diff --git a/crates/kernel/src/delete_face.rs b/crates/kernel/src/delete_face.rs
new file mode 100644
index 00000000..df81dc40
--- /dev/null
+++ b/crates/kernel/src/delete_face.rs
@@ -0,0 +1,343 @@
+//! Delete Face with healing: faces are removed and their planar neighbours extend to close the
+//! gap, as when a fillet, chamfer, boss or hole is taken off a part.
+//!
+//! The body is rebuilt from its own topology. Faces away from the gap are kept as they are.
+//! Each neighbouring face (planar) keeps its edges that don't touch the gap; a loop that ran
+//! entirely along deleted faces (a hole's rim, a boss's footprint) is dropped; a corner on the
+//! gap moves to where its planes meet the neighbours across the gap (a fillet's tangent points
+//! go to the sharp corner), and the stretch of loop that bordered deleted faces closes with a
+//! straight edge between the moved corners. Anything else (curved neighbours, a gap the
+//! neighbours cannot close) is refused, naming the face.
+
+use std::collections::{BTreeSet, HashMap};
+
+use solvecraft_geom::Vec3;
+use truck_modeling::{self as mt, builder};
+
+use crate::body::{Body, Solid, from_p3, p3};
+use crate::{KernelError, Result, guard};
+
+fn fail(m: impl Into<String>) -> KernelError {
+    KernelError::Invalid(format!("Delete Face: {}", m.into()))
+}
+
+/// Outward plane (unit normal, offset) of a face, if it is planar: sampled along its edges,
+/// the surface's outward normal stays the same and the points stay on one plane.
+fn face_plane(f: &mt::Face, tol: f64) -> Option<(Vec3, f64)> {
+    use mt::{BoundedCurve, ParametricCurve, ParametricSurface3D, SearchNearestParameter};
+    let surf = f.oriented_surface();
+    let mut pts: Vec<(Vec3, Vec3)> = Vec::new();
+    let mut last: Option<(f64, f64)> = None;
+    for w in f.boundaries() {
+        for e in w.edge_iter() {
+            let c = e.oriented_curve();
+            let (t0, t1) = c.range_tuple();
+            for k in 0..6 {
+                let p = c.subs(t0 + (t1 - t0) * k as f64 / 6.0);
+                let (u, v) = surf.search_nearest_parameter(p, last, 50)?;
+                last = Some((u, v));
+                let n = surf.normal(u, v);
+                pts.push((from_p3(p), Vec3::new(n.x, n.y, n.z).normalized()?));
+            }
+        }
+    }
+    let (p0, n0) = *pts.first()?;
+    let d = n0.dot(p0);
+    pts.iter().all(|(p, n)| n.dot(n0) > 1.0 - 1e-9 && (n0.dot(*p) - d).abs() <= tol).then_some((n0, d))
+}
+
+type Key = (i64, i64, i64);
+
+/// Key of a point for sharing vertices and edges between rebuilt faces.
+fn key(p: Vec3, q: f64) -> Key {
+    let r = |x: f64| (x / q).round() as i64;
+    (r(p.x), r(p.y), r(p.z))
+}
+
+/// Delete faces (indices in the body's face order, as in its mesh's `tri_face`) and heal the
+/// gap by extending the neighbouring planes.
+pub fn delete_faces(body: &Body, faces: &[usize]) -> Result<Body> {
+    body.require_brep("Delete Face")?;
+    let all: Vec<mt::Face> = body.solid.face_iter().cloned().collect();
+    let n = all.len();
+    if faces.is_empty() {
+        return Err(fail("no faces given"));
+    }
+    let del: BTreeSet<usize> = faces.iter().copied().collect();
+    if let Some(bad) = del.iter().find(|f| **f >= n) {
+        return Err(fail(format!("there is no face {bad} (the body has {n})")));
+    }
+    if del.len() >= n {
+        return Err(fail("that would delete every face"));
+    }
+    let size = body.size().max(1e-9);
+    // Edge and vertex → faces.
