diff --git a/docs/coverage.md b/docs/coverage.md
index aff1465..84527eb 100644
--- a/docs/coverage.md
+++ b/docs/coverage.md
@@ -42,7 +42,7 @@ the page cannot quietly disagree with the gate.
 | Model | Elements | Extrude | Brep | OBB | Empty | OBB rate | Collapsed | AABB ratio p50 | p90 | max |
 |---|---|---|---|---|---|---|---|---|---|---|
 | `ifcopenhouse` | 40 | 34 | 0 | 0 | 6 | 0.0% | 0 | 1.0000 | 1.0000 | 1.0000 |
-| `duplex_a` | 218 | 146 | 0 | 69 | 3 | 32.1% | 0 | 1.0000 | 1.0000 | 1.1156 |
+| `duplex_a` | 218 | 146 | 65 | 4 | 3 | 1.9% | 0 | 1.0000 | 1.0000 | 1.1156 |
 | `fzk_haus` | 85 | 16 | 64 | 2 | 3 | 2.4% | 0 | 1.0000 | 1.0000 | 1.0334 |
 
 ## What falls back, and how often
@@ -86,7 +86,6 @@ at least one unhandled item type below.
 
 | Item type | Occurrences |
 |---|---|
-| `IFCFACEBASEDSURFACEMODEL` | 65 |
 | `IFCPOLYGONALBOUNDEDHALFSPACE` | 11 |
 
 ## Known Gate 1 violations
diff --git a/geometry/brep.go b/geometry/brep.go
index 78b83c4..d56675a 100644
--- a/geometry/brep.go
+++ b/geometry/brep.go
@@ -10,15 +10,23 @@ const (
 	attrBoundOrientation = 1 // IfcFaceBound.Orientation
 	attrLoopPolygon      = 0 // IfcPolyLoop.Polygon
 	attrSbsmBoundary     = 0 // IfcShellBasedSurfaceModel.SbsmBoundary
+	attrFbsmFaces        = 0 // IfcFaceBasedSurfaceModel.FbsmFaces
 )
 
-// shellBasedSurfaceModelMesh unions the faces of every shell (IfcClosedShell
-// or IfcOpenShell) in an IfcShellBasedSurfaceModel's SbsmBoundary set, raw
-// units. Used by multi-shell family instances (e.g. a door's frame/leaf/
-// hardware, each its own shell) that mix this representation type with plain
-// IfcFacetedBrep siblings.
-func shellBasedSurfaceModelMesh(sbsm *step.Instance) (verts []float32, tris []uint32, ok bool) {
-	boundaryV, has := sbsm.Get(attrSbsmBoundary)
+// surfaceModelMesh unions the faces of every shell or face set in a surface
+// model's boundary attribute, raw units.
+//
+// Shared by IfcShellBasedSurfaceModel (SbsmBoundary, a SET of IfcShell) and
+// IfcFaceBasedSurfaceModel (FbsmFaces, a SET of IfcConnectedFaceSet). Two
+// different schema entities with the same shape: a set of things brepMesh
+// already tessellates. attr is a parameter rather than assumed, because the
+// two constants agreeing at 0 is a fact about the schema, not a rule.
+//
+// Used by multi-shell family instances (a door's frame/leaf/hardware, each its
+// own shell) that mix these representation types with plain IfcFacetedBrep
+// siblings in the same element.
+func surfaceModelMesh(m *step.Instance, attr int) (verts []float32, tris []uint32, ok bool) {
+	boundaryV, has := m.Get(attr)
 	if !has || boundaryV.Kind != step.KindList {
 		return nil, nil, false
 	}
diff --git a/geometry/brep_test.go b/geometry/brep_test.go
index f135f87..dd457f9 100644
--- a/geometry/brep_test.go
+++ b/geometry/brep_test.go
@@ -1,6 +1,7 @@
 package geometry
 
 import (
+	"strings"
 	"testing"
 
