diff --git a/src/ifcopenshell-python/ifcopenshell/util/schema.py b/src/ifcopenshell-python/ifcopenshell/util/schema.py
index bdd6d489d0..e755095bdf 100644
--- a/src/ifcopenshell-python/ifcopenshell/util/schema.py
+++ b/src/ifcopenshell-python/ifcopenshell/util/schema.py
@@ -16,6 +16,7 @@
 # You should have received a copy of the GNU Lesser General Public License
 # along with IfcOpenShell.  If not, see <http://www.gnu.org/licenses/>.
 
+import functools
 import json
 import os
 import time
@@ -148,6 +149,57 @@ def get_subtypes(
     return get_classes(declaration)
 
 
+def _enum_value_outside_target(attribute: ifcopenshell_wrapper.attribute, value: Any) -> bool:
+    """``True`` when ``attribute`` is an enumeration and the string ``value``
+    is not in its declared items. Used by the Migrator to silently skip enum
+    values that exist in the source schema but not the target — without
+    parsing C++ wrapper error strings."""
+    if not isinstance(value, str):
+        return False
+    try:
+        enum_items = ifcopenshell.util.attribute.get_enum_items(attribute)
+    except (AssertionError, AttributeError):
+        return False
+    return value not in enum_items
+
+
+@functools.cache
+def geometry_classes_introduced_after(target_schema: IFC_SCHEMA, source_schema: IFC_SCHEMA = "IFC4") -> frozenset[str]:
+    """``IfcRepresentationItem`` subclasses present in ``source_schema`` but
+    missing in ``target_schema``.
+
+    Derived from the loaded schema declarations once per (source, target) pair
+    and cached. The result is the canonical set of geometry classes a
+    downgrade from ``source_schema`` to ``target_schema`` must convert
+    (``IfcPolygonalFaceSet``, ``IfcTriangulatedFaceSet``, ``IfcAdvancedBrep``,
+    B-splines, advanced surfaces, alignment curves on IFC4X3 → 2X3, …) or
+    purge. Defaults match the IFC4 → IFC2X3 case for backwards compatibility
+    with the original caller."""
+    source = ifcopenshell_wrapper.schema_by_name(source_schema)
+    target = ifcopenshell_wrapper.schema_by_name(target_schema)
+    target_names = {decl.name() for decl in target.entities()}
+    result: set[str] = set()
+    for decl in source.entities():
+        if decl.name() in target_names:
+            continue
+        cursor: Any = decl
+        while cursor is not None:
+            if cursor.name() == "IfcRepresentationItem":
+                result.add(decl.name())
+                break
+            cursor = cursor.supertype()
+    return frozenset(result)
+
+
+def ifc4_only_geometry_classes() -> frozenset[str]:
+    """Backwards-compatible alias for the IFC4 → IFC2X3 geometry-gap set.
+
+    New code should call :func:`geometry_classes_introduced_after` with the
+    explicit (target, source) pair so IFC4X3 → IFC2X3 downgrades pick up the
+    additional IFC4X3-only geometry classes."""
+    return geometry_classes_introduced_after("IFC2X3", "IFC4")
+
+
 def reassign_class(
     ifc_file: Union[ifcopenshell.file, None], element: ifcopenshell.entity_instance, new_class: str
 ) -> ifcopenshell.entity_instance:
@@ -263,7 +315,20 @@ class Migrator:
     migrated_ids: dict[int, int]
     attribute_overrides: dict[int, dict[int, str]]
 
-    def __init__(self):
+    def __init__(self, *, fallback_element_to_proxy: bool = False) -> None:
+        """Construct a schema migrator.
+
+        :param fallback_element_to_proxy: When ``True`` and the target schema is
+            IFC2X3, IFC4 entity classes that have no direct IFC2X3 equivalent
+            but inherit from ``IfcElement`` / ``IfcElementType`` are migrated as
+            ``IfcBuildingElementProxy`` / ``IfcBuildingElementProxyType``
+            respectively, instead of raising. Caller code is then responsible
+            for preserving the lost original class information out-of-band (the
+            ``Migrate`` ifcpatch recipe encodes it into ``ObjectType``).
+            Defaults to ``False`` so non-recipe callers keep the strict
+            failure-on-unmappable contract.