+    let mut efaces: HashMap<mt::EdgeID, Vec<usize>> = HashMap::new();
+    let mut vfaces: HashMap<mt::VertexID, Vec<usize>> = HashMap::new();
+    for (i, f) in all.iter().enumerate() {
+        for e in f.edge_iter() {
+            let v = efaces.entry(e.id()).or_default();
+            if !v.contains(&i) {
+                v.push(i);
+            }
+        }
+        for v in f.vertex_iter() {
+            let l = vfaces.entry(v.id()).or_default();
+            if !l.contains(&i) {
+                l.push(i);
+            }
+        }
+    }
+    // Neighbours: faces sharing an edge with a deleted face; they must be planar.
+    let mut neighbours: BTreeSet<usize> = BTreeSet::new();
+    for fs in efaces.values() {
+        if fs.iter().any(|f| del.contains(f)) {
+            neighbours.extend(fs.iter().filter(|f| !del.contains(f)));
+        }
+    }
+    if neighbours.is_empty() {
+        return Err(fail("the faces don't border the rest of the body"));
+    }
+    let mut planes: HashMap<usize, (Vec3, f64)> = HashMap::new();
+    for &f in &neighbours {
+        // Planar by its geometry (boolean results may carry a plane as another surface type).
+        match all.get(f).and_then(|x| face_plane(x, size * 1e-6)) {
+            Some(p) => {
+                planes.insert(f, p);
+            }
+            None => {
+                let by = efaces
+                    .values()
+                    .find(|fs| fs.contains(&f) && fs.iter().any(|x| del.contains(x)))
+                    .and_then(|fs| fs.iter().find(|x| del.contains(x)).copied())
+                    .unwrap_or(0);
+                return Err(fail(format!("face {by} borders face {f}, which is curved; only planar neighbours can extend to close the gap yet")));
+            }
+        }
+    }
+    // Corners across the gap: three neighbour planes meeting near the deleted faces.
+    let (mut lo, mut hi) =
+        (Vec3::new(f64::INFINITY, f64::INFINITY, f64::INFINITY), Vec3::new(f64::NEG_INFINITY, f64::NEG_INFINITY, f64::NEG_INFINITY));
+    for &f in &del {
+        for v in all.get(f).into_iter().flat_map(|x| x.vertex_iter()) {
+            let p = from_p3(v.point());
+            lo = lo.min(p);
+            hi = hi.max(p);
+        }
+    }
+    let reach = (hi - lo).len().max(size * 1e-3);
+    let near = |p: Vec3| {
+        p.x >= lo.x - reach && p.y >= lo.y - reach && p.z >= lo.z - reach && p.x <= hi.x + reach && p.y <= hi.y + reach && p.z <= hi.z + reach
+    };
+    let on = |p: Vec3, f: usize| planes.get(&f).is_some_and(|(n, d)| (n.dot(p) - d).abs() <= size * 1e-6);
+    let nb: Vec<usize> = neighbours.iter().copied().collect();
+    let mut corners: Vec<Vec3> = Vec::new();
+    for i in 0..nb.len() {
+        for j in (i + 1)..nb.len() {
+            for k in (j + 1)..nb.len() {
+                let (Some(a), Some(b), Some(c)) =
+                    (nb.get(i).and_then(|x| planes.get(x)), nb.get(j).and_then(|x| planes.get(x)), nb.get(k).and_then(|x| planes.get(x)))
+                else {
+                    continue;
+                };
+                let den = a.0.dot(b.0.cross(c.0));
+                if den.abs() < 1e-9 {
+                    continue;
+                }
+                let x = (b.0.cross(c.0) * a.1 + c.0.cross(a.0) * b.1 + a.0.cross(b.0) * c.1) / den;
+                if x.is_finite() && near(x) {
+                    corners.push(x);
+                }
+            }
+        }
+    }
+    // Where each vertex on the gap goes: the nearest corner on all of its remaining planes.
