diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_polyhedral_envelope.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_polyhedral_envelope.cpp
new file mode 100644
index 00000000000..5a06fecd980
--- /dev/null
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_polyhedral_envelope.cpp
@@ -0,0 +1,103 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Surface_mesh.h>
+#include <CGAL/Polyhedron_3.h>
+
+#include <CGAL/IO/OFF_reader.h>
+
+#include <CGAL/Polyhedral_envelope.h>
+#include <CGAL/Polygon_mesh_processing/repair_self_intersections.h>
+
+namespace PMP = CGAL::Polygon_mesh_processing;
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel EPIC;
+typedef CGAL::Exact_predicates_exact_constructions_kernel EPEC;
+
+void test_API()
+{
+  std::cout << "---- test_API() ----\n";
+  std::vector<EPIC::Point_3> points;
+  std::vector<std::array<int, 3> > triangles;
+  std::ifstream in("data/eight.off");
+  CGAL::read_OFF(in, points, triangles);
+  CGAL::Surface_mesh<EPIC::Point_3> sm;
+  CGAL::Polyhedron_3<EPIC> poly;
+  PMP::polygon_soup_to_polygon_mesh(points, triangles, sm);
+  PMP::polygon_soup_to_polygon_mesh(points, triangles, poly);
+
+  // build from the same kernel
+  {
+    CGAL::Polyhedral_envelope<EPIC> envelope;
+    assert(envelope.is_empty());
+    envelope = CGAL::Polyhedral_envelope<EPIC>(sm,0.0001);
+    assert(!envelope.is_empty());
+    assert(envelope(sm));
+    assert(envelope(poly));
+    assert(envelope(points, triangles));
+
+    envelope=CGAL::Polyhedral_envelope<EPIC>(points,triangles,0.0001);
+    assert(!envelope.is_empty());
+    assert(envelope(sm));
+    assert(envelope(poly));
+    assert(envelope(points, triangles));
+
+    std::vector<decltype(sm)::Face_index> subfaces(faces(sm).begin(), std::next(faces(sm).begin(), 150));
+    envelope=CGAL::Polyhedral_envelope<EPIC>(subfaces,sm,0.0001);
+    assert(!envelope.is_empty());
+    assert(!envelope(sm));
+    assert(!envelope(poly));
+    assert(!envelope(points, triangles));
+  }
+
+  // build from different kernels
+  {
+    auto sm_np = CGAL::parameters::vertex_point_map(
+      CGAL::make_cartesian_converter_property_map<EPEC::Point_3>(
+        get(boost::vertex_point, sm)));
+    auto poly_np = CGAL::parameters::vertex_point_map(
+      CGAL::make_cartesian_converter_property_map<EPEC::Point_3>(
+        get(boost::vertex_point, poly)));
+    auto soup_np =  CGAL::parameters::point_map(
+      CGAL::make_cartesian_converter_property_map<EPEC::Point_3>(
+        CGAL::Identity_property_map<EPIC::Point_3>()));
+
+    CGAL::Polyhedral_envelope<EPEC> envelope(poly,0.0001,poly_np);
+    assert(envelope(sm, sm_np));
+    assert(envelope(poly, poly_np));
+    assert(envelope(points, triangles, soup_np));
+
+    envelope = CGAL::Polyhedral_envelope<EPEC>(points,triangles,0.0001, soup_np);
+    assert(envelope(sm, sm_np));
+    assert(envelope(poly, poly_np));
+    assert(envelope(points, triangles, soup_np));
+
+    std::vector<decltype(sm)::Face_index> subfaces(faces(sm).begin(), std::next(faces(sm).begin(), 150));
+    envelope=CGAL::Polyhedral_envelope<EPEC>(subfaces,sm,0.0001,sm_np);
+    assert(!envelope.is_empty());
+    assert(!envelope(sm, sm_np));
+    assert(!envelope(poly, poly_np));
+    assert(!envelope(points, triangles, soup_np));
+  }
+}
+
+void test_remove_si()
+{
+  std::cout << "---- test_remove_si() ----\n";
+  CGAL::Surface_mesh<EPIC::Point_3> tm;
+  std::ifstream in("data/pig.off");
+  in >> tm;
+  assert(tm.vertices().size()!=0);
+
+  // try with a small bound --> reject fix
+  PMP::experimental::remove_self_intersections(tm, CGAL::parameters::polyhedral_envelope_epsilon(0.0001));
+  assert(PMP::does_self_intersect(tm));
+  // try with a larger bound --> accept fix
+  PMP::experimental::remove_self_intersections(tm, CGAL::parameters::polyhedral_envelope_epsilon(0.001));
+  assert(!PMP::does_self_intersect(tm));
+}
+
+int main()
+{
+  test_remove_si();
+  test_API();
+}
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