+        """
+        self.fallback_element_to_proxy = fallback_element_to_proxy
         self.migrated_ids = {}
         self.attribute_overrides = {}
         self.class_4_to_2x3 = json.load(open(os.path.join(cwd, "class_4_to_2x3.json"), "r"))
@@ -379,6 +444,17 @@ class Migrator:
         self.migrated_ids[element.id()] = new_element.id()
         return new_element
 
+    @staticmethod
+    def _is_subclass_of(ifc_class: str, ancestor: str, source_file: ifcopenshell.file) -> bool:
+        schema = ifcopenshell_wrapper.schema_by_name(source_file.schema_identifier)
+        try:
+            return is_a(schema.declaration_by_name(ifc_class), ancestor)
+        except RuntimeError:
+            # Class doesn't exist in the source schema — happens for cross-schema
+            # introspection of an entity created with a name the wrapper doesn't
+            # recognise. Treat as "not a subclass".
+            return False
+
     def migrate_class(
         self, element: ifcopenshell.entity_instance, new_file: ifcopenshell.file
     ) -> ifcopenshell.entity_instance:
@@ -389,15 +465,44 @@ class Migrator:
             if isinstance(value, float):
                 ifc_class = "IfcQuantityNumber"
         try:
-            new_element = new_file.create_entity(ifc_class)
+            return new_file.create_entity(ifc_class)
         except:
-            # The element does not exist in this schema
-            # Complex migration is not yet supported (e.g. polygonal face set to faceted brep)
-            if new_file.schema == "IFC2X3":
-                new_element = new_file.create_entity(self.class_4_to_2x3[ifc_class])
-            elif new_file.schema == "IFC4":
-                new_element = new_file.create_entity(self.class_2x3_to_4[ifc_class])
-        return new_element
+            pass
+
+        # The class does not exist in the target schema — look up an equivalent.
+        # The lookup tables use empty-string as a sentinel meaning "no direct
+        # equivalent, needs geometric translation" (e.g. polygonal face set →
+        # faceted brep). Callers that want a clean downgrade are expected to
+        # preprocess such carriers before calling the Migrator; see the
+        # `Migrate` ifcpatch recipe.
+        if new_file.schema == "IFC2X3":
+            equivalent = self.class_4_to_2x3.get(ifc_class, None)
+        elif new_file.schema == "IFC4":
+            equivalent = self.class_2x3_to_4.get(ifc_class, None)
+        else:
+            equivalent = None
+
+        # IfcBuildingElementProxy fallback is opt-in (see constructor) — only
+        # the IfcElement / IfcElementType subtrees have a meaningful generic
+        # IFC2X3 stand-in; non-element IFC4-only classes (rels, geometry items,
+        # materials, times) still raise below.
+        if not equivalent and new_file.schema == "IFC2X3" and self.fallback_element_to_proxy:
+            if self._is_subclass_of(ifc_class, "IfcElement", element.wrapped_data.file):
+                equivalent = "IfcBuildingElementProxy"
+            elif self._is_subclass_of(ifc_class, "IfcElementType", element.wrapped_data.file):
+                equivalent = "IfcBuildingElementProxyType"
+
+        if not equivalent:
+            inverses = element.wrapped_data.file.get_inverse(element)
+            inverse_hint = ", ".join(f"#{i.id()}={i.is_a()}" for i in list(inverses)[:3])
+            if len(inverses) > 3:
+                inverse_hint += f", … (+{len(inverses) - 3} more)"
+            raise NotImplementedError(
+                f"Cannot migrate #{element.id()}={ifc_class} to schema "
+                f"{new_file.schema}: no direct equivalent exists. "
+                f"Referenced by: {inverse_hint or '(no inverses)'}."
+            )
+        return new_file.create_entity(equivalent)
 
     def migrate_attributes(
         self,
@@ -526,11 +631,40 @@ class Migrator:
                     new_value.append(self.migrate(item, new_file))
                 value = new_value
         if value is not None:
+            if _enum_value_outside_target(attribute, value):
+                # Enum value present in source schema but missing in target
+                # (typically a downgrade after a cross-class fallback, e.g.
+                # IfcLamp.PredefinedType=COMPACTFLUORESCENT copied onto
+                # IfcBuildingElementProxy.CompositionType whose enum is
+                # IfcElementCompositionEnum). Leave the attribute unset rather
+                # than abort the whole entity's migration. Detected
+                # structurally so other RuntimeError causes (type mismatches,
+                # invalid values) still propagate.
