diff --git a/crates/fj-kernel/src/builder/face.rs b/crates/fj-kernel/src/builder/face.rs
index 37125b254..3dc980233 100644
--- a/crates/fj-kernel/src/builder/face.rs
+++ b/crates/fj-kernel/src/builder/face.rs
@@ -1,14 +1,13 @@
-use fj_interop::{ext::ArrayExt, mesh::Color};
-use fj_math::Point;
+use fj_interop::mesh::Color;
 
 use crate::{
-    objects::{Cycle, Face, GlobalEdge, Objects, Surface},
+    objects::{Face, Objects, Surface},
     operations::Insert,
     services::Service,
     storage::Handle,
 };
 
-use super::{CycleBuilder, HalfEdgeBuilder, SurfaceBuilder};
+use super::CycleBuilder;
 
 /// Builder API for [`Face`]
 pub struct FaceBuilder {
@@ -28,45 +27,6 @@ impl FaceBuilder {
         }
     }
 
-    /// Create a triangle
-    pub fn triangle(
-        points: [impl Into<Point<3>>; 3],
-        edges: [Option<Handle<GlobalEdge>>; 3],
-        objects: &mut Service<Objects>,
-    ) -> (Handle<Face>, [Handle<GlobalEdge>; 3]) {
-        let [a, b, c] = points.map(Into::into);
-
-        let surface =
-            SurfaceBuilder::plane_from_points([a, b, c]).insert(objects);
-        let (exterior, global_edges) = {
-            let half_edges = [[a, b], [b, c], [c, a]].zip_ext(edges).map(
-                |(points, global_form)| {
-                    let mut builder =
-                        HalfEdgeBuilder::line_segment_from_global_points(
-                            points, &surface, None,
-                        );
-
-                    if let Some(global_form) = global_form {
-                        builder = builder.with_global_form(global_form);
-                    }
-
-                    builder.build(objects).insert(objects)
-                },
-            );
-
-            let cycle = Cycle::new(half_edges.clone()).insert(objects);
-
-            let global_edges =
-                half_edges.map(|half_edge| half_edge.global_form().clone());
-
-            (cycle, global_edges)
-        };
-
-        let face = Face::new(surface, exterior, [], None).insert(objects);
-
-        (face, global_edges)
-    }
-
     /// Replace the face's exterior cycle
     pub fn with_exterior(mut self, exterior: CycleBuilder) -> Self {
         self.exterior = exterior;
diff --git a/crates/fj-kernel/src/builder/mod.rs b/crates/fj-kernel/src/builder/mod.rs
index 1cbad97ac..5349098a1 100644
--- a/crates/fj-kernel/src/builder/mod.rs
+++ b/crates/fj-kernel/src/builder/mod.rs
@@ -4,10 +4,5 @@
 mod cycle;
 mod edge;
 mod face;
-mod shell;
-mod surface;
 
