diff --git a/src/kernel/algorithms/approximation.rs b/src/kernel/algorithms/approximation.rs
index 6b01c7912..f7accdc1c 100644
--- a/src/kernel/algorithms/approximation.rs
+++ b/src/kernel/algorithms/approximation.rs
@@ -150,10 +150,7 @@ mod tests {
         kernel::{
             geometry::Surface,
             shape::Shape,
-            topology::{
-                edges::{Cycle, Edge},
-                faces::Face,
-            },
+            topology::{edges::Cycle, faces::Face},
         },
         math::{Point, Scalar, Segment},
     };
@@ -214,11 +211,9 @@ mod tests {
         let v2 = shape.vertices().add(b);
         let v3 = shape.vertices().add(c);
 
-        let ab = shape
-            .edges()
-            .add(Edge::line_segment([v1.clone(), v2.clone()]));
-        let bc = shape.edges().add(Edge::line_segment([v2, v3.clone()]));
-        let ca = shape.edges().add(Edge::line_segment([v3, v1]));
+        let ab = shape.edges().add_line_segment([v1.clone(), v2.clone()]);
+        let bc = shape.edges().add_line_segment([v2, v3.clone()]);
+        let ca = shape.edges().add_line_segment([v3, v1]);
 
         let cycle = Cycle {
             edges: vec![ab, bc, ca],
@@ -255,19 +250,18 @@ mod tests {
         let v3 = shape.vertices().add(c);
         let v4 = shape.vertices().add(d);
 
-        let ab = shape
-            .edges()
-            .add(Edge::line_segment([v1.clone(), v2.clone()]));
-        let bc = shape.edges().add(Edge::line_segment([v2, v3.clone()]));
-        let cd = shape.edges().add(Edge::line_segment([v3, v4.clone()]));
-        let da = shape.edges().add(Edge::line_segment([v4, v1]));
+        let ab = shape.edges().add_line_segment([v1.clone(), v2.clone()]);
+        let bc = shape.edges().add_line_segment([v2, v3.clone()]);
+        let cd = shape.edges().add_line_segment([v3, v4.clone()]);
+        let da = shape.edges().add_line_segment([v4, v1]);
 
         let abcd = shape.cycles().add(Cycle {
             edges: vec![ab, bc, cd, da],
         });
 
+        let surface = shape.surfaces().add(Surface::x_y_plane());
         let face = Face::Face {
-            surface: Surface::x_y_plane(),
+            surface,
             cycles: vec![abcd],
         };
 
diff --git a/src/kernel/algorithms/sweep.rs b/src/kernel/algorithms/sweep.rs
index b5e123b01..be4e8932a 100644
--- a/src/kernel/algorithms/sweep.rs
+++ b/src/kernel/algorithms/sweep.rs
@@ -71,10 +71,7 @@ mod tests {
         kernel::{
             geometry::{surfaces::Swept, Surface},
             shape::{handle::Handle, Shape},
-            topology::{
-                edges::{Cycle, Edge},
-                faces::Face,
-            },
+            topology::{edges::Cycle, faces::Face},
         },
         math::{Point, Scalar, Vector},
     };
@@ -115,24 +112,22 @@ mod tests {
             let b = shape.vertices().add(b.into());
             let c = shape.vertices().add(c.into());
 
-            let ab = shape
-                .edges()
-                .add(Edge::line_segment([a.clone(), b.clone()]));
-            let bc = shape
-                .edges()
-                .add(Edge::line_segment([b.clone(), c.clone()]));
-            let ca = shape
-                .edges()
-                .add(Edge::line_segment([c.clone(), a.clone()]));
+            let ab = shape.edges().add_line_segment([a.clone(), b.clone()]);
+            let bc = shape.edges().add_line_segment([b.clone(), c.clone()]);
+            let ca = shape.edges().add_line_segment([c.clone(), a.clone()]);
 
             let cycles = shape.cycles().add(Cycle {
                 edges: vec![ab, bc, ca],
             });
 