+                return
             setattr(new_element, attribute.name(), value)
 
     def generate_default_value(self, attribute: ifcopenshell_wrapper.attribute, new_file: ifcopenshell.file) -> Any:
         if attribute.name() in self.default_values:
             return self.default_values[attribute.name()]
+        elif attribute.name() == "Position":
+            # IFC4 relaxed Position to OPTIONAL for many profile defs; IFC2X3
+            # still requires it. Synthesize a unit placement at origin so
+            # IfcIShapeProfileDef and friends downgrade without crashing
+            # downstream validators.
+            try:
+                type_name = attribute.type_of_attribute().as_named_type().declared_type().name()
+            except Exception:
+                type_name = None
+            if type_name == "IfcAxis2Placement2D":
+                return new_file.create_entity(
+                    "IfcAxis2Placement2D",
+                    Location=new_file.create_entity("IfcCartesianPoint", (0.0, 0.0)),
+                )
+            if type_name == "IfcAxis2Placement3D":
+                return new_file.create_entity(
+                    "IfcAxis2Placement3D",
+                    Location=new_file.create_entity("IfcCartesianPoint", (0.0, 0.0, 0.0)),
+                )
         elif attribute.name() == "OwnerHistory":
             self.default_entities[attribute.name()] = new_file.create_entity(
                 "IfcOwnerHistory",
diff --git a/src/ifcopenshell-python/ifcopenshell/util/shape_builder.py b/src/ifcopenshell-python/ifcopenshell/util/shape_builder.py
index d9d18f0b5f..eb5bbbdcdb 100644
--- a/src/ifcopenshell-python/ifcopenshell/util/shape_builder.py
+++ b/src/ifcopenshell-python/ifcopenshell/util/shape_builder.py
@@ -21,7 +21,7 @@ from __future__ import annotations
 import collections.abc
 from collections.abc import Sequence
 from itertools import chain
-from math import atan, cos, degrees, pi, radians, sin, sqrt, tan
+from math import atan, atan2, cos, degrees, hypot, isclose, pi, radians, sin, sqrt, tan
 from typing import TYPE_CHECKING, Any, Literal, Optional, Union
 
 import numpy as np
@@ -301,6 +301,130 @@ def intersect_x_axis_2d(p1: VectorType, p2: VectorType, y=0) -> Optional[float]:
     return x1 + t * (x2 - x1)
 
 
+def arc_to_polyline_points(
+    start: VectorType, mid: VectorType, end: VectorType, subdivisions: int = 16
+) -> list[tuple[float, ...]]:
+    """Approximate a circular arc through (start, mid, end) with chord points.
+
+    The arc is determined uniquely by three points — a circle is fit in the
+    XY plane and the angle is walked from start through mid to end, sampling
+    ``subdivisions + 1`` points inclusive of the endpoints. Falls back to a
+    straight chord ``[start, end]`` for collinear / degenerate inputs.
+
+    Only planar arcs in the XY plane are supported. For 3D inputs (length 3
+    tuples), the Z coordinate of each output point is held constant at
+    ``start[2]``. Inputs where start/mid/end have differing Z values raise
+    ``ValueError`` rather than silently project — caller should rotate the
+    arc into the XY plane first if it lives in a non-axis-aligned plane.
+
+    :raises ValueError: if subdivisions < 1, or if 3D inputs have mismatched
+        Z coordinates (non-planar arc).
+    """
+    if subdivisions < 1:
+        raise ValueError(f"subdivisions must be >= 1, got {subdivisions}")
+    if len(start) >= 3:
+        # Tolerance accommodates floating-point noise from kernel transforms
+        # — IFC point coordinates that the author wrote as the same Z value
+        # may diverge by ~1e-15 after placement-matrix round-trips.
+        z_tol = 1e-9
+        if not (isclose(start[2], mid[2], abs_tol=z_tol) and isclose(start[2], end[2], abs_tol=z_tol)):
+            raise ValueError(
+                f"arc_to_polyline_points only handles arcs in the XY plane; "
+                f"got mismatched Z coordinates ({start[2]}, {mid[2]}, {end[2]})."
