diff --git a/openmc/surface.py b/openmc/surface.py
index 6c29ed458..eb44a4fe8 100644
--- a/openmc/surface.py
+++ b/openmc/surface.py
@@ -1376,7 +1376,7 @@ class Cone(Surface):
 
     @property
     def r2(self):
-        return self.coefficients['r2']
+        return self.coefficients['R2']
 
     @x0.setter
     def x0(self, x0):
diff --git a/tests/unit_tests/test_surface.py b/tests/unit_tests/test_surface.py
new file mode 100644
index 000000000..ded6cf1f2
--- /dev/null
+++ b/tests/unit_tests/test_surface.py
@@ -0,0 +1,258 @@
+import numpy as np
+import openmc
+import pytest
+
+
+def assert_infinite_bb(s):
+    ll, ur = (-s).bounding_box
+    assert np.all(np.isinf(ll))
+    assert np.all(np.isinf(ur))
+    ll, ur = (+s).bounding_box
+    assert np.all(np.isinf(ll))
+    assert np.all(np.isinf(ur))
+
+
+def test_plane():
+    s = openmc.Plane(A=1, B=2, C=-1, D=3, name='my plane')
+    assert s.a == 1
+    assert s.b == 2
+    assert s.c == -1
+    assert s.d == 3
+    assert s.boundary_type == 'transmission'
+    assert s.name == 'my plane'
+    assert s.type == 'plane'
+
+    # Generic planes don't have well-defined bounding boxes
+    assert_infinite_bb(s)
+
+    # evaluate method
+    x, y, z = (4, 3, 6)
+    assert s.evaluate((x, y, z)) == pytest.approx(s.a*x + s.b*y + s.c*z - s.d)
+
+    # Make sure repr works
+    repr(s)
+
+
+def test_xplane():
+    s = openmc.XPlane(x0=3., boundary_type='reflective')
+    assert s.x0 == 3.
+    assert s.boundary_type == 'reflective'
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert ll == pytest.approx((3., -np.inf, -np.inf))
+    assert np.all(np.isinf(ur))
+    ll, ur = (-s).bounding_box
+    assert ur == pytest.approx((3., np.inf, np.inf))
+    assert np.all(np.isinf(ll))
+
+    # __contains__ on associated half-spaces
+    assert (5, 0, 0) in +s
+    assert (5, 0, 0) not in -s
+    assert (-2, 1, 10) in -s
+    assert (-2, 1, 10) not in +s
+
+    # evaluate method
+    assert s.evaluate((5., 0., 0.)) == pytest.approx(2.)
+
+    # Make sure repr works
+    repr(s)
+
+
+def test_yplane():
+    s = openmc.YPlane(y0=3.)
+    assert s.y0 == 3.
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert ll == pytest.approx((-np.inf, 3., -np.inf))
+    assert np.all(np.isinf(ur))
+    ll, ur = s.bounding_box('-')
+    assert ur == pytest.approx((np.inf, 3., np.inf))
+    assert np.all(np.isinf(ll))
+
+    # __contains__ on associated half-spaces
+    assert (0, 5, 0) in +s
+    assert (0, 5, 0) not in -s
+    assert (-2, 1, 10) in -s
+    assert (-2, 1, 10) not in +s
+
+    # evaluate method
+    assert s.evaluate((0., 0., 0.)) == pytest.approx(-3.)
+
+def test_zplane():
+    s = openmc.ZPlane(z0=3.)
+    assert s.z0 == 3.
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert ll == pytest.approx((-np.inf, -np.inf, 3.))
+    assert np.all(np.isinf(ur))
+    ll, ur = (-s).bounding_box
+    assert ur == pytest.approx((np.inf, np.inf, 3.))
+    assert np.all(np.isinf(ll))
+
+    # __contains__ on associated half-spaces
+    assert (0, 0, 5) in +s
+    assert (0, 0, 5) not in -s
+    assert (-2, 1, -10) in -s
+    assert (-2, 1, -10) not in +s
+
+    # evaluate method
+    assert s.evaluate((0., 0., 10.)) == pytest.approx(7.)