+            let surface =
+                shape
+                    .surfaces()
+                    .add(Surface::Swept(Swept::plane_from_points(
+                        [a, b, c].map(|vertex| vertex.point()),
+                    )));
             let abc = Face::Face {
-                surface: Surface::Swept(Swept::plane_from_points(
-                    [a, b, c].map(|vertex| vertex.point()),
-                )),
+                surface,
                 cycles: vec![cycles],
             };
 
diff --git a/src/kernel/algorithms/transform.rs b/src/kernel/algorithms/transform.rs
index 31ab73d17..7cb6ae16f 100644
--- a/src/kernel/algorithms/transform.rs
+++ b/src/kernel/algorithms/transform.rs
@@ -44,6 +44,9 @@ pub fn transform_face(
                 let mut edges = Vec::new();
 
                 for edge in &cycle.edges {
+                    let curve =
+                        shape.curves().add(edge.curve.transform(transform));
+
                     let vertices = edge.vertices.clone().map(|vertices| {
                         vertices.map(|vertex| {
                             let point =
@@ -53,10 +56,7 @@ pub fn transform_face(
                         })
                     });
 
-                    let edge = Edge {
-                        curve: edge.curve.transform(transform),
-                        vertices,
-                    };
+                    let edge = Edge { curve, vertices };
                     let edge = shape.edges().add(edge);
 
                     edges.push(edge);
@@ -65,9 +65,11 @@ pub fn transform_face(
                 cycles_trans.push(shape.cycles().add(Cycle { edges }));
             }
 
+            let surface = shape.surfaces().add(surface.transform(transform));
+
             Face::Face {
                 cycles: cycles_trans,
-                surface: surface.transform(transform),
+                surface,
             }
         }
         Face::Triangles(mut triangles) => {
diff --git a/src/kernel/shape/curves.rs b/src/kernel/shape/curves.rs
new file mode 100644
index 000000000..4d891936f
--- /dev/null
+++ b/src/kernel/shape/curves.rs
@@ -0,0 +1,13 @@
+use crate::kernel::geometry::Curve;
+
+use super::handle::{Handle, Storage};
+
+/// API to access the curves of a shape
+pub struct Curves;
+
+impl Curves {
+    /// Add a curve to the shape
+    pub fn add(&mut self, curve: Curve) -> Handle<Curve> {
+        Storage::new(curve).handle()
+    }
+}
diff --git a/src/kernel/shape/edges.rs b/src/kernel/shape/edges.rs
index 625ebfff9..921b5250c 100644
--- a/src/kernel/shape/edges.rs
+++ b/src/kernel/shape/edges.rs
@@ -1,9 +1,20 @@
-use crate::kernel::topology::edges::Edge;
+use crate::{
+    kernel::{
+        geometry::{Circle, Curve, Line},
+        topology::{edges::Edge, vertices::Vertex},
+    },
+    math::{Point, Scalar, Vector},
+};
 
-use super::handle::{Handle, Storage};
+use super::{
+    curves::Curves,
+    handle::{Handle, Storage},
+};
 
 /// The edges of a shape
-pub struct Edges;
+pub struct Edges {
+    pub(super) curves: Curves,
+}
 