+            )
+    sx, sy = start[0], start[1]
+    mx, my = mid[0], mid[1]
+    ex, ey = end[0], end[1]
+    d = 2 * (sx * (my - ey) + mx * (ey - sy) + ex * (sy - my))
+    if abs(d) < 1e-12:
+        return [tuple(start), tuple(end)]
+    cx = ((sx**2 + sy**2) * (my - ey) + (mx**2 + my**2) * (ey - sy) + (ex**2 + ey**2) * (sy - my)) / d
+    cy = ((sx**2 + sy**2) * (ex - mx) + (mx**2 + my**2) * (sx - ex) + (ex**2 + ey**2) * (mx - sx)) / d
+    a_start = atan2(sy - cy, sx - cx)
+    a_mid = atan2(my - cy, mx - cx)
+    a_end = atan2(ey - cy, ex - cx)
+    sweep = _signed_sweep_through_mid(a_start, a_mid, a_end)
+    radius = hypot(sx - cx, sy - cy)
+    pts: list[tuple[float, ...]] = []
+    for i in range(subdivisions + 1):
+        t = i / subdivisions
+        angle = a_start + sweep * t
+        x = cx + radius * cos(angle)
+        y = cy + radius * sin(angle)
+        if len(start) == 2:
+            pts.append((x, y))
+        else:
+            pts.append((x, y, start[2]))
+    return pts
+
+
+def _signed_sweep_through_mid(a_start: float, a_mid: float, a_end: float) -> float:
+    """Total angle (radians) from a_start to a_end going through a_mid."""
+    two_pi = 2 * pi
+    ccw_total = (a_end - a_start) % two_pi
+    ccw_to_mid = (a_mid - a_start) % two_pi
+    if ccw_to_mid <= ccw_total:
+        return ccw_total
+    return -((a_start - a_end) % two_pi)
+
+
+def polygonal_face_set_to_faceted_brep(face_set: ifcopenshell.entity_instance) -> ifcopenshell.entity_instance:
+    """Convert an ``IfcPolygonalFaceSet`` or ``IfcTriangulatedFaceSet`` into an
+    ``IfcFacetedBrep`` in the same file, preserving vertex coordinates and face
+    topology (including inner voids on ``IfcIndexedPolygonalFaceWithVoids``).
+
+    The returned brep is the canonical IFC2X3-compatible form of these IFC4
+    tessellated representations. The caller is responsible for rewiring inverse
+    references and removing the source face set when downgrading.
+
+    :raises TypeError: if ``face_set`` is not an ``IfcPolygonalFaceSet`` or
+        ``IfcTriangulatedFaceSet``.
+    :raises ValueError: if ``face_set.Coordinates`` is missing or any face's
+        coordinate index references a vertex outside the coordinate list.
+    """
+    if not (face_set.is_a("IfcPolygonalFaceSet") or face_set.is_a("IfcTriangulatedFaceSet")):
+        raise TypeError(
+            f"polygonal_face_set_to_faceted_brep expected IfcPolygonalFaceSet or "
+            f"IfcTriangulatedFaceSet, got {face_set.is_a()}."
+        )
+    if face_set.Coordinates is None:
+        raise ValueError(f"{face_set.is_a()} #{face_set.id()} has no Coordinates point list.")
+    ifc_file = face_set.file
+    coords = face_set.Coordinates.CoordList
+    vertex_count = len(coords)
+    ifc_points = [ifc_file.createIfcCartesianPoint(tuple(c)) for c in coords]
+
+    def _resolve(indices: Sequence[int]) -> list[ifcopenshell.entity_instance]:
+        # IfcIndexedPolygonalFace.CoordIndex / IfcTriangulatedFaceSet.CoordIndex
+        # are 1-based. Out-of-range hits early with a clear message rather
+        # than the cryptic IndexError from list[i-1].
+        out = []
+        for index in indices:
+            if not 1 <= index <= vertex_count:
+                raise ValueError(
+                    f"{face_set.is_a()} #{face_set.id()} face references vertex {index}, "
+                    f"outside CoordList range 1..{vertex_count}."
+                )
+            out.append(ifc_points[index - 1])
+        return out
+
+    ifc_faces: list[ifcopenshell.entity_instance] = []
+    if face_set.is_a("IfcTriangulatedFaceSet"):
+        for triangle in face_set.CoordIndex:
+            loop = ifc_file.createIfcPolyLoop(_resolve(triangle))
+            ifc_faces.append(ifc_file.createIfcFace([ifc_file.createIfcFaceOuterBound(loop, True)]))
+    else:  # IfcPolygonalFaceSet
+        for indexed_face in face_set.Faces:
+            outer_loop = ifc_file.createIfcPolyLoop(_resolve(indexed_face.CoordIndex))
+            bounds = [ifc_file.createIfcFaceOuterBound(outer_loop, True)]
+            if indexed_face.is_a("IfcIndexedPolygonalFaceWithVoids"):
+                for inner in indexed_face.InnerCoordIndices or ():
+                    bounds.append(ifc_file.createIfcFaceBound(ifc_file.createIfcPolyLoop(_resolve(inner)), True))
+            ifc_faces.append(ifc_file.createIfcFace(bounds))
+
+    return ifc_file.createIfcFacetedBrep(ifc_file.createIfcClosedShell(ifc_faces))
+
+
 # Note: using ShapeBuilder try not to reuse IFC elements in the process
 # otherwise you might run into situation where builder.mirror or other operation
 # is applied twice during one run to the same element
diff --git a/src/ifcopenshell-python/test/util/test_schema.py b/src/ifcopenshell-python/test/util/test_schema.py
