diff --git a/crates/fj-kernel/src/algorithms/approx/faces.rs b/crates/fj-kernel/src/algorithms/approx/faces.rs
index 0171214ae..09346e893 100644
--- a/crates/fj-kernel/src/algorithms/approx/faces.rs
+++ b/crates/fj-kernel/src/algorithms/approx/faces.rs
@@ -105,7 +105,7 @@ mod tests {
         let g = Point::from([2., 2., 0.]);
         let h = Point::from([1., 2., 0.]);
 
-        let face = Face::builder(Surface::x_y_plane(), &mut shape)
+        let face = Face::builder(Surface::xy_plane(), &mut shape)
             .with_exterior_polygon([a, b, c, d])
             .with_interior_polygon([e, f, g, h])
             .build()?;
diff --git a/crates/fj-kernel/src/algorithms/triangulation/mod.rs b/crates/fj-kernel/src/algorithms/triangulation/mod.rs
index 8d5643c5d..aa207dc99 100644
--- a/crates/fj-kernel/src/algorithms/triangulation/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulation/mod.rs
@@ -96,7 +96,7 @@ mod tests {
         let c = [2., 2., 0.];
         let d = [0., 1., 0.];
 
-        Face::builder(Surface::x_y_plane(), &mut shape)
+        Face::builder(Surface::xy_plane(), &mut shape)
             .with_exterior_polygon([a, b, c, d])
             .build()?;
 
@@ -123,7 +123,7 @@ mod tests {
         let g = [3., 3., 0.];
         let h = [1., 2., 0.];
 
-        Face::builder(Surface::x_y_plane(), &mut shape)
+        Face::builder(Surface::xy_plane(), &mut shape)
             .with_exterior_polygon([a, b, c, d])
             .with_interior_polygon([e, f, g, h])
             .build()?;
diff --git a/crates/fj-kernel/src/algorithms/triangulation/polygon.rs b/crates/fj-kernel/src/algorithms/triangulation/polygon.rs
index aeb9e251c..5ab3f37d3 100644
--- a/crates/fj-kernel/src/algorithms/triangulation/polygon.rs
+++ b/crates/fj-kernel/src/algorithms/triangulation/polygon.rs
@@ -235,7 +235,7 @@ mod tests {
         let e = [2., 1.];
         let f = [1., 2.];
 
-        let polygon = Polygon::new(Surface::x_y_plane())
+        let polygon = Polygon::new(Surface::xy_plane())
             .with_exterior(PolyChain::from([a, b, c]).close())
             .with_interiors([PolyChain::from([d, e, f]).close()]);
 
@@ -248,7 +248,7 @@ mod tests {
         let b = [2., 1.];
         let c = [0., 2.];
 
-        let polygon = Polygon::new(Surface::x_y_plane())
+        let polygon = Polygon::new(Surface::xy_plane())
             .with_exterior(PolyChain::from([a, b, c]).close());
 
         assert_contains_point(polygon, [1., 1.]);
@@ -264,7 +264,7 @@ mod tests {
         let e = [2., 1.];
         let f = [1., 3.];
 
-        let polygon = Polygon::new(Surface::x_y_plane())
+        let polygon = Polygon::new(Surface::xy_plane())
             .with_exterior(PolyChain::from([a, b, c]).close())
             .with_interiors([PolyChain::from([d, e, f]).close()]);
 
@@ -278,7 +278,7 @@ mod tests {
         let c = [3., 0.];
         let d = [3., 4.];
 
-        let polygon = Polygon::new(Surface::x_y_plane())
+        let polygon = Polygon::new(Surface::xy_plane())
             .with_exterior(PolyChain::from([a, b, c, d]).close());
 
         assert_contains_point(polygon, [1., 1.]);
@@ -291,7 +291,7 @@ mod tests {
         let b = [2., 1.];
         let c = [3., 1.];
         let d = [0., 2.];
-        let polygon = Polygon::new(Surface::x_y_plane())
+        let polygon = Polygon::new(Surface::xy_plane())
             .with_exterior(PolyChain::from([a, b, c, d]).close());
         assert_contains_point(polygon, [1., 1.]);
 