+    let mut moved: HashMap<mt::VertexID, Vec3> = HashMap::new();
+    for &f in &del {
+        for v in all.get(f).into_iter().flat_map(|x| x.vertex_iter()) {
+            let Some(fs) = vfaces.get(&v.id()) else { continue };
+            let keep: Vec<usize> = fs.iter().copied().filter(|x| !del.contains(x)).collect();
+            if keep.is_empty() || keep.len() >= 3 {
+                continue;
+            }
+            if keep.iter().any(|x| !planes.contains_key(x)) {
+                return Err(fail(format!("a corner of face {f} touches a face that cannot move")));
+            }
+            let p = from_p3(v.point());
+            let best = corners.iter().filter(|c| keep.iter().all(|x| on(**c, *x))).min_by(|a, b| a.dist(p).total_cmp(&b.dist(p)));
+            if let Some(c) = best {
+                moved.insert(v.id(), *c);
+            }
+        }
+    }
+    let q = size * 1e-7;
+    guard("delete face", || {
+        // Shared vertices and new straight edges between the rebuilt faces.
+        let mut verts: HashMap<Key, mt::Vertex> = HashMap::new();
+        for v in body.solid.vertex_iter() {
+            if !moved.contains_key(&v.id()) {
+                verts.insert(key(from_p3(v.point()), q), v.clone());
+            }
+        }
+        let mut lines: HashMap<(Key, Key), mt::Edge> = HashMap::new();
+        let mut line = |a: Vec3, b: Vec3, verts: &mut HashMap<Key, mt::Vertex>| -> mt::Edge {
+            let (ka, kb) = (key(a, q), key(b, q));
+            if let Some(e) = lines.get(&(ka, kb)) {
+                return e.clone();
+            }
+            if let Some(e) = lines.get(&(kb, ka)) {
+                return e.inverse();
+            }
+            let va = verts.entry(ka).or_insert_with(|| builder::vertex(p3(a))).clone();
+            let vb = verts.entry(kb).or_insert_with(|| builder::vertex(p3(b))).clone();
+            let e = builder::line(&va, &vb);
+            lines.insert((ka, kb), e.clone());
+            e
+        };
+        let mut out: Vec<mt::Face> = Vec::new();
+        for (fi, f) in all.iter().enumerate() {
+            if del.contains(&fi) {
+                continue;
+            }
+            if !neighbours.contains(&fi) {
+                // Untouched, unless one of its corners moves.
+                if f.vertex_iter().any(|v| moved.contains_key(&v.id())) {
+                    return Err(fail(format!("face {fi} meets the gap only at a corner; it cannot follow")));
+                }
+                out.push(f.clone());
+                continue;
+            }
+            let pos = |v: &mt::Vertex| moved.get(&v.id()).copied().unwrap_or_else(|| from_p3(v.point()));
+            let gap = |e: &mt::Edge| efaces.get(&e.id()).is_some_and(|fs| fs.iter().any(|x| del.contains(x)));
+            let mut wires: Vec<mt::Wire> = Vec::new();
+            for w in f.boundaries() {
+                let edges: Vec<mt::Edge> = w.edge_iter().cloned().collect();
+                if edges.iter().all(gap) {
+                    continue;
+                }
+                // Start after a gap stretch so stretches don't wrap around.
+                let m = edges.len();
+                let start = (0..m).find(|i| edges.get((i + m - 1) % m).is_some_and(gap) && edges.get(*i).is_some_and(|e| !gap(e))).unwrap_or(0);
+                let mut new_edges: Vec<mt::Edge> = Vec::new();
+                let mut pending: Option<Vec3> = None;
+                for k in 0..m {
+                    let Some(e) = edges.get((start + k) % m) else { continue };
+                    if gap(e) {
+                        pending.get_or_insert(pos(e.front()));
+                        continue;
+                    }
+                    let (a, b) = (pos(e.front()), pos(e.back()));
+                    if let Some(p) = pending.take()
+                        && p.dist(a) > q * 10.0
+                    {
+                        new_edges.push(line(p, a, &mut verts));
+                    }
+                    let moves = moved.contains_key(&e.front().id()) || moved.contains_key(&e.back().id());
+                    if !moves {
+                        new_edges.push(e.clone());
+                    } else if matches!(e.oriented_curve(), mt::Curve::Line(_)) {
+                        if a.dist(b) > q * 10.0 {
+                            new_edges.push(line(a, b, &mut verts));
+                        }
+                    } else {
+                        return Err(fail(format!("face {fi} has a curved edge that would have to stretch")));
+                    }
+                }
+                // A gap stretch at the end closes back to the first edge.
