diff --git a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
index 1f355df13..35ee1f673 100644
--- a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
@@ -187,9 +187,9 @@ mod tests {
         ];
 
         let face = Face::builder(&stores, surface)
-            .build_polygon_from_points(exterior)
-            .with_hole(interior)
-            .into_face();
+            .with_exterior_polygon_from_points(exterior)
+            .with_interior_polygon_from_points(interior)
+            .build();
 
         let expected =
             CurveFaceIntersection::from_intervals([[[1.], [2.]], [[4.], [5.]]]);
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_face.rs b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
index 806700be7..1e93b9151 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
@@ -84,8 +84,8 @@ mod tests {
         let surfaces = [Surface::xy_plane(), Surface::xz_plane()];
         let [a, b] = surfaces.map(|surface| {
             Face::builder(&stores, surface)
-                .build_polygon_from_points(points)
-                .into_face()
+                .with_exterior_polygon_from_points(points)
+                .build()
         });
 
         let intersection = FaceFaceIntersection::compute([&a, &b], &stores);
@@ -107,8 +107,8 @@ mod tests {
         let surfaces = [Surface::xy_plane(), Surface::xz_plane()];
         let [a, b] = surfaces.map(|surface| {
             Face::builder(&stores, surface)
-                .build_polygon_from_points(points)
-                .into_face()
+                .with_exterior_polygon_from_points(points)
+                .build()
         });
 
         let intersection = FaceFaceIntersection::compute([&a, &b], &stores);
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_point.rs b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
index 92742d0f3..8b1a8dcea 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_point.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
@@ -143,8 +143,8 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[0., 0.], [1., 1.], [0., 2.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[0., 0.], [1., 1.], [0., 2.]])
+            .build();
         let point = Point::from([2., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -156,8 +156,8 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[0., 0.], [2., 1.], [0., 2.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[0., 0.], [2., 1.], [0., 2.]])
+            .build();
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -172,8 +172,8 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[4., 2.], [0., 4.], [0., 0.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[4., 2.], [0., 4.], [0., 0.]])
+            .build();
         let point = Point::from([1., 2.]);
 
         let intersection = (&face, &point).intersect();
@@ -188,8 +188,13 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[0., 0.], [2., 1.], [3., 0.], [3., 4.]])
-            .into_face();
+            .with_exterior_polygon_from_points([
+                [0., 0.],
+                [2., 1.],
+                [3., 0.],
+                [3., 4.],
+            ])
+            .build();
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -204,8 +209,13 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[0., 0.], [2., 1.], [3., 1.], [0., 2.]])
-            .into_face();
+            .with_exterior_polygon_from_points([
+                [0., 0.],
+                [2., 1.],
+                [3., 1.],
+                [0., 2.],
+            ])
+            .build();
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -220,14 +230,14 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [0., 0.],
                 [2., 1.],
                 [3., 1.],
                 [4., 0.],
                 [4., 5.],
             ])
-            .into_face();
+            .build();
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -242,8 +252,8 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[0., 0.], [2., 0.], [0., 1.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[0., 0.], [2., 0.], [0., 1.]])
+            .build();
         let point = Point::from([1., 0.]);
 
         let intersection = (&face, &point).intersect();
@@ -267,8 +277,8 @@ mod tests {
         let stores = Stores::new();
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
+            .build();
         let point = Point::from([1., 0.]);
 
         let intersection = (&face, &point).intersect();
diff --git a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
index 0201a4efd..30e9ee513 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
@@ -169,13 +169,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::yz_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face()
+            .build()
             .translate([-1., 0., 0.], &stores);
 
         assert_eq!((&ray, &face).intersect(), None);
@@ -188,13 +188,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::yz_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face()
+            .build()
             .translate([1., 0., 0.], &stores);
 
         assert_eq!(
@@ -210,13 +210,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::yz_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face()
+            .build()
             .translate([0., 0., 2.], &stores);
 
         assert_eq!((&ray, &face).intersect(), None);
@@ -229,13 +229,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::yz_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face()
+            .build()
             .translate([1., 1., 0.], &stores);
 