 	"github.com/blox-eng/goifc/model"
@@ -33,3 +34,71 @@ func TestBrep_FacetedFaces(t *testing.T) {
 		t.Errorf("brep world min = %v, want {10 20 5}", e.BBoxMin)
 	}
 }
+
+// IfcFaceBasedSurfaceModel had no dispatch case at all, so every element built
+// from one degraded to a bounding box. It is the top entry of the measured gap
+// list (65 occurrences), and in duplex_a it hides 235 IfcConnectedFaceSets no
+// other path can reach.
+func TestFaceBasedSurfaceModel_Tessellates(t *testing.T) {
+	f, err := step.ParseFile("testdata/synthetic/face_based_surface_model.ifc")
+	if err != nil {
+		t.Fatal(err)
+	}
+	r, err := model.Extract(f)
+	if err != nil {
+		t.Fatal(err)
+	}
+	s, err := Build(f, r)
+	if err != nil {
+		t.Fatal(err)
+	}
+	e := s.Elements[0]
+	if e.Source != SourceBrep {
+		t.Fatalf("source = %q, want brep — the element fell back to a box", e.Source)
+	}
+	// Two quad faces -> 2 triangles each -> 12 indices, same as known_box.ifc.
+	if len(e.Tris) != 12 {
+		t.Errorf("tris = %d indices, want 12", len(e.Tris))
+	}
+	if !closeVec(e.BBoxMin, [3]float64{10, 20, 5}, 1e-6) {
+		t.Errorf("world min = %v, want {10 20 5}", e.BBoxMin)
+	}
+}
+
+// An empty or unusable FbsmFaces set must decline so the element falls back to
+// its OBB box. Returning an empty mesh that still claims SourceBrep would
+// produce a zero-volume element — the "Collapsed" case the coverage page
+// exists to surface, reported as a success.
+//
+// Note what the second case does and does not pin. surfaceModelMesh and
+// brepMesh do not type-check set members: brepMesh reads attribute 0 of
+// whatever it is handed. An IfcCartesianPoint's attribute 0 is Coordinates,
+// which IS a list, so it gets that far — and declines only because the list
+// holds reals rather than entity references. So this pins "attribute 0 is not
+// a list of face refs", not "the member is rejected for having the wrong
+// type". A wrong-typed member whose attribute 0 happened to be a list of
+// references would still be walked as a shell.
+func TestFaceBasedSurfaceModel_EmptyDeclines(t *testing.T) {
+	for _, tc := range []struct{ name, faces string }{
+		{"empty set", "()"},
+		{"member whose attribute 0 is not a list of face refs", "(#22)"}, // an IfcCartesianPoint
+	} {
+		t.Run(tc.name, func(t *testing.T) {
+			f, err := step.Parse(strings.NewReader(
+				"ISO-10303-21;\nHEADER;\nFILE_SCHEMA(('IFC4'));\nENDSEC;\nDATA;\n" +
+					"#22=IFCCARTESIANPOINT((0.,0.,0.));\n" +
+					"#61=IFCFACEBASEDSURFACEMODEL(" + tc.faces + ");\n" +
+					"ENDSEC;\nEND-ISO-10303-21;\n"))
+			if err != nil {
+				t.Fatal(err)
+			}
+			item, ok := f.ByID(61)
+			if !ok {
+				t.Fatal("fixture instance #61 missing")
+			}
+			if _, _, gotOK := surfaceModelMesh(item, attrFbsmFaces); gotOK {
+				t.Error("surfaceModelMesh accepted an unusable FbsmFaces set; want ok=false so the caller boxes the element")
+			}
+		})
+	}
+}
diff --git a/geometry/geometry.go b/geometry/geometry.go
index a0a83b5..ba0138b 100644
--- a/geometry/geometry.go
+++ b/geometry/geometry.go
@@ -120,7 +120,15 @@ func tessellateItemDepth(item *step.Instance, unitScale float64, depth int) ([]f
 		// overall reported Source stayed "brep" (since brep still won on the other
 		// sibling items) — a few stray boxed sub-shells shift the whole element's