-pub use self::{
-    cycle::CycleBuilder, edge::HalfEdgeBuilder, face::FaceBuilder,
-    shell::ShellBuilder, surface::SurfaceBuilder,
-};
+pub use self::{cycle::CycleBuilder, edge::HalfEdgeBuilder, face::FaceBuilder};
diff --git a/crates/fj-kernel/src/builder/shell.rs b/crates/fj-kernel/src/builder/shell.rs
deleted file mode 100644
index 81f14bf95..000000000
--- a/crates/fj-kernel/src/builder/shell.rs
+++ /dev/null
@@ -1,38 +0,0 @@
-use fj_math::Point;
-
-use crate::{
-    objects::{Objects, Shell},
-    services::Service,
-};
-
-use super::FaceBuilder;
-
-/// Builder API for [`Shell`]
-pub struct ShellBuilder {}
-
-impl ShellBuilder {
-    /// Create a tetrahedron from the provided points
-    pub fn tetrahedron(
-        points: [impl Into<Point<3>>; 4],
-        objects: &mut Service<Objects>,
-    ) -> Shell {
-        let [a, b, c, d] = points.map(Into::into);
-
-        let (base, [ab, bc, ca]) =
-            FaceBuilder::triangle([a, b, c], [None, None, None], objects);
-        let (side_a, [_, bd, da]) =
-            FaceBuilder::triangle([a, b, d], [Some(ab), None, None], objects);
-        let (side_b, [_, _, dc]) = FaceBuilder::triangle(
-            [c, a, d],
-            [Some(ca), Some(da), None],
-            objects,
-        );
-        let (side_c, _) = FaceBuilder::triangle(
-            [b, c, d],
-            [Some(bc), Some(dc), Some(bd)],
-            objects,
-        );
-
-        Shell::new([base, side_a, side_b, side_c])
-    }
-}
diff --git a/crates/fj-kernel/src/operations/build/face.rs b/crates/fj-kernel/src/operations/build/face.rs
new file mode 100644
index 000000000..e4c5af4c3
--- /dev/null
+++ b/crates/fj-kernel/src/operations/build/face.rs
@@ -0,0 +1,66 @@
+use fj_interop::ext::ArrayExt;
+use fj_math::Point;
+
+use crate::{
+    builder::HalfEdgeBuilder,
+    objects::{Cycle, Face, GlobalEdge, Objects, Surface},
+    operations::Insert,
+    services::Service,
+    storage::Handle,
+};
+
+use super::BuildSurface;
+
+/// Build a [`Face`]
+pub trait BuildFace {
+    /// Build a triangle
+    fn triangle(
+        points: [impl Into<Point<3>>; 3],
+        edges: [Option<Handle<GlobalEdge>>; 3],
+        objects: &mut Service<Objects>,
+    ) -> Triangle {
+        let [a, b, c] = points.map(Into::into);
+
+        let surface = Surface::plane_from_points([a, b, c]).insert(objects);
+        let (exterior, edges) = {
+            let half_edges = [[a, b], [b, c], [c, a]].zip_ext(edges).map(
+                |(points, global_form)| {
+                    let mut builder =
+                        HalfEdgeBuilder::line_segment_from_global_points(
+                            points, &surface, None,
+                        );
+
+                    if let Some(global_form) = global_form {
+                        builder = builder.with_global_form(global_form);
+                    }
+
+                    builder.build(objects).insert(objects)
+                },
+            );
+
+            let cycle = Cycle::new(half_edges.clone()).insert(objects);
+
+            let global_edges =
+                half_edges.map(|half_edge| half_edge.global_form().clone());
+
+            (cycle, global_edges)
+        };
+
+        let face = Face::new(surface, exterior, [], None);
+
+        Triangle { face, edges }
+    }
+}
+
+impl BuildFace for Face {}
+
+/// A triangle
+///
+/// Returned by [`BuildFace::triangle`].
+pub struct Triangle {
+    /// The face that forms the triangle
+    pub face: Face,
+
+    /// The edges of the triangle
+    pub edges: [Handle<GlobalEdge>; 3],
+}
diff --git a/crates/fj-kernel/src/operations/build/mod.rs b/crates/fj-kernel/src/operations/build/mod.rs
new file mode 100644
index 000000000..be6dfed0e
--- /dev/null
+++ b/crates/fj-kernel/src/operations/build/mod.rs
@@ -0,0 +1,9 @@
+mod face;
+mod shell;
+mod surface;
+
+pub use self::{
+    face::{BuildFace, Triangle},
+    shell::BuildShell,
+    surface::BuildSurface,
+};
diff --git a/crates/fj-kernel/src/operations/build/shell.rs b/crates/fj-kernel/src/operations/build/shell.rs
new file mode 100644
index 000000000..6d4a917f1
--- /dev/null
+++ b/crates/fj-kernel/src/operations/build/shell.rs
@@ -0,0 +1,41 @@
+use fj_math::Point;
+
+use crate::{
+    objects::{Face, Objects, Shell},
+    operations::Insert,
+    services::Service,
+};
+
+use super::{BuildFace, Triangle};
+
+/// Build a [`Shell`]
+pub trait BuildShell {
+    /// Build a tetrahedron from the provided points
+    fn tetrahedron(
+        points: [impl Into<Point<3>>; 4],
+        objects: &mut Service<Objects>,
+    ) -> Shell {
+        let [a, b, c, d] = points.map(Into::into);
+
+        let Triangle {
+            face: base,
+            edges: [ab, bc, ca],
+        } = Face::triangle([a, b, c], [None, None, None], objects);
+        let Triangle {
+            face: side_a,
+            edges: [_, bd, da],
+        } = Face::triangle([a, b, d], [Some(ab), None, None], objects);
+        let Triangle {
+            face: side_b,
+            edges: [_, _, dc],
+        } = Face::triangle([c, a, d], [Some(ca), Some(da), None], objects);
+        let Triangle { face: side_c, .. } =
+            Face::triangle([b, c, d], [Some(bc), Some(dc), Some(bd)], objects);
+
+        let faces =
+            [base, side_a, side_b, side_c].map(|face| face.insert(objects));
+        Shell::new(faces)
+    }
+}
+
+impl BuildShell for Shell {}
diff --git a/crates/fj-kernel/src/builder/surface.rs b/crates/fj-kernel/src/operations/build/surface.rs
similarity index 62%
rename from crates/fj-kernel/src/builder/surface.rs
rename to crates/fj-kernel/src/operations/build/surface.rs
index 1b595f4aa..bd7bab739 100644
--- a/crates/fj-kernel/src/builder/surface.rs
+++ b/crates/fj-kernel/src/operations/build/surface.rs
@@ -5,12 +5,10 @@ use crate::{
     objects::Surface,
 };
 
