diff --git a/crates/fj-kernel/src/algorithms/approx/faces.rs b/crates/fj-kernel/src/algorithms/approx/faces.rs
index ad977d0e4..54295316b 100644
--- a/crates/fj-kernel/src/algorithms/approx/faces.rs
+++ b/crates/fj-kernel/src/algorithms/approx/faces.rs
@@ -84,7 +84,6 @@ mod tests {
     use crate::{
         geometry,
         objects::{Face, Surface},
-        shape::Shape,
     };
 
     use super::{CycleApprox, FaceApprox, Tolerance};
@@ -95,8 +94,6 @@ mod tests {
 
         let tolerance = Tolerance::from_scalar(Scalar::ONE)?;
 
-        let mut shape = Shape::new();
-
         let a = Point::from([0., 0.]);
         let b = Point::from([3., 0.]);
         let c = Point::from([3., 3.]);
@@ -107,7 +104,7 @@ mod tests {
         let g = Point::from([2., 2.]);
         let h = Point::from([1., 2.]);
 
-        let face = Face::builder(Surface::xy_plane(), &mut shape)
+        let face = Face::builder(Surface::xy_plane())
             .with_exterior_polygon([a, b, c, d])
             .with_interior_polygon([e, f, g, h])
             .build();
diff --git a/crates/fj-kernel/src/algorithms/sweep.rs b/crates/fj-kernel/src/algorithms/sweep.rs
index 2ebc7a77b..4ffee264f 100644
--- a/crates/fj-kernel/src/algorithms/sweep.rs
+++ b/crates/fj-kernel/src/algorithms/sweep.rs
@@ -273,7 +273,6 @@ mod tests {
         algorithms::Tolerance,
         iter::ObjectIters,
         objects::{Face, Surface},
-        shape::Shape,
     };
 
     #[test]
@@ -362,9 +361,7 @@ mod tests {
     ) -> anyhow::Result<()> {
         let tolerance = Tolerance::from_scalar(Scalar::ONE)?;
 
-        let mut shape = Shape::new();
-
-        let sketch = Face::builder(Surface::xy_plane(), &mut shape)
+        let sketch = Face::builder(Surface::xy_plane())
             .with_exterior_polygon([[0., 0.], [1., 0.], [0., 1.]])
             .build();
 
@@ -376,11 +373,10 @@ mod tests {
             .map(|vertex| vertex.into())
             .collect();
 
-        let mut shape = Shape::new();
         let faces = expected_surfaces.into_iter().map(|surface| {
             let surface = Surface::plane_from_points(surface);
 
-            Face::builder(surface, &mut shape)
+            Face::builder(surface)
                 .with_exterior_polygon(expected_vertices.clone())
                 .build()
         });
diff --git a/crates/fj-kernel/src/algorithms/triangulation/mod.rs b/crates/fj-kernel/src/algorithms/triangulation/mod.rs
index 7ca4f6ff9..77a37ab07 100644
--- a/crates/fj-kernel/src/algorithms/triangulation/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulation/mod.rs
@@ -89,19 +89,16 @@ mod tests {
     use crate::{
         algorithms::Tolerance,
         objects::{Face, Surface},
-        shape::Shape,
     };
 
     #[test]
     fn simple() -> anyhow::Result<()> {
-        let mut shape = Shape::new();
-
         let a = [0., 0.];
         let b = [2., 0.];
         let c = [2., 2.];
         let d = [0., 1.];
 
-        let face = Face::builder(Surface::xy_plane(), &mut shape)
+        let face = Face::builder(Surface::xy_plane())
             .with_exterior_polygon([a, b, c, d])
             .build();
 
@@ -122,8 +119,6 @@ mod tests {
 
     #[test]
     fn simple_hole() -> anyhow::Result<()> {
-        let mut shape = Shape::new();
-
         let a = [0., 0.];
         let b = [4., 0.];
         let c = [4., 4.];
@@ -134,7 +129,7 @@ mod tests {
         let g = [3., 3.];
         let h = [1., 2.];
 
-        let face = Face::builder(Surface::xy_plane(), &mut shape)
+        let face = Face::builder(Surface::xy_plane())
             .with_exterior_polygon([a, b, c, d])
             .with_interior_polygon([e, f, g, h])
             .build();
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index 49756fe02..f5c9f1cfa 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -439,10 +439,7 @@ impl<T> Iterator for Iter<T> {
 
 #[cfg(test)]
 mod tests {
-    use crate::{
-        objects::{Curve, Cycle, Edge, Face, Surface, Vertex},
-        shape::Shape,
-    };
+    use crate::objects::{Curve, Cycle, Edge, Face, Surface, Vertex};
 
     use super::ObjectIters as _;
 
@@ -488,8 +485,7 @@ mod tests {
 
     #[test]
     fn face() {
-        let mut shape = Shape::new();
-        let face = Face::builder(Surface::xy_plane(), &mut shape)
+        let face = Face::builder(Surface::xy_plane())
             .with_exterior_polygon([[0., 0.], [1., 0.], [0., 1.]])
             .build();
 
diff --git a/crates/fj-kernel/src/objects/face.rs b/crates/fj-kernel/src/objects/face.rs
index ceae1f963..e5bcee02a 100644
--- a/crates/fj-kernel/src/objects/face.rs
+++ b/crates/fj-kernel/src/objects/face.rs
@@ -3,10 +3,7 @@ use std::hash::{Hash, Hasher};
 use fj_interop::mesh::Color;
 use fj_math::Triangle;
 
-use crate::{
-    builder::FaceBuilder,
-    shape::{LocalForm, Shape},
-};
+use crate::{builder::FaceBuilder, shape::LocalForm};
 
 use super::{Cycle, Surface};
 
@@ -57,7 +54,7 @@ impl Face {
         })
     }
     /// Build a face using the [`FaceBuilder`] API
-    pub fn builder(surface: Surface, _shape: &mut Shape) -> FaceBuilder {
+    pub fn builder(surface: Surface) -> FaceBuilder {
         FaceBuilder::new(surface)
     }
 
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 26bc242fd..8f032a553 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -2,7 +2,6 @@ use fj_interop::debug::DebugInfo;
 use fj_kernel::{
     algorithms::Tolerance,
     objects::{Face, Surface},
-    shape::Shape,
     validation::{validate, Validated, ValidationConfig, ValidationError},
 };
 use fj_math::{Aabb, Point};
@@ -16,12 +15,10 @@ impl ToShape for fj::Sketch {
         _: Tolerance,
         _: &mut DebugInfo,
     ) -> Result<Validated<Vec<Face>>, ValidationError> {
-        let mut tmp = Shape::new();
-
         let surface = Surface::xy_plane();
         let points = self.to_points().into_iter().map(Point::from);
 
-        let sketch = Face::builder(surface, &mut tmp)
+        let sketch = Face::builder(surface)
             .with_exterior_polygon(points)
             .with_color(self.color())
             .build();