diff --git a/src/ifcgeom/mapping/IfcAsymmetricIShapeProfileDef.cpp b/src/ifcgeom/mapping/IfcAsymmetricIShapeProfileDef.cpp
new file mode 100644
index 0000000000..dce783f978
--- /dev/null
+++ b/src/ifcgeom/mapping/IfcAsymmetricIShapeProfileDef.cpp
@@ -0,0 +1,92 @@
+/********************************************************************************
+ *                                                                              *
+ * This file is part of IfcOpenShell.                                           *
+ *                                                                              *
+ * IfcOpenShell is free software: you can redistribute it and/or modify         *
+ * it under the terms of the Lesser GNU General Public License as published by  *
+ * the Free Software Foundation, either version 3.0 of the License, or          *
+ * (at your option) any later version.                                          *
+ *                                                                              *
+ * IfcOpenShell is distributed in the hope that it will be useful,              *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of               *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the                 *
+ * Lesser GNU General Public License for more details.                          *
+ *                                                                              *
+ * You should have received a copy of the Lesser GNU General Public License     *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>.         *
+ *                                                                              *
+ ********************************************************************************/
+
+#include "mapping.h"
+#define mapping POSTFIX_SCHEMA(mapping)
+using namespace ifcopenshell::geometry;
+
+#include "../profile_helper.h"
+
+// In IFC2X3 IfcAsymmetricIShapeProfileDef is a subtype of IfcIShapeProfileDef and is
+// therefore dispatched (and handled) by the IfcIShapeProfileDef mapping. From IFC4
+// onwards it is a standalone subtype of IfcParameterizedProfileDef with its own
+// Bottom*/Top* attributes, so nothing mapped it and the extrusion came out empty.
+// The presence of the standalone BottomFlangeWidth attribute is the discriminator:
+// it is only defined in the schemas where the type is standalone (IFC4 / IFC4X3).
+#ifdef SCHEMA_IfcAsymmetricIShapeProfileDef_HAS_BottomFlangeWidth
+
+taxonomy::ptr mapping::map_impl(const IfcSchema::IfcAsymmetricIShapeProfileDef* inst) {
+	// Bottom flange (half width), overall depth (half), web (half thickness).
+	const double xb = inst->BottomFlangeWidth() / 2.0 * length_unit_;
+	const double xt = inst->TopFlangeWidth() / 2.0 * length_unit_;
+	const double y = inst->OverallDepth() / 2.0 * length_unit_;
+	const double d1 = inst->WebThickness() / 2.0 * length_unit_;
+
+	// Bottom flange thickness; top flange thickness defaults to the bottom one.
+	const double ftb = inst->BottomFlangeThickness() * length_unit_;
+	const double ftt = inst->TopFlangeThickness().get_value_or(inst->BottomFlangeThickness()) * length_unit_;
+
+	// Optional fillet radii (web/flange transition) and flange edge radii.
+	const double fb = inst->BottomFlangeFilletRadius().get_value_or(0.) * length_unit_;
+	const double ft_top = inst->TopFlangeFilletRadius().get_value_or(0.) * length_unit_;
+	const double feb = inst->BottomFlangeEdgeRadius().get_value_or(0.) * length_unit_;
+	const double fet = inst->TopFlangeEdgeRadius().get_value_or(0.) * length_unit_;
+
+	// Optional flange slopes: the inner edge of the flange rises towards the web.
+	const double bottomSlope = inst->BottomFlangeSlope().get_value_or(0.) * angle_unit_;
+	const double topSlope = inst->TopFlangeSlope().get_value_or(0.) * angle_unit_;
+	const double dyb = (xb - d1) * tan(bottomSlope);
+	const double dyt = (xt - d1) * tan(topSlope);
+
+	const double tol = settings_.get<settings::Precision>().get();
+
+	if (xb < tol || xt < tol || y < tol || d1 < tol || ftb < tol || ftt < tol) {
+		logger_.Message(Logger::LOG_NOTICE, "GEO", 264, "Skipping zero sized profile:", inst);
+		return nullptr;
+	}
+
+	taxonomy::matrix4::ptr m4;
+	bool has_position = true;
+#ifdef SCHEMA_IfcParameterizedProfileDef_Position_IS_OPTIONAL
+	has_position = !!inst->Position();
+#endif
+	if (has_position) {
+		m4 = taxonomy::cast<taxonomy::matrix4>(map(inst->Position()));
+	}
+
+	// Twelve corner points, running counter-clockwise from the bottom-left, with the
+	// bottom flange (xb) possibly wider than the top flange (xt). Fillet/edge radii are
+	// attached to the corner they round, matching the symmetric IfcIShapeProfileDef.
+	return profile_helper(m4, {
+		{{-xb,-y}},
+		{{xb,-y}},
+		{{xb,-y + ftb}, {feb}},
+		{{d1,-y + ftb + dyb},{fb} },
+		{{d1,y - ftt - dyt},{ft_top} },
+		{{xt,y - ftt}, {fet}},
+		{{xt,y}},
+		{{-xt,y}},
+		{{-xt,y - ftt}, {fet}},
+		{{-d1,y - ftt - dyt},{ft_top} },
+		{{-d1,-y + ftb + dyb},{fb} },
+		{{-xb,-y + ftb}, {feb}}
+	});
+}
+
+#endif
diff --git a/src/ifcgeom/mapping/mapping.i b/src/ifcgeom/mapping/mapping.i
index c67d0f7f4a..8766238dc3 100644
--- a/src/ifcgeom/mapping/mapping.i
+++ b/src/ifcgeom/mapping/mapping.i
@@ -89,7 +89,11 @@ BIND(IfcRectangleHollowProfileDef);
 BIND(IfcRectangleProfileDef);
 BIND(IfcTrapeziumProfileDef);
 BIND(IfcCShapeProfileDef);
-// IfcAsymmetricIShapeProfileDef included
+// In IFC2X3 IfcAsymmetricIShapeProfileDef is a subtype of IfcIShapeProfileDef and is
+// mapped by it; from IFC4 onwards it is a standalone type and needs its own binding.
+#ifdef SCHEMA_IfcAsymmetricIShapeProfileDef_HAS_BottomFlangeWidth
+BIND(IfcAsymmetricIShapeProfileDef);
+#endif
 BIND(IfcIShapeProfileDef);
 BIND(IfcLShapeProfileDef);
 BIND(IfcTShapeProfileDef);