index cb45b6e8db..802e426936 100644
--- a/src/ifcopenshell-python/test/util/test_schema.py
+++ b/src/ifcopenshell-python/test/util/test_schema.py
@@ -16,6 +16,9 @@
 # You should have received a copy of the GNU Lesser General Public License
 # along with IfcOpenShell.  If not, see <http://www.gnu.org/licenses/>.
 
+import pytest
+
+import ifcopenshell
 import ifcopenshell.api.project
 import ifcopenshell.util.schema as subject
 import test.bootstrap
@@ -119,6 +122,157 @@ END-ISO-10303-21;
         assert isinstance(qt_float_count_measure_ifc4x3[3], float)
         assert qt_float_count_measure_ifc4x3[3] == 723.0
 
+    def test_migrate_class_raises_clear_error_for_ifc4_only_non_element_class_to_ifc2x3(self):
+        """IFC4-only non-element classes (geometry items, etc.) have no
+        IfcBuildingElementProxy fallback and must surface a clear error naming
+        the failing class — not the cryptic 'Entity name not found in schema'."""
+        ifc4_file = ifcopenshell.api.project.create_file()
+        point_list = ifc4_file.create_entity("IfcCartesianPointList2D", CoordList=((0.0, 0.0), (1.0, 0.0)))
+        ifc2x3_file = ifcopenshell.api.project.create_file(version="IFC2X3")
+
+        migrator = subject.Migrator()
+        with pytest.raises(NotImplementedError) as exc_info:
+            migrator.migrate(point_list, ifc2x3_file)
+
+        message = str(exc_info.value)
+        assert "IfcCartesianPointList2D" in message
+        assert "IFC2X3" in message
+
+    def test_migrate_class_falls_back_to_ifcbuildingelementproxy_when_opt_in(self):
+        """With ``fallback_element_to_proxy=True``, IFC4-only IfcElement
+        subclasses (IfcLamp, IfcPipeSegment, IfcGeographicElement, …) migrate
+        as IfcBuildingElementProxy instead of raising. Default behavior
+        (no opt-in) raises so non-recipe callers keep the strict contract."""
+        ifc4_file = ifcopenshell.api.project.create_file()
+        lamp = ifc4_file.create_entity("IfcLamp", GlobalId="2K6Z3DR8X37AS9XFvX8GcW")
+        ifc2x3_file = ifcopenshell.api.project.create_file(version="IFC2X3")
+
+        # Default migrator raises (strict contract preserved).
+        with pytest.raises(NotImplementedError, match="IfcLamp"):
+            subject.Migrator().migrate(lamp, ifc2x3_file)
+
+        # Opt-in migrator substitutes IfcBuildingElementProxy.
+        ifc2x3_file = ifcopenshell.api.project.create_file(version="IFC2X3")
+        new_lamp = subject.Migrator(fallback_element_to_proxy=True).migrate(lamp, ifc2x3_file)
+        assert new_lamp.is_a("IfcBuildingElementProxy")
+
+
+class TestGetFallbackSchema:
+    """Pins the schema-identifier normalisation contract relied on by callers
+    that need to map upstream variants (IFC4X3_ADD2, IFC2X3_TC1, IFC4_ADD2, …)
+    to a base schema name for compatibility tables / downgrade detection."""
+
+    def test_ifc4x3_variants_collapse_to_ifc4x3(self):
+        # Longest-prefix-first: IFC4X3_ADD2 must NOT be misclassified as IFC4
+        # — the function checks IFC4X3 before IFC4.
+        assert subject.get_fallback_schema("IFC4X3") == "IFC4X3"
+        assert subject.get_fallback_schema("IFC4X3_ADD1") == "IFC4X3"
+        assert subject.get_fallback_schema("IFC4X3_ADD2") == "IFC4X3"
+        assert subject.get_fallback_schema("IFC4X3_RC1") == "IFC4X3"
+
+    def test_ifc4_variants_collapse_to_ifc4(self):
+        assert subject.get_fallback_schema("IFC4") == "IFC4"
+        assert subject.get_fallback_schema("IFC4_ADD1") == "IFC4"
+        assert subject.get_fallback_schema("IFC4_ADD2") == "IFC4"
+        # IFC4X1 / IFC4X2 are draft schemas — collapse to IFC4 by design.