         let edge = face
@@ -259,13 +259,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::yz_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face()
+            .build()
             .translate([1., 1., 1.], &stores);
 
         let vertex = face
@@ -287,13 +287,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face();
+            .build();
 
         assert_eq!(
             (&ray, &face).intersect(),
@@ -308,13 +308,13 @@ mod tests {
         let ray = HorizontalRayToTheRight::from([0., 0., 0.]);
 
         let face = Face::builder(&stores, Surface::xy_plane())
-            .build_polygon_from_points([
+            .with_exterior_polygon_from_points([
                 [-1., -1.],
                 [1., -1.],
                 [1., 1.],
                 [-1., 1.],
             ])
-            .into_face()
+            .build()
             .translate([0., 0., 1.], &stores);
 
         assert_eq!((&ray, &face).intersect(), None)
diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index 123a45992..947c3820f 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -198,18 +198,17 @@ mod tests {
 
         let expected_face = {
             let surface = Surface::xz_plane();
-            let builder = HalfEdge::builder(&stores, surface);
 
-            let bottom =
-                builder.build_line_segment_from_points([[0., 0.], [1., 0.]]);
-            let top = builder
+            let bottom = HalfEdge::builder(&stores, surface)
+                .build_line_segment_from_points([[0., 0.], [1., 0.]]);
+            let top = HalfEdge::builder(&stores, surface)
                 .build_line_segment_from_points([[0., 1.], [1., 1.]])
                 .reverse();
-            let left = builder
+            let left = HalfEdge::builder(&stores, surface)
                 .build_line_segment_from_points([[0., 0.], [0., 1.]])
                 .reverse();
-            let right =
-                builder.build_line_segment_from_points([[1., 0.], [1., 1.]]);
+            let right = HalfEdge::builder(&stores, surface)
+                .build_line_segment_from_points([[1., 0.], [1., 1.]]);
 
             let cycle = Cycle::new(surface, [bottom, right, top, left]);
 
diff --git a/crates/fj-kernel/src/algorithms/sweep/face.rs b/crates/fj-kernel/src/algorithms/sweep/face.rs
index 4715edb2d..36906cfbd 100644
--- a/crates/fj-kernel/src/algorithms/sweep/face.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/face.rs
@@ -95,12 +95,12 @@ mod tests {
             .sweep(UP, &stores);
 
         let bottom = Face::builder(&stores, surface)
-            .build_polygon_from_points(TRIANGLE)
-            .into_face()
+            .with_exterior_polygon_from_points(TRIANGLE)
+            .build()
             .reverse();
         let top = Face::builder(&stores, surface.translate(UP, &stores))
-            .build_polygon_from_points(TRIANGLE)
-            .into_face();
+            .with_exterior_polygon_from_points(TRIANGLE)
+            .build();
 
         assert!(solid.find_face(&bottom).is_some());
         assert!(solid.find_face(&top).is_some());
@@ -130,12 +130,12 @@ mod tests {
             .sweep(DOWN, &stores);
 
         let bottom = Face::builder(&stores, surface.translate(DOWN, &stores))
-            .build_polygon_from_points(TRIANGLE)
-            .into_face()
+            .with_exterior_polygon_from_points(TRIANGLE)
+            .build()
             .reverse();
         let top = Face::builder(&stores, surface)
-            .build_polygon_from_points(TRIANGLE)
-            .into_face();
+            .with_exterior_polygon_from_points(TRIANGLE)
+            .build();
 
         assert!(solid.find_face(&bottom).is_some());
         assert!(solid.find_face(&top).is_some());
diff --git a/crates/fj-kernel/src/algorithms/triangulate/mod.rs b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
index d29ae4752..5912fc12d 100644
--- a/crates/fj-kernel/src/algorithms/triangulate/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
@@ -101,8 +101,8 @@ mod tests {
 
         let surface = Surface::xy_plane();
         let face = Face::builder(&stores, surface)
-            .build_polygon_from_points([a, b, c, d])
-            .into_face();
+            .with_exterior_polygon_from_points([a, b, c, d])
+            .build();
 
         let a = Point::from(a).to_xyz();
         let b = Point::from(b).to_xyz();
@@ -135,9 +135,9 @@ mod tests {
 
         let surface = Surface::xy_plane();
         let face = Face::builder(&stores, surface)
-            .build_polygon_from_points([a, b, c, d])
-            .with_hole([e, f, g, h])
-            .into_face();
+            .with_exterior_polygon_from_points([a, b, c, d])
+            .with_interior_polygon_from_points([e, f, g, h])
+            .build();
 
         let triangles = triangulate(face)?;
 
