interiors().map(|cycle| {
+            cycle
+                .reverse_curve_coordinate_systems(services)
+                .insert(services)
+        });
+
+        Region::new(exterior, interiors, self.color())
+    }
+}