+        assert subject.get_fallback_schema("IFC4X1") == "IFC4"
+        assert subject.get_fallback_schema("IFC4X2") == "IFC4"
+
+    def test_ifc2x3_variants_collapse_to_ifc2x3(self):
+        assert subject.get_fallback_schema("IFC2X3") == "IFC2X3"
+        assert subject.get_fallback_schema("IFC2X3_TC1") == "IFC2X3"
+        assert subject.get_fallback_schema("IFC2X3_FINAL") == "IFC2X3"
+
+    def test_unknown_version_asserts(self):
+        # Asserts under non-optimised Python; in -O mode would return the
+        # unmodified input. Caller should guard accordingly.
+        with pytest.raises(AssertionError):
+            subject.get_fallback_schema("IFC10")
+
+
+class TestIfc4OnlyGeometryClasses:
+    def test_known_ifc4_only_classes_present(self):
+        result = subject.ifc4_only_geometry_classes()
+        # Classes that genuinely don't exist in IFC2X3 and inherit
+        # IfcRepresentationItem in IFC4.
+        for name in (
+            "IfcPolygonalFaceSet",
+            "IfcTriangulatedFaceSet",
+            "IfcIndexedPolyCurve",
+            "IfcCartesianPointList3D",
+            "IfcAdvancedBrep",
+        ):
+            assert name in result, f"{name} should be classified as IFC4-only geometry"
+
+    def test_ifc2x3_compatible_classes_absent(self):
+        result = subject.ifc4_only_geometry_classes()
+        # Classes that exist in both schemas — must NOT be flagged.
+        for name in ("IfcPolyline", "IfcFacetedBrep", "IfcCartesianPoint", "IfcExtrudedAreaSolid"):
+            assert name not in result, f"{name} exists in IFC2X3, should not be IFC4-only"
+
+    def test_non_geometry_ifc4_only_classes_absent(self):
+        result = subject.ifc4_only_geometry_classes()
+        # IFC4-only but not IfcRepresentationItem subclasses — out of scope.
+        for name in ("IfcEvent", "IfcWorkCalendar", "IfcLamp"):
+            assert name not in result, f"{name} is not an IfcRepresentationItem subclass"
+
+    def test_result_is_cached_frozenset(self):
+        first = subject.ifc4_only_geometry_classes()
+        second = subject.ifc4_only_geometry_classes()
+        assert first is second  # @functools.cache returns the same object
+
+
+class TestGeometryClassesIntroducedAfter:
+    """Generalised version of ``ifc4_only_geometry_classes`` — pins the
+    schema-aware contract that supports IFC4X3 → IFC2X3 downgrades, not just
+    IFC4 → IFC2X3."""
+
+    def test_ifc4_to_ifc2x3_matches_legacy_helper(self):
+        # The legacy ``ifc4_only_geometry_classes`` is now a thin alias.
+        assert subject.geometry_classes_introduced_after("IFC2X3", "IFC4") == subject.ifc4_only_geometry_classes()
+
+    def test_ifc4x3_to_ifc2x3_is_superset_of_ifc4_to_ifc2x3(self):
+        # IFC4X3 is a superset of IFC4 — every IFC4-only geometry class is
+        # also missing from IFC2X3 when the source is IFC4X3, plus any new
+        # IFC4X3-only geometry (alignment curves, distance expressions, …).
+        ifc4_gap = subject.geometry_classes_introduced_after("IFC2X3", "IFC4")
+        ifc4x3_gap = subject.geometry_classes_introduced_after("IFC2X3", "IFC4X3")
+        assert ifc4_gap <= ifc4x3_gap
+
+    def test_ifc4_to_ifc4x3_is_empty(self):
+        # IFC4X3 contains every IFC4 IfcRepresentationItem subclass — no
+        # IFC4 class is missing from IFC4X3.
+        assert subject.geometry_classes_introduced_after("IFC4X3", "IFC4") == frozenset()
+
+
+class TestEnumValueOutsideTarget:
+    @staticmethod
+    def _attr(class_name: str, attr_name: str):
+        schema = ifcopenshell.ifcopenshell_wrapper.schema_by_name("IFC2X3")
+        decl = schema.declaration_by_name(class_name)
+        return next(a for a in decl.all_attributes() if a.name() == attr_name)
+
+    def test_enum_value_present_in_target_returns_false(self):
+        # IfcCovering.PredefinedType is IfcCoveringTypeEnum — CEILING is valid.
