diff --git a/crates/fj-kernel/src/operations/build/mod.rs b/crates/fj-kernel/src/operations/build/mod.rs
index 7f2e1a85a..fe6010c3b 100644
--- a/crates/fj-kernel/src/operations/build/mod.rs
+++ b/crates/fj-kernel/src/operations/build/mod.rs
@@ -2,12 +2,14 @@ mod cycle;
 mod edge;
 mod face;
 mod shell;
+mod solid;
 mod surface;
 
 pub use self::{
     cycle::BuildCycle,
     edge::BuildHalfEdge,
     face::{BuildFace, Polygon},
-    shell::{BuildShell, Tetrahedron},
+    shell::{BuildShell, TetrahedronShell},
+    solid::{BuildSolid, Tetrahedron},
     surface::BuildSurface,
 };
diff --git a/crates/fj-kernel/src/operations/build/shell.rs b/crates/fj-kernel/src/operations/build/shell.rs
index c18b6bc06..41ed095af 100644
--- a/crates/fj-kernel/src/operations/build/shell.rs
+++ b/crates/fj-kernel/src/operations/build/shell.rs
@@ -2,7 +2,9 @@ use fj_math::Point;
 
 use crate::{
     objects::{Face, Shell},
-    operations::{Insert, IsInsertedYes, JoinCycle, UpdateFace},
+    operations::{
+        Insert, IsInserted, IsInsertedNo, IsInsertedYes, JoinCycle, UpdateFace,
+    },
     services::Services,
 };
 
@@ -31,7 +33,7 @@ pub trait BuildShell {
     fn tetrahedron(
         points: [impl Into<Point<3>>; 4],
         services: &mut Services,
-    ) -> Tetrahedron {
+    ) -> TetrahedronShell {
         let [a, b, c, d] = points.map(Into::into);
 
         let abc = Face::triangle([a, b, c], services);
@@ -64,7 +66,7 @@ pub trait BuildShell {
 
         let [abc, bad, dac, cbd] = triangles;
 
-        Tetrahedron {
+        TetrahedronShell {
             shell,
             abc,
             bad,
@@ -83,9 +85,9 @@ impl BuildShell for Shell {}
 /// `d`, in the order in which they are passed.
 ///
 /// Returned by [`BuildShell::tetrahedron`].
-pub struct Tetrahedron {
+pub struct TetrahedronShell<I: IsInserted = IsInsertedNo> {
     /// The shell that forms the tetrahedron
-    pub shell: Shell,
+    pub shell: I::T<Shell>,
 
     /// The face formed by the points `a`, `b`, and `c`.
     pub abc: Polygon<3, IsInsertedYes>,
diff --git a/crates/fj-kernel/src/operations/build/solid.rs b/crates/fj-kernel/src/operations/build/solid.rs
new file mode 100644
index 000000000..080405ee5
--- /dev/null
+++ b/crates/fj-kernel/src/operations/build/solid.rs
@@ -0,0 +1,44 @@
+use fj_math::Point;
+
+use crate::{
+    objects::{Shell, Solid},
+    operations::{
+        build::shell::BuildShell, Insert, IsInsertedYes, TetrahedronShell,
+        UpdateSolid,
+    },
+    services::Services,
+};
+
+/// Build a [`Solid`]
+pub trait BuildSolid {
+    /// Build an empty solid
+    fn empty() -> Solid {
+        Solid::new([])
+    }
+
+    /// Build a tetrahedron from the provided points
+    ///
+    /// See [`BuildShell::tetrahedron`] for more information.
+    fn tetrahedron(
+        points: [impl Into<Point<3>>; 4],
+        services: &mut Services,
+    ) -> Tetrahedron {
+        let shell = Shell::tetrahedron(points, services).insert(services);
+        let solid = Solid::empty().add_shell(shell.shell.clone());
+
+        Tetrahedron { solid, shell }
+    }
+}
+
+impl BuildSolid for Solid {}
+
+/// A tetrahedron
+///
+/// Returned by [`BuildSolid::tetrahedron`].
+pub struct Tetrahedron {
+    /// The solid that forms the tetrahedron
+    pub solid: Solid,
+
+    /// The shell of the tetrahedron
+    pub shell: TetrahedronShell<IsInsertedYes>,
+}
diff --git a/crates/fj-kernel/src/operations/insert.rs b/crates/fj-kernel/src/operations/insert.rs
index 6cf0eebc4..66b6a1b42 100644
--- a/crates/fj-kernel/src/operations/insert.rs
+++ b/crates/fj-kernel/src/operations/insert.rs
@@ -7,7 +7,7 @@ use crate::{
     storage::Handle,
 };
 