+                if let (Some(p), Some(first)) = (pending, new_edges.first()) {
+                    let a = from_p3(first.front().point());
+                    if p.dist(a) > q * 10.0 {
+                        new_edges.push(line(p, a, &mut verts));
+                    }
+                }
+                if new_edges.is_empty() {
+                    return Err(fail(format!("face {fi} would lose its boundary")));
+                }
+                wires.push(new_edges.into());
+            }
+            let face = builder::try_attach_plane(&wires).map_err(|e| fail(format!("face {fi} cannot close: {e}")))?;
+            // Keep the face's outward side.
+            let (nrm, _) = planes.get(&fi).copied().ok_or_else(|| fail("plane"))?;
+            let face = match face.surface() {
+                mt::Surface::Plane(pl) => {
+                    let pn = pl.normal();
+                    let along = Vec3::new(pn.x, pn.y, pn.z).dot(nrm);
+                    if (along > 0.0) == face.orientation() { face } else { face.inverse() }
+                }
+                _ => face,
+            };
+            out.push(face);
+        }
+        let shell: mt::Shell = out.into();
+        let solid = Solid::try_new(vec![shell]).map_err(|e| fail(format!("the neighbouring faces do not close the gap ({e})")))?;
+        Body::new(solid)
+    })
+}
+
+#[cfg(test)]
+mod tests {
+    use solvecraft_geom::Vec3;
+
+    use super::delete_faces;
+    use crate::{BoolOp, boolean, box_solid, chamfer, cylinder, fillet};
+
+    fn volume(b: &crate::Body) -> f64 {
+        b.tessellate(1e-3).unwrap().measure().volume
+    }
+
+    /// The faces of `b` with every triangle corner passing `keep`.
+    fn faces_where(b: &crate::Body, keep: impl Fn(Vec3) -> bool) -> Vec<usize> {
+        let m = b.tessellate(1e-3).unwrap();
+        let n = m.tri_face.iter().max().map(|x| *x as usize + 1).unwrap_or(0);
+        (0..n)
+            .filter(|f| {
+                m.triangles.iter().zip(&m.tri_face).filter(|(_, x)| **x as usize == *f).all(|(t, _)| m.tri(t).unwrap().iter().all(|p| keep(*p)))
+            })
+            .collect()
+    }
+
+    #[test]
+    fn delete_fillet_chamfer_hole_and_boss_faces() {
+        let sharp = 24000.0;
+        let b = box_solid(Vec3::ZERO, Vec3::new(40.0, 30.0, 20.0)).unwrap();
+        // A fillet on a box edge: deleting it gives the sharp box back, exactly.
+        let f = fillet(&b, &[Vec3::new(20.0, 30.0, 20.0)], 5.0).unwrap();
+        assert!(volume(&f) < sharp - 1.0);
+        let fi = faces_where(&f, |p| p.y > 25.0 - 1e-6 && p.z > 15.0 - 1e-6 && (p.y < 30.0 - 1e-9 || p.z < 20.0 - 1e-9));
+        assert_eq!(fi.len(), 1, "{fi:?}");
+        let back = delete_faces(&f, &fi).unwrap();
+        assert!((volume(&back) - sharp).abs() < 1e-9 * sharp, "{}", volume(&back));
+        assert_eq!(back.face_count(), 6);
+        // A chamfer likewise.