-/// Builder API for [`Surface`]
-pub struct SurfaceBuilder {}
-
-impl SurfaceBuilder {
-    /// Create a plane from the provided points
-    pub fn plane_from_points(points: [impl Into<Point<3>>; 3]) -> Surface {
+/// Build a [`Surface`]
+pub trait BuildSurface {
+    /// Build a plane from the provided points
+    fn plane_from_points(points: [impl Into<Point<3>>; 3]) -> Surface {
         let [a, b, c] = points.map(Into::into);
 
         let geometry = SurfaceGeometry {
@@ -21,3 +19,5 @@ impl SurfaceBuilder {
         Surface::new(geometry)
     }
 }
+
+impl BuildSurface for Surface {}
diff --git a/crates/fj-kernel/src/operations/mod.rs b/crates/fj-kernel/src/operations/mod.rs
index 052dc3eef..0cfabab4c 100644
--- a/crates/fj-kernel/src/operations/mod.rs
+++ b/crates/fj-kernel/src/operations/mod.rs
@@ -1,5 +1,9 @@
 //! Operations to update shapes
 
+mod build;
 mod insert;
 
-pub use self::insert::Insert;
+pub use self::{
+    build::{BuildFace, BuildShell, BuildSurface, Triangle},
+    insert::Insert,
+};
diff --git a/crates/fj-kernel/src/validate/shell.rs b/crates/fj-kernel/src/validate/shell.rs
index caa9818dd..1e4abccaa 100644
--- a/crates/fj-kernel/src/validate/shell.rs
+++ b/crates/fj-kernel/src/validate/shell.rs
@@ -193,9 +193,9 @@ impl ShellValidationError {
 mod tests {
     use crate::{
         assert_contains_err,
-        builder::{CycleBuilder, FaceBuilder, ShellBuilder},
+        builder::{CycleBuilder, FaceBuilder},
         objects::Shell,
-        operations::Insert,
+        operations::{BuildShell, Insert},
         services::Services,
         validate::{shell::ShellValidationError, Validate, ValidationError},
     };
@@ -204,7 +204,7 @@ mod tests {
     fn coincident_not_identical() -> anyhow::Result<()> {
         let mut services = Services::new();
 
-        let valid = ShellBuilder::tetrahedron(
+        let valid = Shell::tetrahedron(
             [[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.]],
             &mut services.objects,
         );
@@ -246,7 +246,7 @@ mod tests {
     fn shell_not_watertight() -> anyhow::Result<()> {
         let mut services = Services::new();
 
-        let valid = ShellBuilder::tetrahedron(
+        let valid = Shell::tetrahedron(
             [[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.]],
             &mut services.objects,
         );