-use super::Polygon;
+use super::{Polygon, TetrahedronShell};
 
 /// Insert an object into its respective store
 ///
@@ -91,3 +91,17 @@ impl<const D: usize> Insert for Polygon<D, IsInsertedNo> {
         }
     }
 }
+
+impl Insert for TetrahedronShell<IsInsertedNo> {
+    type Inserted = TetrahedronShell<IsInsertedYes>;
+
+    fn insert(self, services: &mut Services) -> Self::Inserted {
+        TetrahedronShell {
+            shell: self.shell.insert(services),
+            abc: self.abc,
+            bad: self.bad,
+            dac: self.dac,
+            cbd: self.cbd,
+        }
+    }
+}
diff --git a/crates/fj-kernel/src/operations/mod.rs b/crates/fj-kernel/src/operations/mod.rs
index de4ebc596..313bdeaae 100644
--- a/crates/fj-kernel/src/operations/mod.rs
+++ b/crates/fj-kernel/src/operations/mod.rs
@@ -7,10 +7,12 @@ mod update;
 
 pub use self::{
     build::{
-        BuildCycle, BuildFace, BuildHalfEdge, BuildShell, BuildSurface,
-        Polygon, Tetrahedron,
+        BuildCycle, BuildFace, BuildHalfEdge, BuildShell, BuildSolid,
+        BuildSurface, Polygon, Tetrahedron, TetrahedronShell,
     },
     insert::{Insert, IsInserted, IsInsertedNo, IsInsertedYes},
     join::JoinCycle,
-    update::{UpdateCycle, UpdateFace, UpdateHalfEdge, UpdateShell},
+    update::{
+        UpdateCycle, UpdateFace, UpdateHalfEdge, UpdateShell, UpdateSolid,
+    },
 };
diff --git a/crates/fj-kernel/src/operations/update/mod.rs b/crates/fj-kernel/src/operations/update/mod.rs
index 73f5d0874..431b97368 100644
--- a/crates/fj-kernel/src/operations/update/mod.rs
+++ b/crates/fj-kernel/src/operations/update/mod.rs
@@ -2,8 +2,9 @@ mod cycle;
 mod edge;
 mod face;
 mod shell;
+mod solid;
 
 pub use self::{
     cycle::UpdateCycle, edge::UpdateHalfEdge, face::UpdateFace,
-    shell::UpdateShell,
+    shell::UpdateShell, solid::UpdateSolid,
 };
diff --git a/crates/fj-kernel/src/operations/update/solid.rs b/crates/fj-kernel/src/operations/update/solid.rs
new file mode 100644
index 000000000..9c0e340f7
--- /dev/null
+++ b/crates/fj-kernel/src/operations/update/solid.rs
@@ -0,0 +1,17 @@
+use crate::{
+    objects::{Shell, Solid},
+    storage::Handle,
+};
+
+/// Update a [`Solid`]
+pub trait UpdateSolid {
+    /// Add a shell to the solid
+    fn add_shell(&self, shell: Handle<Shell>) -> Solid;
+}
+
+impl UpdateSolid for Solid {
+    fn add_shell(&self, shell: Handle<Shell>) -> Solid {
+        let shells = self.shells().cloned().chain([shell]);
+        Solid::new(shells)
+    }
+}
diff --git a/crates/fj-kernel/src/validate/shell.rs b/crates/fj-kernel/src/validate/shell.rs
index c20622333..91915bc3e 100644
--- a/crates/fj-kernel/src/validate/shell.rs
+++ b/crates/fj-kernel/src/validate/shell.rs
@@ -235,6 +235,7 @@ mod tests {
 
         Ok(())
     }
+
     #[test]
     fn shell_not_watertight() -> anyhow::Result<()> {
         let mut services = Services::new();