diff --git a/test/localgeodesicfefunctiontest.cc b/test/localgeodesicfefunctiontest.cc
index b3ab0d3e75d28f49cd8dbdfd5364c03c29904c24..a7605dea84a6fb012314bfc94b658c0c4abf7233 100644
--- a/test/localgeodesicfefunctiontest.cc
+++ b/test/localgeodesicfefunctiontest.cc
@@ -143,6 +143,7 @@ void testUnitVectors()
 
     std::vector<TargetSpace> corners(dim+1);
 
+    // test some simplex
     FieldVector<double,3> input;
     input[0] = 1;  input[1] = 0;  input[2] = 0;
     corners[0] = input;
@@ -153,6 +154,15 @@ void testUnitVectors()
 
     testPermutationInvariance(corners);
     testDerivative(corners);
+
+    // test the constant function, i.e., everything is mapped onto a single point
+    input[0] = 1;  input[1] = 0;  input[2] = 0;
+    corners[0] = input;
+    corners[1] = input;
+    corners[2] = input;
+
+    testPermutationInvariance(corners);
+    testDerivative(corners);
 }
 
 void testUnitVectors2()