 impl Edges {
     /// Add an edge to the shape
@@ -23,4 +34,36 @@ impl Edges {
     pub fn add(&mut self, edge: Edge) -> Handle<Edge> {
         Storage::new(edge).handle()
     }
+
+    /// Add a circle to the shape
+    ///
+    /// Calls [`Edges::add`] internally, and is subject to the same
+    /// restrictions.
+    pub fn add_circle(&mut self, radius: Scalar) -> Handle<Edge> {
+        let curve = self.curves.add(Curve::Circle(Circle {
+            center: Point::origin(),
+            radius: Vector::from([radius, Scalar::ZERO]),
+        }));
+        self.add(Edge {
+            curve,
+            vertices: None,
+        })
+    }
+
+    /// Add a line segment to the shape
+    ///
+    /// Calls [`Edges::add`] internally, and is subject to the same
+    /// restrictions.
+    pub fn add_line_segment(
+        &mut self,
+        vertices: [Handle<Vertex>; 2],
+    ) -> Handle<Edge> {
+        let curve = self.curves.add(Curve::Line(Line::from_points(
+            vertices.clone().map(|vertex| vertex.point()),
+        )));
+        self.add(Edge {
+            curve,
+            vertices: Some(vertices),
+        })
+    }
 }
diff --git a/src/kernel/shape/mod.rs b/src/kernel/shape/mod.rs
index 265fab1a4..75fe2bfcd 100644
--- a/src/kernel/shape/mod.rs
+++ b/src/kernel/shape/mod.rs
@@ -1,7 +1,9 @@
+pub mod curves;
 pub mod cycles;
 pub mod edges;
 pub mod faces;
 pub mod handle;
+pub mod surfaces;
 pub mod vertices;
 
 use crate::math::Scalar;
@@ -9,8 +11,8 @@ use crate::math::Scalar;
 use super::topology::{edges::Cycle, faces::Face, vertices::Vertex};
 
 use self::{
-    cycles::Cycles, edges::Edges, faces::Faces, handle::Storage,
-    vertices::Vertices,
+    curves::Curves, cycles::Cycles, edges::Edges, faces::Faces,
+    handle::Storage, surfaces::Surfaces, vertices::Vertices,
 };
 
 /// The boundary representation of a shape
@@ -56,6 +58,16 @@ impl Shape {
         self
     }
 
+    /// Access the shape's curves
+    pub fn curves(&mut self) -> Curves {
+        Curves
+    }
+
+    /// Access the shape's surfaces
+    pub fn surfaces(&mut self) -> Surfaces {
+        Surfaces
+    }
+
     /// Access the shape's vertices
     pub fn vertices(&mut self) -> Vertices {
         Vertices {
@@ -66,7 +78,7 @@ impl Shape {
 
     /// Access the shape's edges
     pub fn edges(&mut self) -> Edges {
-        Edges
+        Edges { curves: Curves }
     }
 
     /// Access the shape's cycles
diff --git a/src/kernel/shape/surfaces.rs b/src/kernel/shape/surfaces.rs
new file mode 100644
index 000000000..2de37daff
--- /dev/null
+++ b/src/kernel/shape/surfaces.rs
@@ -0,0 +1,13 @@
+use crate::kernel::geometry::Surface;
+
+use super::handle::{Handle, Storage};
+
+/// API to access the surfaces of a shape
+pub struct Surfaces;
+
+impl Surfaces {
+    /// Add a surface to the shape
+    pub fn add(&mut self, surface: Surface) -> Handle<Surface> {
+        Storage::new(surface).handle()
+    }
+}
diff --git a/src/kernel/shapes/circle.rs b/src/kernel/shapes/circle.rs
index 3cf0a37bc..5ce6c3441 100644
--- a/src/kernel/shapes/circle.rs
+++ b/src/kernel/shapes/circle.rs
@@ -3,10 +3,7 @@ use crate::{
     kernel::{
         geometry::Surface,
         shape::Shape,
-        topology::{
-            edges::{Cycle, Edge},
-            faces::Face,
-        },
+        topology::{edges::Cycle, faces::Face},
     },
     math::{Aabb, Point, Scalar},
 };
@@ -20,16 +17,12 @@ impl ToShape for fj::Circle {
         // Circles have just a single round edge with no vertices. So none need
         // to be added here.
 