+        attr = self._attr("IfcCovering", "PredefinedType")
+        assert subject._enum_value_outside_target(attr, "CEILING") is False
+
+    def test_enum_value_missing_in_target_returns_true(self):
+        # IfcCoveringTypeEnum has no COMPACTFLUORESCENT (an IfcLampTypeEnum value).
+        attr = self._attr("IfcCovering", "PredefinedType")
+        assert subject._enum_value_outside_target(attr, "COMPACTFLUORESCENT") is True
+
+    def test_non_enum_attribute_returns_false(self):
+        # IfcCovering.Name is IfcLabel — not an enum, so the helper must return False.
+        attr = self._attr("IfcCovering", "Name")
+        assert subject._enum_value_outside_target(attr, "anything") is False
+
+    def test_non_string_value_returns_false(self):
+        attr = self._attr("IfcCovering", "PredefinedType")
+        assert subject._enum_value_outside_target(attr, 42) is False
+
+
+class TestExtendedMaterialProperties(test.bootstrap.IFC4):
     def test_migrate_extended_material_properties_ifc2x3_ifc4(self):
         ifc2x3_file = ifcopenshell.api.project.create_file(version="IFC2X3")
         material = ifc2x3_file.createIfcMaterial(Name="Material")
diff --git a/src/ifcopenshell-python/test/util/test_shape_builder.py b/src/ifcopenshell-python/test/util/test_shape_builder.py
index 6a01a74201..d024ffc13a 100644
--- a/src/ifcopenshell-python/test/util/test_shape_builder.py
+++ b/src/ifcopenshell-python/test/util/test_shape_builder.py
@@ -16,7 +16,7 @@
 # You should have received a copy of the GNU Lesser General Public License
 # along with IfcOpenShell.  If not, see <http://www.gnu.org/licenses/>.
 
-from math import degrees, radians
+from math import degrees, radians, sqrt
 from typing import Any, Union
 
 import numpy as np
@@ -28,6 +28,7 @@ import test.bootstrap
 from ifcopenshell.util.shape_builder import (
     ShapeBuilder,
     V,
+    arc_to_polyline_points,
     is_x,
     np_angle,
     np_angle_signed,
@@ -36,9 +37,116 @@ from ifcopenshell.util.shape_builder import (
     np_normal,
     np_rotation_matrix,
     np_to_3d,
+    polygonal_face_set_to_faceted_brep,
 )
 
 
+class TestArcToPolylinePoints:
+    def test_quarter_arc_2d_samples_n_plus_one_points(self):
+        # Quarter arc from (1,0) through (cos45°, sin45°) to (0,1) — unit circle.
+        sqrt_half = sqrt(0.5)
+        points = arc_to_polyline_points((1.0, 0.0), (sqrt_half, sqrt_half), (0.0, 1.0), 8)
+        assert len(points) == 9
+        assert points[0] == pytest.approx((1.0, 0.0), abs=1e-9)
+        assert points[-1] == pytest.approx((0.0, 1.0), abs=1e-9)
+        for x, y in points:
+            assert x * x + y * y == pytest.approx(1.0, abs=1e-9)
+
+    def test_collinear_inputs_fall_back_to_straight_chord(self):
+        points = arc_to_polyline_points((0.0, 0.0), (1.0, 0.0), (2.0, 0.0), 16)
+        assert points == [(0.0, 0.0), (2.0, 0.0)]
+
+    def test_3d_inputs_with_constant_z_preserved(self):
+        points = arc_to_polyline_points((1.0, 0.0, 5.0), (0.7071, 0.7071, 5.0), (0.0, 1.0, 5.0), 4)
+        assert len(points) == 5
+        assert all(p[2] == 5.0 for p in points)
+
+    def test_3d_inputs_with_mismatched_z_raises(self):
+        with pytest.raises(ValueError, match="XY plane"):
+            arc_to_polyline_points((1.0, 0.0, 0.0), (0.0, 1.0, 1.0), (-1.0, 0.0, 0.0))
+
+    def test_3d_inputs_with_near_equal_z_pass_within_tolerance(self):
+        # Real IFC files often have float noise of ~1e-15 in Z values that the
+        # author meant to be identical — kernel transforms introduce it. The
+        # planar check tolerates this rather than rejecting valid input.