@@ -188,8 +188,8 @@ mod tests {
 
         let surface = Surface::xy_plane();
         let face = Face::builder(&stores, surface)
-            .build_polygon_from_points([a, b, c, d, e])
-            .into_face();
+            .with_exterior_polygon_from_points([a, b, c, d, e])
+            .build();
 
         let triangles = triangulate(face)?;
 
diff --git a/crates/fj-kernel/src/builder/curve.rs b/crates/fj-kernel/src/builder/curve.rs
index 543782856..bc421a319 100644
--- a/crates/fj-kernel/src/builder/curve.rs
+++ b/crates/fj-kernel/src/builder/curve.rs
@@ -19,7 +19,7 @@ pub struct CurveBuilder<'a> {
 
 impl<'a> CurveBuilder<'a> {
     /// Build a line that represents the u-axis on the surface
-    pub fn build_u_axis(&self) -> Curve {
+    pub fn build_u_axis(self) -> Curve {
         let a = Point::origin();
         let b = a + Vector::unit_u();
 
@@ -27,7 +27,7 @@ impl<'a> CurveBuilder<'a> {
     }
 
     /// Build a line that represents the v-axis on the surface
-    pub fn build_v_axis(&self) -> Curve {
+    pub fn build_v_axis(self) -> Curve {
         let a = Point::origin();
         let b = a + Vector::unit_v();
 
@@ -35,7 +35,7 @@ impl<'a> CurveBuilder<'a> {
     }
 
     /// Build a circle from the given radius
-    pub fn build_circle_from_radius(&self, radius: impl Into<Scalar>) -> Curve {
+    pub fn build_circle_from_radius(self, radius: impl Into<Scalar>) -> Curve {
         let radius = radius.into();
 
         let path = SurfacePath::circle_from_radius(radius);
diff --git a/crates/fj-kernel/src/builder/cycle.rs b/crates/fj-kernel/src/builder/cycle.rs
index f582a4ade..798bbd5ca 100644
--- a/crates/fj-kernel/src/builder/cycle.rs
+++ b/crates/fj-kernel/src/builder/cycle.rs
@@ -19,7 +19,7 @@ pub struct CycleBuilder<'a> {
 impl<'a> CycleBuilder<'a> {
     /// Create a polygon from a list of points
     pub fn build_polygon_from_points(
-        &self,
+        self,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Cycle {
         let mut points: Vec<_> = points.into_iter().map(Into::into).collect();
diff --git a/crates/fj-kernel/src/builder/edge.rs b/crates/fj-kernel/src/builder/edge.rs
index 949ae29a3..f8611d45d 100644
--- a/crates/fj-kernel/src/builder/edge.rs
+++ b/crates/fj-kernel/src/builder/edge.rs
@@ -23,7 +23,7 @@ pub struct HalfEdgeBuilder<'a> {
 impl<'a> HalfEdgeBuilder<'a> {
     /// Build a circle from the given radius
     pub fn build_circle_from_radius(
-        &self,
+        self,
         radius: impl Into<Scalar>,
     ) -> HalfEdge {
         let curve = Curve::builder(self.stores, self.surface)
@@ -62,7 +62,7 @@ impl<'a> HalfEdgeBuilder<'a> {
 