@@ -301,7 +301,7 @@ mod tests {
         let c = [3., 1.];
         let d = [4., 0.];
         let e = [4., 5.];
-        let polygon = Polygon::new(Surface::x_y_plane())
+        let polygon = Polygon::new(Surface::xy_plane())
             .with_exterior(PolyChain::from([a, b, c, d, e]).close());
         assert_contains_point(polygon, [1., 1.]);
     }
diff --git a/crates/fj-kernel/src/geometry/curves/mod.rs b/crates/fj-kernel/src/geometry/curves/mod.rs
index cee793cb8..0bb26324c 100644
--- a/crates/fj-kernel/src/geometry/curves/mod.rs
+++ b/crates/fj-kernel/src/geometry/curves/mod.rs
@@ -32,6 +32,22 @@ impl Curve {
         })
     }
 
+    /// Construct a `Curve` that represents the y-axis
+    pub fn y_axis() -> Self {
+        Self::Line(Line {
+            origin: Point::origin(),
+            direction: Vector::unit_y(),
+        })
+    }
+
+    /// Construct a `Curve` that represents the z-axis
+    pub fn z_axis() -> Self {
+        Self::Line(Line {
+            origin: Point::origin(),
+            direction: Vector::unit_z(),
+        })
+    }
+
     /// Access the origin of the curve's coordinate system
     pub fn origin(&self) -> Point<3> {
         match self {
diff --git a/crates/fj-kernel/src/geometry/surfaces/mod.rs b/crates/fj-kernel/src/geometry/surfaces/mod.rs
index 37619b20a..0c88f1adc 100644
--- a/crates/fj-kernel/src/geometry/surfaces/mod.rs
+++ b/crates/fj-kernel/src/geometry/surfaces/mod.rs
@@ -16,14 +16,30 @@ pub enum Surface {
 }
 
 impl Surface {
-    /// Construct a `Surface` that represents the x-y plane
-    pub fn x_y_plane() -> Self {
+    /// Construct a `Surface` that represents the xy-plane
+    pub fn xy_plane() -> Self {
         Self::SweptCurve(SweptCurve {
             curve: Curve::x_axis(),
             path: Vector::unit_y(),
         })
     }
 
+    /// Construct a `Surface` that represents the xz-plane
+    pub fn xz_plane() -> Self {
+        Self::SweptCurve(SweptCurve {
+            curve: Curve::x_axis(),
+            path: Vector::unit_z(),
+        })
+    }
+
+    /// Construct a `Surface` that represents the yz-plane
+    pub fn yz_plane() -> Self {
+        Self::SweptCurve(SweptCurve {
+            curve: Curve::y_axis(),
+            path: Vector::unit_z(),
+        })
+    }
+
     /// Create a new instance that is reversed
     #[must_use]
     pub fn reverse(self) -> Self {
diff --git a/crates/fj-kernel/src/shape/api.rs b/crates/fj-kernel/src/shape/api.rs
index dc23c5d9b..4c3e9e7e3 100644
--- a/crates/fj-kernel/src/shape/api.rs
+++ b/crates/fj-kernel/src/shape/api.rs
@@ -214,7 +214,7 @@ mod tests {
 
         let point = Point::from([1., 0., 0.]);
         let curve = Curve::x_axis();
-        let surface = Surface::x_y_plane();
+        let surface = Surface::xy_plane();
 
         assert!(shape.get_handle(&point).is_none());
         assert!(shape.get_handle(&curve).is_none());
@@ -396,7 +396,7 @@ mod tests {
         }
 
         fn add_surface(&mut self) -> Handle<Surface> {
-            self.insert(Surface::x_y_plane()).unwrap()
+            self.insert(Surface::xy_plane()).unwrap()
         }
 
         fn add_edge(&mut self) -> anyhow::Result<Handle<Edge>> {
diff --git a/crates/fj-operations/src/circle.rs b/crates/fj-operations/src/circle.rs
index b10557ead..a0dcff129 100644
--- a/crates/fj-operations/src/circle.rs
+++ b/crates/fj-operations/src/circle.rs
@@ -22,7 +22,7 @@ impl ToShape for fj::Circle {
         shape.insert(Cycle { edges: vec![edge] }).unwrap();
 
         let cycles = shape.cycles().collect();
-        let surface = shape.insert(Surface::x_y_plane()).unwrap();
+        let surface = shape.insert(Surface::xy_plane()).unwrap();
         shape
             .insert(Face::Face {
                 exteriors: cycles,
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index a2ec6b2b4..bafd17c9a 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -46,7 +46,7 @@ impl ToShape for fj::Sketch {
             shape.insert(Cycle { edges }).unwrap();
         };
 
-        let surface = shape.insert(Surface::x_y_plane()).unwrap();
+        let surface = shape.insert(Surface::xy_plane()).unwrap();
         let face = Face::Face {
             exteriors: shape.cycles().collect(),
             interiors: Vec::new(),