diff --git a/pyomo/core/kernel/conic.py b/pyomo/core/kernel/conic.py
index 1bb5f1b6ce8..bd78ba310f4 100644
--- a/pyomo/core/kernel/conic.py
+++ b/pyomo/core/kernel/conic.py
@@ -632,7 +632,7 @@ def as_domain(cls, r, x):
         b = block()
         b.r = variable_tuple([variable(lb=0) for i in range(len(r))])
         b.x = variable()
-        b.c = _build_linking_constraints(list(r) + [x], list(b.r) + [x])
+        b.c = _build_linking_constraints(list(r) + [x], list(b.r) + [b.x])
         b.q = cls(r=b.r, x=b.x)
         return b
 
@@ -934,7 +934,7 @@ def as_domain(cls, r, x):
         b = block()
         b.r = variable_tuple([variable(lb=0) for i in range(len(r))])
         b.x = variable()
-        b.c = _build_linking_constraints(list(r) + [x], list(b.r) + [x])
+        b.c = _build_linking_constraints(list(r) + [x], list(b.r) + [b.x])
         b.q = cls(r=b.r, x=b.x)
         return b
 
diff --git a/pyomo/core/tests/unit/kernel/test_conic.py b/pyomo/core/tests/unit/kernel/test_conic.py
index ccfbcca7e1f..bd97c13fc2e 100644
--- a/pyomo/core/tests/unit/kernel/test_conic.py
+++ b/pyomo/core/tests/unit/kernel/test_conic.py
@@ -35,6 +35,8 @@
     primal_power,
     dual_exponential,
     dual_power,
+    primal_geomean,
+    dual_geomean,
 )
 
 
@@ -784,6 +786,40 @@ def test_as_domain(self):
         x[1].value = None
 
 
+# These mosek 10 constraints can't be evaluated, pprinted, checked for convexity,
+# pickled, etc., so I won't use the _conic_tester_base for them
+class Test_primal_geomean(unittest.TestCase):
+    def test_as_domain(self):
+        b = primal_geomean.as_domain(r=[2, 3], x=6)
+        self.assertIs(type(b), block)
+        self.assertIs(type(b.q), primal_geomean)
+        self.assertIs(type(b.r), variable_tuple)
+        self.assertIs(type(b.x), variable)
+        self.assertIs(type(b.c), constraint_tuple)
+        self.assertExpressionsEqual(b.c[0].body, b.r[0])
+        self.assertExpressionsEqual(b.c[0].rhs, 2)
+        self.assertExpressionsEqual(b.c[1].body, b.r[1])
+        self.assertExpressionsEqual(b.c[1].rhs, 3)
+        self.assertExpressionsEqual(b.c[2].body, b.x)
+        self.assertExpressionsEqual(b.c[2].rhs, 6)
+
+
+class Test_dual_geomean(unittest.TestCase):
+    def test_as_domain(self):
+        b = dual_geomean.as_domain(r=[2, 3], x=6)
+        self.assertIs(type(b), block)
+        self.assertIs(type(b.q), dual_geomean)
+        self.assertIs(type(b.r), variable_tuple)
+        self.assertIs(type(b.x), variable)
+        self.assertIs(type(b.c), constraint_tuple)
+        self.assertExpressionsEqual(b.c[0].body, b.r[0])
+        self.assertExpressionsEqual(b.c[0].rhs, 2)
+        self.assertExpressionsEqual(b.c[1].body, b.r[1])
+        self.assertExpressionsEqual(b.c[1].rhs, 3)
+        self.assertExpressionsEqual(b.c[2].body, b.x)
+        self.assertExpressionsEqual(b.c[2].rhs, 6)
+
+
 class TestMisc(unittest.TestCase):
     def test_build_linking_constraints(self):
         c = _build_linking_constraints([], [])