diff --git a/pytorch3d/csrc/iou_box3d/iou_utils.cuh b/pytorch3d/csrc/iou_box3d/iou_utils.cuh
index 452cf7dc..243174a0 100644
--- a/pytorch3d/csrc/iou_box3d/iou_utils.cuh
+++ b/pytorch3d/csrc/iou_box3d/iou_utils.cuh
@@ -11,7 +11,8 @@
 #include <thrust/device_vector.h>
 #include <cstdio>
 #include "utils/float_math.cuh"
-#include "utils/geometry_utils.cuh"
+
+const auto kEpsilon = 1e-4;
 
 /*
 _PLANES and _TRIS define the 4- and 3-connectivity
diff --git a/pytorch3d/csrc/iou_box3d/iou_utils.h b/pytorch3d/csrc/iou_box3d/iou_utils.h
index fd5b37eb..d602eb3e 100644
--- a/pytorch3d/csrc/iou_box3d/iou_utils.h
+++ b/pytorch3d/csrc/iou_box3d/iou_utils.h
@@ -16,9 +16,9 @@
 #include <queue>
 #include <tuple>
 #include <type_traits>
-#include "utils/geometry_utils.h"
 #include "utils/vec3.h"
 
+const auto kEpsilon = 1e-4;
 /*
 _PLANES and _TRIS define the 4- and 3-connectivity
 of the 8 box corners.
diff --git a/tests/data/real_boxes.pkl b/tests/data/real_boxes.pkl
new file mode 100644
index 00000000..e8b8117a
Binary files /dev/null and b/tests/data/real_boxes.pkl differ
diff --git a/tests/test_iou_box3d.py b/tests/test_iou_box3d.py
index f98e6582..f40ae3a3 100644
--- a/tests/test_iou_box3d.py
+++ b/tests/test_iou_box3d.py
@@ -4,6 +4,7 @@
 # This source code is licensed under the BSD-style license found in the
 # LICENSE file in the root directory of this source tree.
 
+import pickle
 import random
 import unittest
 from typing import List, Tuple, Union
@@ -15,7 +16,6 @@ from pytorch3d.io import save_obj
 from pytorch3d.ops.iou_box3d import _box_planes, _box_triangles, box3d_overlap
 from pytorch3d.transforms.rotation_conversions import random_rotation
 
-
 OBJECTRON_TO_PYTORCH3D_FACE_IDX = [0, 4, 6, 2, 1, 5, 7, 3]
 DATA_DIR = get_tests_dir() / "data"
 DEBUG = False
@@ -167,6 +167,7 @@ class TestIoU3D(TestCaseMixin, unittest.TestCase):
                 device=vol.device,
                 dtype=vol.dtype,
             ),
+            atol=1e-7,
         )
 
         # 7th test: hand coded example and test with meshlab output
@@ -283,20 +284,36 @@ class TestIoU3D(TestCaseMixin, unittest.TestCase):
         self.assertClose(vols, torch.tensor([[vol_inters]], device=device), atol=1e-1)
         self.assertClose(ious, torch.tensor([[iou]], device=device), atol=1e-1)
 
+    def _test_real_boxes(self, overlap_fn, device):
+        data_filename = "./real_boxes.pkl"
+        with open(DATA_DIR / data_filename, "rb") as f:
+            example = pickle.load(f)
+
+        verts1 = torch.FloatTensor(example["verts1"])
+        verts2 = torch.FloatTensor(example["verts2"])
+        boxes = torch.stack((verts1, verts2)).to(device)
+
+        iou_expected = torch.eye(2).to(device)
+        vol, iou = overlap_fn(boxes, boxes)
+        self.assertClose(iou, iou_expected)
+
     def test_iou_naive(self):
         device = get_random_cuda_device()
         self._test_iou(self._box3d_overlap_naive_batched, device)
         self._test_compare_objectron(self._box3d_overlap_naive_batched, device)
+        self._test_real_boxes(self._box3d_overlap_naive_batched, device)
 
     def test_iou_cpu(self):
         device = torch.device("cpu")
         self._test_iou(box3d_overlap, device)
         self._test_compare_objectron(box3d_overlap, device)
+        self._test_real_boxes(box3d_overlap, device)
 
     def test_iou_cuda(self):
         device = torch.device("cuda:0")
         self._test_iou(box3d_overlap, device)
         self._test_compare_objectron(box3d_overlap, device)
+        self._test_real_boxes(box3d_overlap, device)
 
     def _test_compare_objectron(self, overlap_fn, device):
         # Load saved objectron data
@@ -656,7 +673,7 @@ def is_inside(
     n: torch.Tensor,
     points: torch.Tensor,
     return_proj: bool = True,
-    eps: float = 1e-6,
+    eps: float = 1e-4,
 ):
     """
     Computes whether point is "inside" the plane.
@@ -778,17 +795,17 @@ def clip_tri_by_plane_oneout(
             vout is "outside" the plane and vin1, vin2 are "inside"
     Returns:
         verts: tensor of shape (4, 3) containing the new vertices formed after clipping the
-            original intersectiong triangle (vout, vin1, vin2)
+            original intersecting triangle (vout, vin1, vin2)
         faces: tensor of shape (2, 3) defining the vertex indices forming the two new triangles
             which are "inside" the plane formed after clipping
     """
     device = plane.device
     # point of intersection between plane and (vin1, vout)
     pint1, a1 = plane_edge_point_of_intersection(plane, n, vin1, vout)
-    assert a1 >= eps and a1 <= 1.0, a1
+    assert a1 >= -eps and a1 <= 1.0 + eps, a1
     # point of intersection between plane and (vin2, vout)
     pint2, a2 = plane_edge_point_of_intersection(plane, n, vin2, vout)
-    assert a2 >= 0.0 and a2 <= 1.0, a2
+    assert a2 >= -eps and a2 <= 1.0 + eps, a2
 
     verts = torch.stack((vin1, pint1, pint2, vin2), dim=0)  # 4x3
     faces = torch.tensor(
@@ -823,10 +840,10 @@ def clip_tri_by_plane_twoout(
     device = plane.device
     # point of intersection between plane and (vin, vout1)
     pint1, a1 = plane_edge_point_of_intersection(plane, n, vin, vout1)
-    assert a1 >= eps and a1 <= 1.0, a1
+    assert a1 >= -eps and a1 <= 1.0 + eps, a1
     # point of intersection between plane and (vin, vout2)
     pint2, a2 = plane_edge_point_of_intersection(plane, n, vin, vout2)
-    assert a2 >= eps and a2 <= 1.0, a2
+    assert a2 >= -eps and a2 <= 1.0 + eps, a2
 
     verts = torch.stack((vin, pint1, pint2), dim=0)  # 3x3
     faces = torch.tensor(
@@ -917,6 +934,7 @@ def box3d_overlap_naive(box1: torch.Tensor, box2: torch.Tensor):
             `iou = vol / (vol1 + vol2 - vol)`
     """
     device = box1.device
+
     # For boxes1 we compute the unit directions n1 corresponding to quad_faces
     n1 = box_planar_dir(box1)  # (6, 3)
     # For boxes2 we compute the unit directions n2 corresponding to quad_faces