 		// AABB by a few mm-cm without ever showing up as a Source mismatch.
-		if v, t, ok := shellBasedSurfaceModelMesh(item); ok {
+		if v, t, ok := surfaceModelMesh(item, attrSbsmBoundary); ok {
+			return scaleVerts(v, unitScale), t, SourceBrep
+		}
+	case item.IsA("IfcFaceBasedSurfaceModel"):
+		// FbsmFaces is a SET of IfcConnectedFaceSet — union their faces, the
+		// same traversal the shell-based case above does over IfcShell.
+		// Without this case duplex_a's 235 nested face sets are unreachable,
+		// and every element built from one becomes a box.
+		if v, t, ok := surfaceModelMesh(item, attrFbsmFaces); ok {
 			return scaleVerts(v, unitScale), t, SourceBrep
 		}
 	case item.IsA("IfcBooleanClippingResult"), item.IsA("IfcBooleanResult"):
diff --git a/geometry/testdata/synthetic/face_based_surface_model.ifc b/geometry/testdata/synthetic/face_based_surface_model.ifc
new file mode 100644
index 0000000..ad866cb
--- /dev/null
+++ b/geometry/testdata/synthetic/face_based_surface_model.ifc
@@ -0,0 +1,43 @@
+ISO-10303-21;
+HEADER;
+FILE_DESCRIPTION((''),'2;1');
+FILE_NAME('face_based_surface_model.ifc','',(''),(''),'','','');
+FILE_SCHEMA(('IFC4'));
+ENDSEC;
+DATA;
+/* The same two faces as known_box.ifc, reached through an
+   IfcFaceBasedSurfaceModel -> IfcConnectedFaceSet pair instead of an
+   IfcFacetedBrep -> IfcClosedShell pair. duplex_a.ifc nests 235
+   IfcConnectedFaceSets behind 40 of these, and before the dispatch case
+   existed every one of them was unreachable: the element fell back to its
+   OBB box. */
+#1=IFCPROJECT('0proj',$,'P',$,$,$,$,(#20),#10);
+#10=IFCUNITASSIGNMENT((#11));
+#11=IFCSIUNIT(*,.LENGTHUNIT.,$,.METRE.);
+#20=IFCGEOMETRICREPRESENTATIONCONTEXT($,'Model',3,1.E-05,#21,$);
+#21=IFCAXIS2PLACEMENT3D(#22,$,$);
+#22=IFCCARTESIANPOINT((0.,0.,0.));
+#30=IFCCARTESIANPOINT((10.,20.,5.));
+#31=IFCAXIS2PLACEMENT3D(#30,$,$);
+#32=IFCLOCALPLACEMENT($,#31);
+#40=IFCCARTESIANPOINT((0.,0.,0.));
+#41=IFCCARTESIANPOINT((1.,0.,0.));
+#42=IFCCARTESIANPOINT((1.,1.,0.));
+#43=IFCCARTESIANPOINT((0.,1.,0.));
+#44=IFCCARTESIANPOINT((0.,0.,1.));
+#45=IFCCARTESIANPOINT((1.,0.,1.));
+#46=IFCCARTESIANPOINT((1.,1.,1.));
+#47=IFCCARTESIANPOINT((0.,1.,1.));
+#50=IFCPOLYLOOP((#40,#41,#42,#43));
+#51=IFCFACEOUTERBOUND(#50,.T.);
+#52=IFCFACE((#51));
+#53=IFCPOLYLOOP((#44,#45,#46,#47));
+#54=IFCFACEOUTERBOUND(#53,.T.);
+#55=IFCFACE((#54));
+#60=IFCCONNECTEDFACESET((#52,#55));
+#61=IFCFACEBASEDSURFACEMODEL((#60));
+#62=IFCSHAPEREPRESENTATION(#20,'Body','SurfaceModel',(#61));
+#63=IFCPRODUCTDEFINITIONSHAPE($,$,(#62));
+#70=IFCBUILDINGELEMENTPROXY('0fbsm',$,'FaceSetBox',$,$,#32,#63,$);
+ENDSEC;
+END-ISO-10303-21;
diff --git a/geometry/unhandled.go b/geometry/unhandled.go
index f3dd2c8..4bf0795 100644
--- a/geometry/unhandled.go
+++ b/geometry/unhandled.go
@@ -18,6 +18,7 @@ var handledItemTypes = []string{
 	"IfcConnectedFaceSet",
 	"IfcOpenShell",
 	"IfcShellBasedSurfaceModel",
+	"IfcFaceBasedSurfaceModel",
 	"IfcBooleanClippingResult",
 	"IfcBooleanResult",
 }
diff --git a/parity/testdata/baseline.json b/parity/testdata/baseline.json
index 85e76e1..d26fe75 100644
--- a/parity/testdata/baseline.json
+++ b/parity/testdata/baseline.json
@@ -2,8 +2,8 @@
   "duplex_a": {
     "total": 218,
     "extrude": 146,
-    "brep": 0,
-    "obb": 69,
+    "brep": 65,
+    "obb": 4,
     "empty": 3
   },
   "fzk_haus": {