+        sqrt_half = sqrt(0.5)
+        points = arc_to_polyline_points(
+            (1.0, 0.0, 5.0), (sqrt_half, sqrt_half, 5.0 + 1e-15), (0.0, 1.0, 5.0 - 2e-16), 4
+        )
+        assert len(points) == 5
+
+    def test_subdivisions_zero_raises(self):
+        with pytest.raises(ValueError, match="subdivisions"):
+            arc_to_polyline_points((1.0, 0.0), (0.0, 1.0), (-1.0, 0.0), 0)
+
+
+class TestPolygonalFaceSetToFacetedBrep(test.bootstrap.IFC4):
+    def test_triangulated_face_set_preserves_coordinates(self):
+        coords = self.file.create_entity(
+            "IfcCartesianPointList3D",
+            CoordList=((0.0, 0.0, 0.0), (1.0, 0.0, 0.0), (0.0, 1.0, 0.0), (0.5, 0.5, 1.0)),
+        )
+        face_set = self.file.create_entity(
+            "IfcTriangulatedFaceSet", Coordinates=coords, CoordIndex=[(1, 2, 4), (2, 3, 4), (3, 1, 4), (1, 3, 2)]
+        )
+
+        brep = polygonal_face_set_to_faceted_brep(face_set)
+
+        assert brep.is_a("IfcFacetedBrep")
+        assert len(brep.Outer.CfsFaces) == 4
+        # Every CoordList vertex appears in the brep at the same coordinate.
+        brep_points = {tuple(p.Coordinates) for f in brep.Outer.CfsFaces for p in f.Bounds[0].Bound.Polygon}
+        assert (0.0, 0.0, 0.0) in brep_points
+        assert (1.0, 0.0, 0.0) in brep_points
+        assert (0.0, 1.0, 0.0) in brep_points
+        assert (0.5, 0.5, 1.0) in brep_points
+
+    def test_polygonal_face_set_with_voids_preserves_inner_bounds(self):
+        # Quad with a triangular hole through it.
+        coords = self.file.create_entity(
+            "IfcCartesianPointList3D",
+            CoordList=(
+                (0.0, 0.0, 0.0),
+                (4.0, 0.0, 0.0),
+                (4.0, 4.0, 0.0),
+                (0.0, 4.0, 0.0),
+                (1.0, 1.0, 0.0),
+                (3.0, 1.0, 0.0),
+                (2.0, 3.0, 0.0),
+            ),
+        )
+        face = self.file.create_entity(
+            "IfcIndexedPolygonalFaceWithVoids",
+            CoordIndex=(1, 2, 3, 4),
+            InnerCoordIndices=[(5, 6, 7)],
+        )
+        face_set = self.file.create_entity("IfcPolygonalFaceSet", Coordinates=coords, Faces=[face])
+
+        brep = polygonal_face_set_to_faceted_brep(face_set)
+
+        assert len(brep.Outer.CfsFaces) == 1
+        bounds = brep.Outer.CfsFaces[0].Bounds
+        # Outer + 1 inner bound.
+        assert len(bounds) == 2
+        outer = next(b for b in bounds if b.is_a("IfcFaceOuterBound"))
+        inner = next(b for b in bounds if not b.is_a("IfcFaceOuterBound"))
+        assert len(outer.Bound.Polygon) == 4
+        assert len(inner.Bound.Polygon) == 3
+
+    def test_wrong_class_raises_typeerror(self):
+        # An IfcCartesianPointList3D is not a face set.
+        not_a_face_set = self.file.create_entity("IfcCartesianPointList3D", CoordList=((0.0, 0.0, 0.0),))
+        with pytest.raises(TypeError, match="IfcPolygonalFaceSet"):
+            polygonal_face_set_to_faceted_brep(not_a_face_set)
+
+    def test_out_of_range_index_raises_valueerror(self):
+        coords = self.file.create_entity("IfcCartesianPointList3D", CoordList=((0.0, 0.0, 0.0),))
+        # CoordIndex 5 doesn't exist in a 1-vertex coord list.
+        face_set = self.file.create_entity("IfcTriangulatedFaceSet", Coordinates=coords, CoordIndex=[(1, 1, 5)])
+        with pytest.raises(ValueError, match="outside CoordList range"):
+            polygonal_face_set_to_faceted_brep(face_set)
+
+
 class TestMathutilsCompatibleMethods(test.bootstrap.IFC4):
     def test_np_rotation_matrix(self):
         from mathutils import Matrix, Vector  # pyright: ignore[reportMissingImports]  # ty:ignore[unresolved-import]