     /// Build a line segment from two points
     pub fn build_line_segment_from_points(
-        &self,
+        self,
         points: [impl Into<Point<2>>; 2],
     ) -> HalfEdge {
         let points = points.map(Into::into);
diff --git a/crates/fj-kernel/src/builder/face.rs b/crates/fj-kernel/src/builder/face.rs
index 0289b7958..6dccad7b4 100644
--- a/crates/fj-kernel/src/builder/face.rs
+++ b/crates/fj-kernel/src/builder/face.rs
@@ -1,5 +1,3 @@
-use std::ops::Deref;
-
 use fj_math::Point;
 
 use crate::{
@@ -16,63 +14,47 @@ pub struct FaceBuilder<'a> {
 
     /// The surface that the [`Face`] is defined in
     pub surface: Surface,
-}
-
-impl<'a> FaceBuilder<'a> {
-    /// Construct a polygon from a list of points
-    pub fn build_polygon_from_points(
-        &self,
-        points: impl IntoIterator<Item = impl Into<Point<2>>>,
-    ) -> FacePolygon {
-        let cycle = Cycle::builder(self.stores, self.surface)
-            .build_polygon_from_points(points);
-        let face = Face::new(self.surface, cycle);
 
-        FacePolygon {
-            stores: self.stores,
-            face,
-        }
-    }
-}
+    /// The exterior cycle that bounds the [`Face`] on the outside
+    ///
+    /// Must be provided by the caller, directly or using one of the `with_`
+    /// methods, before [`FaceBuilder::build`] is called.
+    pub exterior: Option<Cycle>,
 
-/// A polygon
-#[derive(Clone, Debug)]
-pub struct FacePolygon<'a> {
-    stores: &'a Stores,
-    face: Face,
+    /// The interior cycles that form holes in the [`Face`]
+    pub interiors: Vec<Cycle>,
 }
 
-impl FacePolygon<'_> {
-    /// Add a hole to the polygon
-    pub fn with_hole(
+impl<'a> FaceBuilder<'a> {
+    /// Build the [`Face`] with an exterior polygon from the provided points
+    pub fn with_exterior_polygon_from_points(
         mut self,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Self {
-        let surface = *self.face.surface();
-        self.face =
-            self.face
-                .with_interiors([Cycle::builder(self.stores, surface)
-                    .build_polygon_from_points(points)]);
-
+        self.exterior = Some(
+            Cycle::builder(self.stores, self.surface)
+                .build_polygon_from_points(points),
+        );
         self
     }
 
-    /// Consume the `Polygon` and return the [`Face`] it wraps
-    pub fn into_face(self) -> Face {
-        self.face
-    }
-}
-
-impl From<FacePolygon<'_>> for Face {
-    fn from(polygon: FacePolygon) -> Self {
-        polygon.into_face()
+    /// Build the [`Face`] with an interior polygon from the provided points
+    pub fn with_interior_polygon_from_points(
+        mut self,
+        points: impl IntoIterator<Item = impl Into<Point<2>>>,
+    ) -> Self {
+        self.interiors.push(
+            Cycle::builder(self.stores, self.surface)
+                .build_polygon_from_points(points),
+        );
+        self
     }
-}
 
-impl Deref for FacePolygon<'_> {
-    type Target = Face;
-
-    fn deref(&self) -> &Self::Target {
-        &self.face
+    /// Construct a polygon from a list of points
+    pub fn build(self) -> Face {
+        let exterior = self
+            .exterior
+            .expect("Can't build `Face` without exterior cycle");
+        Face::new(self.surface, exterior).with_interiors(self.interiors)
     }
 }
diff --git a/crates/fj-kernel/src/builder/mod.rs b/crates/fj-kernel/src/builder/mod.rs
index 9bc5b153a..0c73ef261 100644
--- a/crates/fj-kernel/src/builder/mod.rs
+++ b/crates/fj-kernel/src/builder/mod.rs
@@ -13,7 +13,7 @@ pub use self::{
     curve::{CurveBuilder, GlobalCurveBuilder},
     cycle::CycleBuilder,
     edge::HalfEdgeBuilder,
-    face::{FaceBuilder, FacePolygon},
+    face::FaceBuilder,
     shell::ShellBuilder,
     sketch::SketchBuilder,
     solid::SolidBuilder,
diff --git a/crates/fj-kernel/src/builder/shell.rs b/crates/fj-kernel/src/builder/shell.rs
index 435046ad5..95107d69f 100644
--- a/crates/fj-kernel/src/builder/shell.rs
+++ b/crates/fj-kernel/src/builder/shell.rs
@@ -17,7 +17,7 @@ pub struct ShellBuilder<'a> {
 impl<'a> ShellBuilder<'a> {
     /// Create a cube from the length of its edges
     pub fn build_cube_from_edge_length(
-        &self,
+        self,
         edge_length: impl Into<Scalar>,
     ) -> Shell {
         // Let's define a short-hand for half the edge length. We're going to
@@ -38,8 +38,8 @@ impl<'a> ShellBuilder<'a> {
 
