diff --git a/crates/fj-kernel/src/builder/cycle.rs b/crates/fj-kernel/src/builder/cycle.rs
index cc34a6d36..da31da187 100644
--- a/crates/fj-kernel/src/builder/cycle.rs
+++ b/crates/fj-kernel/src/builder/cycle.rs
@@ -50,15 +50,8 @@ impl CycleBuilder for PartialCycle {
         &mut self,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Vec<Partial<HalfEdge>> {
-        let mut points = points.into_iter().map(Into::into);
-
         let mut half_edges = Vec::new();
 
-        if let Some(point) = points.next() {
-            let half_edge = self.add_half_edge_from_point_to_start(point);
-            half_edges.push(half_edge);
-        }
-
         for point in points {
             let half_edge = self.add_half_edge_from_point_to_start(point);
             half_edges.push(half_edge);
diff --git a/crates/fj-kernel/src/builder/shell.rs b/crates/fj-kernel/src/builder/shell.rs
index 77d952867..c673449b4 100644
--- a/crates/fj-kernel/src/builder/shell.rs
+++ b/crates/fj-kernel/src/builder/shell.rs
@@ -9,7 +9,7 @@ use crate::{
     builder::{
         FaceBuilder, HalfEdgeBuilder, SurfaceBuilder, SurfaceVertexBuilder,
     },
-    objects::{HalfEdge, Objects},
+    objects::{Face, HalfEdge, Objects},
     partial::{
         Partial, PartialCycle, PartialFace, PartialHalfEdge, PartialShell,
         PartialSurface, PartialSurfaceVertex,
@@ -19,6 +19,12 @@ use crate::{
 
 /// Builder API for [`PartialShell`]
 pub trait ShellBuilder {
+    /// Add a face to the shell
+    ///
+    /// The face will not be connected to any other faces that the shell might
+    /// already have.
+    fn add_face(&mut self) -> Partial<Face>;
+
     /// Create a cube from the length of its edges
     fn create_cube_from_edge_length(
         edge_length: impl Into<Scalar>,
@@ -27,6 +33,12 @@ pub trait ShellBuilder {
 }
 
 impl ShellBuilder for PartialShell {
+    fn add_face(&mut self) -> Partial<Face> {
+        let face = Partial::default();
+        self.faces.push(face.clone());
+        face
+    }
+
     fn create_cube_from_edge_length(
         edge_length: impl Into<Scalar>,
         objects: &mut Service<Objects>,
@@ -70,8 +82,9 @@ impl ShellBuilder for PartialShell {
                         });
                     let c = a + [Z, Z, edge_length];
 
-                    let (surface, _) =
-                        PartialSurface::plane_from_points([a, b, c]);
+                    let mut surface = PartialSurface::default();
+                    surface.update_as_plane_from_points([a, b, c]);
+
                     Partial::from_partial(surface)
                 })
                 .collect::<Vec<_>>();
diff --git a/crates/fj-kernel/src/builder/surface.rs b/crates/fj-kernel/src/builder/surface.rs
index 54f1efcdd..358e60589 100644
--- a/crates/fj-kernel/src/builder/surface.rs
+++ b/crates/fj-kernel/src/builder/surface.rs
@@ -11,9 +11,10 @@ pub trait SurfaceBuilder: Sized {
     fn from_axes(u: GlobalPath, v: impl Into<Vector<3>>) -> Self;
 
     /// Construct a plane from 3 points
-    fn plane_from_points(
+    fn update_as_plane_from_points(
+        &mut self,
         points: [impl Into<Point<3>>; 3],
-    ) -> (Self, [Point<2>; 3]);
+    ) -> [Point<2>; 3];
 }
 
 impl SurfaceBuilder for PartialSurface {
@@ -25,25 +26,19 @@ impl SurfaceBuilder for PartialSurface {
         }
     }
 
-    fn plane_from_points(
+    fn update_as_plane_from_points(
+        &mut self,
         points: [impl Into<Point<3>>; 3],
-    ) -> (Self, [Point<2>; 3]) {
+    ) -> [Point<2>; 3] {
         let [a, b, c] = points.map(Into::into);
 
         let (u, u_coords) = GlobalPath::line_from_points([a, b]);
         let v = c - a;
 
-        let coords = {
-            let [a, b] = u_coords.map(|point| point.t);
-            [[a, Scalar::ZERO], [b, Scalar::ZERO], [a, Scalar::ONE]]
-                .map(Point::from)
-        };
-
-        (
-            Self {
-                geometry: Some(SurfaceGeometry { u, v }),
-            },
-            coords,
-        )
+        self.geometry = Some(SurfaceGeometry { u, v });
+
+        let [a, b] = u_coords.map(|point| point.t);
+        [[a, Scalar::ZERO], [b, Scalar::ZERO], [a, Scalar::ONE]]
+            .map(Point::from)
     }
 }