+
+    # Make sure repr works
+    repr(s)
+
+
+def test_xcylinder():
+    y, z, r = 3, 5, 2
+    s = openmc.XCylinder(y0=y, z0=z, R=r)
+    assert s.y0 == y
+    assert s.z0 == z
+    assert s.r == r
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert np.all(np.isinf(ll))
+    assert np.all(np.isinf(ur))
+    ll, ur = (-s).bounding_box
+    assert ll == pytest.approx((-np.inf, y-r, z-r))
+    assert ur == pytest.approx((np.inf, y+r, z+r))
+
+    # evaluate method
+    assert s.evaluate((0, y, z)) == pytest.approx(-r**2)
+
+    # Make sure repr works
+    repr(s)
+
+
+def test_periodic():
+    x = openmc.XPlane(boundary_type='periodic')
+    y = openmc.YPlane(boundary_type='periodic')
+    x.periodic_surface = y
+    assert y.periodic_surface == x
+    with pytest.raises(TypeError):
+        x.periodic_surface = openmc.Sphere()
+
+
+def test_ycylinder():
+    x, z, r = 3, 5, 2
+    s = openmc.YCylinder(x0=x, z0=z, R=r)
+    assert s.x0 == x
+    assert s.z0 == z
+    assert s.r == r
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert np.all(np.isinf(ll))
+    assert np.all(np.isinf(ur))
+    ll, ur = (-s).bounding_box
+    assert ll == pytest.approx((x-r, -np.inf, z-r))
+    assert ur == pytest.approx((x+r, np.inf, z+r))
+
+    # evaluate method
+    assert s.evaluate((x, 0, z)) == pytest.approx(-r**2)
+
+
+def test_zcylinder():
+    x, y, r = 3, 5, 2
+    s = openmc.ZCylinder(x0=x, y0=y, R=r)
+    assert s.x0 == x
+    assert s.y0 == y
+    assert s.r == r
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert np.all(np.isinf(ll))
+    assert np.all(np.isinf(ur))
+    ll, ur = (-s).bounding_box
+    assert ll == pytest.approx((x-r, y-r, -np.inf))
+    assert ur == pytest.approx((x+r, y+r, np.inf))
+
+    # evaluate method
+    assert s.evaluate((x, y, 0)) == pytest.approx(-r**2)
+
+    # Make sure repr works
+    repr(s)
+
+
+def test_sphere():
+    x, y, z, r = -3, 5, 6, 2
+    s = openmc.Sphere(x0=x, y0=y, z0=z, R=r)
+    assert s.x0 == x
+    assert s.y0 == y
+    assert s.z0 == z
+    assert s.r == r
+
+    # Check bounding box
+    ll, ur = (+s).bounding_box
+    assert np.all(np.isinf(ll))
+    assert np.all(np.isinf(ur))
+    ll, ur = (-s).bounding_box
+    assert ll == pytest.approx((x-r, y-r, z-r))
+    assert ur == pytest.approx((x+r, y+r, z+r))
+
+    # evaluate method
+    assert s.evaluate((x, y, z)) == pytest.approx(-r**2)
+
+    # Make sure repr works
+    repr(s)
+
+
+def cone_common(apex, r2, cls):
+    x, y, z = apex
+    s = cls(x0=x, y0=y, z0=z, R2=r2)
+    assert s.x0 == x
+    assert s.y0 == y
+    assert s.z0 == z
+    assert s.r2 == r2
+
+    # Check bounding box
+    assert_infinite_bb(s)
+
+    # evaluate method -- should be zero at apex
+    assert s.evaluate((x, y, z)) == pytest.approx(0.0)
+
+    # Make sure repr works
+    repr(s)
+
+
+def test_xcone():
+    apex = (10, 0, 0)
+    r2 = 4
+    cone_common(apex, r2, openmc.XCone)
+
+
+def test_ycone():
+    apex = (10, 0, 0)
+    r2 = 4
+    cone_common(apex, r2, openmc.YCone)
+
+
+def test_zcone():
+    apex = (10, 0, 0)
+    r2 = 4
+    cone_common(apex, r2, openmc.ZCone)
+
+
+def test_quadric():
+    # Make a sphere from a quadric
+    r = 10.0
+    coeffs = {'a': 1, 'b': 1, 'c': 1, 'k': -r**2}
+    s = openmc.Quadric(**coeffs)
+    assert s.a == coeffs['a']
+    assert s.b == coeffs['b']
+    assert s.c == coeffs['c']
+    assert s.k == coeffs['k']
+
+    # All other coeffs should be zero
+    for coeff in ('d', 'e', 'f', 'g', 'h', 'j'):
+        assert getattr(s, coeff) == 0.0
+
+    # Check bounding box
+    assert_infinite_bb(s)
+
+    # evaluate method
+    assert s.evaluate((0., 0., 0.)) == pytest.approx(coeffs['k'])
+    assert s.evaluate((1., 1., 1.)) == pytest.approx(3 + coeffs['k'])