diff --git a/src/CGALRenderer.cc b/src/CGALRenderer.cc
index c9b816c5..a3505856 100644
--- a/src/CGALRenderer.cc
+++ b/src/CGALRenderer.cc
@@ -32,6 +32,7 @@
 // dxfdata.h must come first for Eigen SIMD alignment issues
 #include "dxfdata.h"
 #include "polyset.h"
+#include "polyset-utils.h"
 #include "printutils.h"
 
 #include "CGALRenderer.h"
@@ -44,7 +45,13 @@
 CGALRenderer::CGALRenderer(shared_ptr<const class Geometry> geom)
 {
 	if (shared_ptr<const PolySet> ps = dynamic_pointer_cast<const PolySet>(geom)) {
-		this->polyset = ps;
+		assert(ps->getDimension() == 3);
+		// We need to tessellate here, in case the generated PolySet contains concave polygons
+    // See testdata/scad/3D/features/polyhedron-concave-test.scad
+		PolySet *ps_tri = new PolySet(3, ps->convexValue());
+		ps_tri->setConvexity(ps->getConvexity());
+		PolysetUtils::tessellate_faces(*ps, *ps_tri);
+		this->polyset.reset(ps_tri);
 	}
 	else if (shared_ptr<const Polygon2d> poly = dynamic_pointer_cast<const Polygon2d>(geom)) {
 		this->polyset.reset(poly->tessellate());
diff --git a/src/CSGTermEvaluator.cc b/src/CSGTermEvaluator.cc
index 4adfa62d..bae72d4a 100644
--- a/src/CSGTermEvaluator.cc
+++ b/src/CSGTermEvaluator.cc
@@ -11,6 +11,7 @@
 #include "printutils.h"
 #include "GeometryEvaluator.h"
 #include "polyset.h"
+#include "polyset-utils.h"
 
 #include <string>
 #include <map>
@@ -99,7 +100,20 @@ static shared_ptr<CSGTerm> evaluate_csg_term_from_geometry(const State &state,
 	// We cannot render Polygon2d directly, so we preprocess (tessellate) it here
 	shared_ptr<const Geometry> g = geom;
 	shared_ptr<const Polygon2d> p2d = dynamic_pointer_cast<const Polygon2d>(geom);
-	if (p2d) g.reset(p2d->tessellate());
+	if (p2d) {
+		g.reset(p2d->tessellate());
+	}
+	else {
+		// We cannot render concave polygons, so tessellate any 3D PolySets
+		shared_ptr<const PolySet> ps = dynamic_pointer_cast<const PolySet>(geom);
+		if (ps) {
+			assert(ps->getDimension() == 3);
+			PolySet *ps_tri = new PolySet(3, ps->convexValue());
+			ps_tri->setConvexity(ps->getConvexity());
+			PolysetUtils::tessellate_faces(*ps, *ps_tri);
+			g.reset(ps_tri);
+		}
+	}
 
 	shared_ptr<CSGTerm> t(new CSGTerm(g, state.matrix(), state.color(), stream.str()));
 	if (modinst->isHighlight()) {
diff --git a/tests/regression/cgalpngtest/issue1061-expected.png b/tests/regression/cgalpngtest/issue1061-expected.png
index 78bd8525..ef40d783 100644
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diff --git a/tests/regression/opencsgtest/issue1061-expected.png b/tests/regression/opencsgtest/issue1061-expected.png
index fc626374..ca886ff2 100644
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diff --git a/tests/regression/opencsgtest/polyhedron-concave-test-expected.png b/tests/regression/opencsgtest/polyhedron-concave-test-expected.png
index c45cc11c..8e3dd762 100644
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diff --git a/tests/regression/throwntogethertest/issue1061-expected.png b/tests/regression/throwntogethertest/issue1061-expected.png
index fc626374..ca886ff2 100644
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diff --git a/tests/regression/throwntogethertest/polyhedron-concave-test-expected.png b/tests/regression/throwntogethertest/polyhedron-concave-test-expected.png
index c45cc11c..8e3dd762 100644
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