-        let edge = shape
-            .edges()
-            .add(Edge::circle(Scalar::from_f64(self.radius)));
+        let edge = shape.edges().add_circle(Scalar::from_f64(self.radius));
         shape.cycles().add(Cycle { edges: vec![edge] });
 
         let cycles = shape.cycles().all().collect();
-        shape.faces().add(Face::Face {
-            cycles,
-            surface: Surface::x_y_plane(),
-        });
+        let surface = shape.surfaces().add(Surface::x_y_plane());
+        shape.faces().add(Face::Face { cycles, surface });
 
         shape
     }
diff --git a/src/kernel/shapes/sketch.rs b/src/kernel/shapes/sketch.rs
index de13b0a1e..d69b4ddc2 100644
--- a/src/kernel/shapes/sketch.rs
+++ b/src/kernel/shapes/sketch.rs
@@ -3,10 +3,7 @@ use crate::{
     kernel::{
         geometry::Surface,
         shape::Shape,
-        topology::{
-            edges::{Cycle, Edge},
-            faces::Face,
-        },
+        topology::{edges::Cycle, faces::Face},
     },
     math::{Aabb, Point, Scalar},
 };
@@ -40,16 +37,17 @@ impl ToShape for fj::Sketch {
                 let a = window[0].clone();
                 let b = window[1].clone();
 
-                let edge = shape.edges().add(Edge::line_segment([a, b]));
+                let edge = shape.edges().add_line_segment([a, b]);
                 edges.push(edge);
             }
 
             shape.cycles().add(Cycle { edges });
         };
 
+        let surface = shape.surfaces().add(Surface::x_y_plane());
         let face = Face::Face {
             cycles: shape.cycles().all().collect(),
-            surface: Surface::x_y_plane(),
+            surface,
         };
         shape.faces().add(face);
 
diff --git a/src/kernel/topology/edges.rs b/src/kernel/topology/edges.rs
index e07a04288..20265ffdf 100644
--- a/src/kernel/topology/edges.rs
+++ b/src/kernel/topology/edges.rs
@@ -1,10 +1,4 @@
-use crate::{
-    kernel::{
-        geometry::{Circle, Curve, Line},
-        shape::handle::Handle,
-    },
-    math::{Point, Scalar, Vector},
-};
+use crate::kernel::{geometry::Curve, shape::handle::Handle};
 
 use super::vertices::Vertex;
 
@@ -26,7 +20,7 @@ pub struct Edge {
     /// The edge can be a segment of the curve that is bounded by two vertices,
     /// or if the curve is continuous (i.e. connects to itself), the edge could
     /// be defined by the whole curve, and have no bounding vertices.
-    pub curve: Curve,
+    pub curve: Handle<Curve>,
 
     /// Access the vertices that bound the edge on the curve
     ///
@@ -44,26 +38,3 @@ pub struct Edge {
     /// and store 1D vertices again, at some point.
     pub vertices: Option<[Handle<Vertex>; 2]>,
 }
-
-impl Edge {
-    /// Create a line segment
-    pub fn line_segment(vertices: [Handle<Vertex>; 2]) -> Self {
-        Edge {
-            curve: Curve::Line(Line::from_points(
-                vertices.clone().map(|vertex| vertex.point()),
-            )),
-            vertices: Some(vertices),
-        }
-    }
-
-    /// Create a circle
-    pub fn circle(radius: Scalar) -> Self {
-        Edge {
-            curve: Curve::Circle(Circle {
-                center: Point::origin(),
-                radius: Vector::from([radius, Scalar::ZERO]),
-            }),
-            vertices: None,
-        }
-    }
-}
diff --git a/src/kernel/topology/faces.rs b/src/kernel/topology/faces.rs
index 6aebcfcf2..bfe394287 100644
--- a/src/kernel/topology/faces.rs
+++ b/src/kernel/topology/faces.rs
@@ -26,7 +26,7 @@ pub enum Face {
     /// surface.
     Face {
         /// The surface that defines this face
-        surface: Surface,
+        surface: Handle<Surface>,
 
         /// The cycles that bound the face
         ///