diff --git a/meshmode/mesh/__init__.py b/meshmode/mesh/__init__.py
index f3581346f59189f0c9a9576b58d0d81d822547c0..19fe94e17c7adca0362bbc2b0939496a75593565 100644
--- a/meshmode/mesh/__init__.py
+++ b/meshmode/mesh/__init__.py
@@ -166,15 +166,15 @@ class SimplexElementGroup(MeshElementGroup):
         elif self.dim == 2:
             return (
                 (0, 1),
+                (2, 0),
                 (1, 2),
-                (0, 2),
                 )
         elif self.dim == 3:
             return (
                 (0, 1, 2),
-                (0, 1, 3),
+                (0, 3, 1),
                 (0, 2, 3),
-                (1, 2, 3)
+                (1, 3, 2)
                 )
         else:
             raise NotImplementedError("dim=%d" % self.dim)