diff --git a/nutils/function.py b/nutils/function.py
index b01bbeaa3..bb3de996b 100644
--- a/nutils/function.py
+++ b/nutils/function.py
@@ -4216,7 +4216,7 @@ def sum(arg: IntoArray, axis: Optional[Union[int, Sequence[int]]] = None) -> Arr
         return summed
 
     @implements(numpy.product)
-    def product(arg: IntoArray, axis: int) -> Array:
+    def product(arg: IntoArray, axis: Optional[Union[int, Sequence[int]]] = None) -> Array:
         arg = Array.cast(arg)
         if arg.dtype == bool:
             arg = arg.astype(int)
diff --git a/nutils/mesh.py b/nutils/mesh.py
index 45ac4d921..08fa5690d 100644
--- a/nutils/mesh.py
+++ b/nutils/mesh.py
@@ -734,6 +734,8 @@ def unitcircle(nelems: int, variant: str) -> Tuple[Topology, function.Array]:
             the same topological structure as :func:`unitsquare` with
             ``etype='multipatch'``.
 
+        * ``"triangle"``: unstructured mesh of triangles.
+
     Returns
     -------
     :class:`nutils.topology.TransformChainsTopology`:
@@ -750,6 +752,20 @@ def unitcircle(nelems: int, variant: str) -> Tuple[Topology, function.Array]:
         topo, geom = unitsquare(nelems, 'multipatch')
         return topo, _square_to_circle(geom)
 
+    elif variant == 'triangle':
+        transforms = transformseq.IndexTransforms(ndims=2, length=6)
+        nodes = numpy.zeros((6, 3), dtype=int)
+        nodes[:,1] = 1, 2, 3, 4, 5, 1
+        nodes[:,2] = 2, 3, 4, 5, 6, 6
+        topo = topology.SimplexTopology('X', nodes, transforms, transforms)
+        x = .5
+        y = .5 * numpy.sqrt(3)
+        coords = numpy.array([[0, 0], [1, 0], [x, y], [-x, y], [-1, 0], [-x, -y], [x, -y]])
+        geom = topo.basis('std', 1) @ coords
+        scale = (1 - numpy.product(function.rootcoords('X', 2)))**-.5
+        nrefine = round(numpy.log2(nelems))
+        return topo.refine(nrefine), geom * scale
+
     else:
         raise Exception('invalid variant {!r}'.format(variant))
 
diff --git a/tests/test_mesh.py b/tests/test_mesh.py
index 822485d1c..83a8fd876 100644
--- a/tests/test_mesh.py
+++ b/tests/test_mesh.py
@@ -200,3 +200,4 @@ def test_interface(self):
 
 unitcircle(variant='rectilinear')
 unitcircle(variant='multipatch')
+unitcircle(variant='triangle')