+        let c = chamfer(&b, &[Vec3::new(20.0, 30.0, 20.0)], 4.0).unwrap();
+        let ci = faces_where(&c, |p| p.y > 26.0 - 1e-6 && p.z > 16.0 - 1e-6 && (p.y < 30.0 - 1e-9 || p.z < 20.0 - 1e-9));
+        let back = delete_faces(&c, &ci).unwrap();
+        assert!((volume(&back) - sharp).abs() < 1e-9 * sharp, "{}", volume(&back));
+        // A through hole: deleting its wall fills it.
+        let plate = box_solid(Vec3::ZERO, Vec3::new(40.0, 30.0, 10.0)).unwrap();
+        let pin = cylinder(Vec3::new(20.0, 15.0, -1.0), Vec3::Z, 4.0, 12.0).unwrap();
+        let holed = boolean(&plate, &pin, BoolOp::Cut).unwrap().unwrap();
+        let wall = faces_where(&holed, |p| ((p.x - 20.0).hypot(p.y - 15.0) - 4.0).abs() < 1e-2);
+        assert!(!wall.is_empty());
+        let filled = delete_faces(&holed, &wall).unwrap();
+        assert!((volume(&filled) - 12000.0).abs() < 1e-9 * 12000.0, "{}", volume(&filled));
+        // A blind hole: its wall and floor.
+        let drill = cylinder(Vec3::new(20.0, 15.0, 4.0), Vec3::Z, 3.0, 7.0).unwrap();
+        let blind = boolean(&plate, &drill, BoolOp::Cut).unwrap().unwrap();
+        let hole = faces_where(&blind, |p| (p.x - 20.0).hypot(p.y - 15.0) < 3.0 + 1e-3 && p.z > 4.0 - 1e-6);
+        let filled = delete_faces(&blind, &hole).unwrap();
+        assert!((volume(&filled) - 12000.0).abs() < 1e-9 * 12000.0, "{}", volume(&filled));
+        // A boss on the plate: deleting its wall and top takes it off.
+        let boss = cylinder(Vec3::new(10.0, 10.0, 10.0), Vec3::Z, 3.0, 5.0).unwrap();
+        let bossed = boolean(&plate, &boss, BoolOp::Union).unwrap().unwrap();
+        let bf = faces_where(&bossed, |p| p.z > 10.0 - 1e-9 && (p.x - 10.0).hypot(p.y - 10.0) < 3.0 + 1e-6);
+        let off = delete_faces(&bossed, &bf).unwrap();
+        assert!((volume(&off) - 12000.0).abs() < 1e-9 * 12000.0, "{}", volume(&off));
+        // Errors name what is wrong.
+        assert!(delete_faces(&plate, &[99]).is_err());
+        assert!(delete_faces(&plate, &[0, 1, 2, 3, 4, 5]).is_err());
+        // One face of a box: the sides cannot close it.
+        let top = faces_where(&plate, |p| (p.z - 10.0).abs() < 1e-9);
+        assert!(delete_faces(&plate, &top).is_err());
+    }
+}
diff --git a/crates/kernel/src/lib.rs b/crates/kernel/src/lib.rs
index 9892c2b7..293d418d 100644
--- a/crates/kernel/src/lib.rs
+++ b/crates/kernel/src/lib.rs
@@ -17,6 +17,7 @@ mod body;
 mod build;
 mod coplanar;
 mod curveblend;
+mod delete_face;
 mod freeform;
 mod heal;
 mod helix;
@@ -40,6 +41,7 @@ mod topo;
 pub use blend::{ChamferSide, chamfer, chamfer_sides, fillet};
 pub use body::{Body, EdgeInfo, FaceInfo, FacePaint, Paint};
 pub use build::{PathSeg, box_solid, cylinder, extrude, extrude_tapered, loft, revolve, sphere, sweep, torus};
+pub use delete_face::delete_faces;
 pub use helix::{loft_to_point, sweep_helix};
 pub use iges_in::{MAX_IGES_BYTES, iges_import, iges_to_step};
 pub use iges_out::iges_export_bodies;