         let faces = planes.map(|plane| {
             Face::builder(self.stores, plane)
-                .build_polygon_from_points(points)
-                .into_face()
+                .with_exterior_polygon_from_points(points)
+                .build()
         });
 
         Shell::new().with_faces(faces)
diff --git a/crates/fj-kernel/src/builder/sketch.rs b/crates/fj-kernel/src/builder/sketch.rs
index 0d608b3ef..7a25982fa 100644
--- a/crates/fj-kernel/src/builder/sketch.rs
+++ b/crates/fj-kernel/src/builder/sketch.rs
@@ -19,12 +19,12 @@ pub struct SketchBuilder<'a> {
 impl<'a> SketchBuilder<'a> {
     /// Construct a polygon from a list of points
     pub fn build_polygon_from_points(
-        &self,
+        self,
         points: impl IntoIterator<Item = impl Into<Point<2>>>,
     ) -> Sketch {
         let face = Face::builder(self.stores, self.surface)
-            .build_polygon_from_points(points)
-            .into_face();
+            .with_exterior_polygon_from_points(points)
+            .build();
         Sketch::new().with_faces([face])
     }
 }
diff --git a/crates/fj-kernel/src/builder/solid.rs b/crates/fj-kernel/src/builder/solid.rs
index 08f7c2ebb..335a051d7 100644
--- a/crates/fj-kernel/src/builder/solid.rs
+++ b/crates/fj-kernel/src/builder/solid.rs
@@ -16,7 +16,7 @@ pub struct SolidBuilder<'a> {
 impl<'a> SolidBuilder<'a> {
     /// Create a cube from the length of its edges
     pub fn build_cube_from_edge_length(
-        &self,
+        self,
         edge_length: impl Into<Scalar>,
     ) -> Solid {
         let shell = Shell::builder(self.stores)
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index 39424bb70..477344458 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -403,8 +403,8 @@ mod tests {
 
         let surface = Surface::xy_plane();
         let object = Face::builder(&stores, surface)
-            .build_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
+            .build();
 
         assert_eq!(3, object.curve_iter().count());
         assert_eq!(1, object.cycle_iter().count());
@@ -500,8 +500,8 @@ mod tests {
 
         let surface = Surface::xy_plane();
         let face = Face::builder(&stores, surface)
-            .build_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
-            .into_face();
+            .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
+            .build();
         let object = Sketch::new().with_faces([face]);
 
         assert_eq!(3, object.curve_iter().count());
diff --git a/crates/fj-kernel/src/objects/face.rs b/crates/fj-kernel/src/objects/face.rs
index 21a94387d..948603d94 100644
--- a/crates/fj-kernel/src/objects/face.rs
+++ b/crates/fj-kernel/src/objects/face.rs
@@ -67,7 +67,12 @@ pub struct Face {
 impl Face {
     /// Build a `Face` using [`FaceBuilder`]
     pub fn builder(stores: &Stores, surface: Surface) -> FaceBuilder {
-        FaceBuilder { stores, surface }
+        FaceBuilder {
+            stores,
+            surface,
+            exterior: None,
+            interiors: Vec::new(),
+        }
     }
 
     /// Construct a new instance of `Face`
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 40e21bb3e..a22893d8a 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -37,8 +37,8 @@ impl Shape for fj::Sketch {
                     poly_chain.to_points().into_iter().map(Point::from);
 
                 Face::builder(stores, surface)
-                    .build_polygon_from_points(points)
-                    .into_face()
+                    .with_exterior_polygon_from_points(points)
+                    .build()
                     .with_color(Color(self.color()))
             }
         };