diff --git a/meshmode/discretization/poly_element.py b/meshmode/discretization/poly_element.py
index 91fccdf645862b13233df5e639b4ed02c29cf53d..d0f3823c0b9bb368fa215a7187f39594bb190def 100644
--- a/meshmode/discretization/poly_element.py
+++ b/meshmode/discretization/poly_element.py
@@ -212,7 +212,11 @@ class PolynomialWarpAndBlendElementGroup(_MassMatrixQuadratureElementGroup):
     @memoize_method
     def unit_nodes(self):
         dim = self.mesh_el_group.dim
-        result = mp.warp_and_blend_nodes(dim, self.order)
+        if self.order == 0:
+            result = mp.warp_and_blend_nodes(dim, 1)
+            result = np.mean(result, axis=1).reshape(-1, 1)
+        else:
+            result = mp.warp_and_blend_nodes(dim, self.order)
 
         dim2, nunit_nodes = result.shape
         assert dim2 == dim
diff --git a/meshmode/mesh/generation.py b/meshmode/mesh/generation.py
index c4bf260860d533ef39d7f188abd756aa215d97ac..c524292c1fffd741951b5838729014ac38db64b5 100644
--- a/meshmode/mesh/generation.py
+++ b/meshmode/mesh/generation.py
@@ -321,6 +321,9 @@ def make_group_from_vertices(vertices, vertex_indices, order,
         group_factory = SimplexElementGroup
 
     if issubclass(group_factory, SimplexElementGroup):
+        if order < 1:
+            raise ValueError("can't represent simplices with mesh order < 1")
+
         el_origins = el_vertices[:, :, 0][:, :, np.newaxis]
         # ambient_dim, nelements, nspan_vectors
         spanning_vectors = (