diff --git a/crates/engine/src/cmd/datum.rs b/crates/engine/src/cmd/datum.rs
index 30ca01a..d898b3b 100644
--- a/crates/engine/src/cmd/datum.rs
+++ b/crates/engine/src/cmd/datum.rs
@@ -817,4 +817,47 @@ pub(crate) mod tests {
         assert_eq!(s.journal.len(), journal);
         let _ = std::fs::remove_dir_all(&dir);
     }
+
+    /// A session with the design `commands` (a SolidCraft script) open.
+    pub(crate) fn scripted(commands: Value) -> (crate::tests::TempDir, Session) {
+        let bytes = fieldcraft_geometry::script_design(&json!({"commands": commands}).to_string()).unwrap();
+        let (dir, path) = crate::tests::design_file(&bytes);
+        let mut s = Session::default();
+        s.execute("geometry.open", &json!({"path": path})).unwrap();
+        (dir, s)
+    }
+
+    /// Partition the open design by the planes `x = …` / `y = …` / `z = …` (`(axis, offset)`).
+    pub(crate) fn cut_at(s: &mut Session, planes: &[(usize, f64)]) {
+        for (i, &(k, offset)) in planes.iter().enumerate() {
+            let (name, plane) = (format!("C{i}"), ["yz", "zx", "xy"][k]);
+            s.execute("geometry.datum", &json!({"name": name, "by": {"type": "offset", "plane": plane, "offset": offset}})).unwrap();
+            s.execute("geometry.partition", &json!({"name": format!("P{i}"), "datum": name})).unwrap();
+        }
+    }
+
+    /// A box with a plate-shaped void in its middle that touches no side (#388): the planes
+    /// round the void leave a centre column whose material lies above and below the void, two
+    /// pieces that become separate cells only at the last cut.
+    #[test]
+    fn pieces_that_do_not_touch_are_separate_cells() {
+        let (_dir, mut s) = scripted(json!([
+            {"command": "solid.box", "params": {"length": 106, "width": 76, "height": 20, "corner": [0, 0, 0], "body_name": "Air"}},
+            {"command": "solid.box", "params": {"length": 85, "width": 56, "height": 2, "corner": [13, 13, 9], "operation": "cut"}},
+        ]));
+        let whole = s.design.as_ref().unwrap().bodies[0].measure().unwrap().volume;
+        cut_at(&mut s, &[(0, 22.5), (0, 68.5), (1, 22.5), (1, 59.5)]);
+        let design = s.design.clone().unwrap();
+        let shells: Vec<(&str, usize)> = design.bodies.iter().map(|b| (b.name.as_str(), b.shells().unwrap())).collect();
+        assert!(shells.iter().all(|s| s.1 == 1), "{shells:?}");
+        // 3 × 3 columns, the centre one in two pieces.
+        assert_eq!(shells.len(), 10, "{shells:?}");
+        let volume: f64 = design.bodies.iter().map(|b| b.measure().unwrap().volume).sum();
+        assert!((volume - whole).abs() < 1e-6 * whole, "{volume} vs {whole}");
+        let centre: Vec<&str> = shells.iter().map(|s| s.0).filter(|n| n.ends_with('1') || n.ends_with('2')).collect();
+        assert_eq!(centre.len(), 2, "{centre:?}");
+        // Numbered by centroid: the piece below the void first.
+        let z = |n: &str| design.body(n).unwrap().measure().unwrap().centroid[2];
+        assert!(z(centre[0]) < 9.0 && z(centre[1]) > 11.0, "{centre:?}");
+    }
 }
diff --git a/crates/geometry/src/lib.rs b/crates/geometry/src/lib.rs
index a734474..9caf06d 100644
--- a/crates/geometry/src/lib.rs
+++ b/crates/geometry/src/lib.rs
@@ -215,6 +215,11 @@ impl Shape {
         Ok(guard("size", || Ok(self.body.size()))?)
     }
 
+    /// The boundary shells of the body: one for a solid in one piece without voids.
+    pub fn shells(&self) -> Result<usize> {
+        Ok(guard("shells", || Ok(self.body.shell_count()))?)
+    }
+
     pub fn measure(&self) -> Result<Measure> {
         let m = guard("measure", || solidcraft_kernel::measure(&self.body))?;
         Ok(Measure {
diff --git a/crates/geometry/src/partition.rs b/crates/geometry/src/partition.rs
index 487a347..b3bc563 100644
--- a/crates/geometry/src/partition.rs
+++ b/crates/geometry/src/partition.rs
@@ -165,11 +165,20 @@ enum Split {
 
 /// Cut one body.
 fn split(body: &Shape, plane: &Plane, n: [f64; 3], cut: &Cut) -> Result<Split> {
-    let parts = match guard("partition", || solidcraft_kernel::split_by_plane(&body.body, plane)) {
+    let sides = match guard("partition", || solidcraft_kernel::split_by_plane(&body.body, plane)) {
         Ok(p) if p.len() >= 2 => p,
         Ok(_) => return Ok(Split::Misses),
         Err(e) => return Ok(Split::Failed(e.to_string())),
     };
+    // Each side may fall apart into pieces that do not touch (#388): every piece is a cell.
+    let mut parts = Vec::with_capacity(sides.len());
+    for side in sides {
+        match guard("partition", || side.lumps()) {
+            Ok(pieces) if !pieces.is_empty() => parts.extend(pieces),
+            Ok(_) => parts.push(side),
+            Err(e) => return Ok(Split::Failed(e.to_string())),
+        }
+    }
     let size = body.size()?;
     let tol = (MATCH_TOLERANCE * size).max(1e-4);
     let parent = Faces::of(body, tol)?;