diff --git a/microgen/rve.py b/microgen/rve.py
index 116692a6..a9c2f02a 100644
--- a/microgen/rve.py
+++ b/microgen/rve.py
@@ -1,12 +1,17 @@
 """Representative Volume Element (RVE).
 
-The ``Rve.box`` attribute is a :class:`~microgen.cad.CadShape` wrapping an
-OCCT box; it is built lazily on first access and requires the ``[cad]``
-extra (``cadquery-ocp-novtk``).
+Frozen, immutable container for the RVE bounding box and its periodicity flags.
+
+``Rve.box`` is a :class:`~microgen.cad.CadShape` wrapping an OCCT box; it is
+built lazily on first access and requires the ``[cad]`` extra.  ``Rve.grid``
+returns a :class:`pyvista.StructuredGrid` aligned with the cell — used by
+implicit shapes to sample SDF/level-set fields.
 """
 
 from __future__ import annotations
 
+from dataclasses import dataclass
+from functools import cached_property
 from typing import TYPE_CHECKING
 
 import numpy as np
@@ -16,78 +21,144 @@
 if TYPE_CHECKING:
     from collections.abc import Sequence
 
-    from .cad import CadShape
-
-    Vector3DType = tuple[float, float, float] | Sequence[float]
+    import numpy.typing as npt
+    import pyvista as pv
 
+    from .cad import CadShape
 
+    Vector3DType = (
+        tuple[float, float, float] | Sequence[float] | npt.NDArray[np.float64]
+    )
+    ResolutionType = int | tuple[int, int, int] | Sequence[int]
+
+
+def _validate_center(center: object) -> np.ndarray:
+    if isinstance(center, (tuple, list)) and len(center) == _DIM:
+        return np.asarray(center, dtype=float)
+    if isinstance(center, np.ndarray) and center.shape == (_DIM,):
+        return center.astype(float, copy=True)
+    err_msg = f"center must be an array or Sequence of length {_DIM}"
+    raise ValueError(err_msg)
+
+
+def _validate_dim(dim: object) -> np.ndarray:
+    if isinstance(dim, (int, float)) and not isinstance(dim, bool):
+        arr = np.array([dim] * _DIM, dtype=float)
+    elif isinstance(dim, (tuple, list)) and len(dim) == _DIM:
+        arr = np.asarray(dim, dtype=float)
+    elif isinstance(dim, np.ndarray) and dim.shape == (_DIM,):
+        arr = dim.astype(float, copy=True)
+    else:
+        err_msg = f"dim must be an array or Sequence of length {_DIM}"
+        raise ValueError(err_msg)
+    if np.any(arr <= 0):
+        err_msg = f"dimensions of the RVE must be greater than 0, got {arr.tolist()}"
+        raise ValueError(err_msg)
+    return arr
+
+
+def _validate_pbc(pbc: object) -> tuple[bool, bool, bool]:
+    if isinstance(pbc, bool):
+        return (pbc, pbc, pbc)
+    if isinstance(pbc, (tuple, list)) and len(pbc) == _DIM:
+        return (bool(pbc[0]), bool(pbc[1]), bool(pbc[2]))
+    err_msg = f"pbc must be a bool or Sequence[bool] of length {_DIM}"
+    raise ValueError(err_msg)
+
+
+@dataclass(frozen=True, init=False, eq=False, repr=False)
 class Rve:
-    """Representative Volume Element (RVE).
+    """Representative Volume Element (RVE) — frozen.
 
     :param center: center of the RVE
-    :param dim: dimensions of the RVE
+    :param dim: dimensions of the RVE (scalar → cube)
+    :param pbc: periodic-boundary-condition flags per axis ``(x, y, z)``;
+        defaults to fully periodic. A single ``bool`` is broadcast to all axes.
     """
 
+    center: np.ndarray
+    dim: np.ndarray
+    pbc: tuple[bool, bool, bool]
+
     def __init__(
         self: Rve,
         center: Vector3DType = (0, 0, 0),
         dim: float | Vector3DType = 1,
+        pbc: bool | tuple[bool, bool, bool] | Sequence[bool] = (True, True, True),
     ) -> None:
         """Initialize the RVE."""
-        if isinstance(center, (tuple, list)) and len(center) == _DIM:
-            self.center = np.array(center)
-        elif isinstance(center, np.ndarray) and center.shape == (_DIM,):
-            self.center = center
-        else:
-            err_msg = f"center must be an array or Sequence of length {_DIM}"
-            raise ValueError(err_msg)
-
-        if isinstance(dim, (int, float)):
-            self.dim = np.array([dim for _ in range(_DIM)])
-        elif isinstance(dim, (tuple, list)) and len(dim) == _DIM:
-            self.dim = np.array(dim)
-        elif isinstance(dim, np.ndarray) and dim.shape == (_DIM,):
-            self.dim = dim
-        else:
-            err_msg = f"dim must be an array or Sequence of length {_DIM}"
-            raise ValueError(err_msg)
+        object.__setattr__(self, "center", _validate_center(center))
+        object.__setattr__(self, "dim", _validate_dim(dim))
+        object.__setattr__(self, "pbc", _validate_pbc(pbc))
+
+    @cached_property
+    def min_point(self: Rve) -> np.ndarray:
+        """Min corner ``center - 0.5 * dim``."""
+        return self.center - 0.5 * self.dim
+
+    @cached_property
+    def max_point(self: Rve) -> np.ndarray:
+        """Max corner ``center + 0.5 * dim``."""
+        return self.center + 0.5 * self.dim
+
+    @cached_property
+    def box(self: Rve) -> CadShape:
+        """Return a :class:`~microgen.cad.CadShape` box of the RVE (cached).
 
-        if np.any(self.dim <= 0):
-            err_msg = f"dimensions of the RVE must be greater than 0, got {self.dim}"
-            raise ValueError(err_msg)
+        Requires the ``[cad]`` extra.
+        """
+        from .cad import make_box  # noqa: PLC0415
 
-        self.min_point = self.center - 0.5 * self.dim
-        self.max_point = self.center + 0.5 * self.dim
+        return make_box(tuple(self.dim), tuple(self.center))
 
-        self._cached_box: CadShape | None = None
+    def grid(self: Rve, resolution: ResolutionType) -> pv.StructuredGrid:
+        """Return a structured grid aligned with the RVE.
 
-    @property
-    def box(self) -> CadShape:
-        """Return a :class:`~microgen.cad.CadShape` box of the RVE (cached).
-
-        Requires the ``[cad]`` extra.
+        :param resolution: points per axis — int (broadcast to all 3 axes) or
+            length-3 sequence.  The grid spans ``min_point`` → ``max_point``
+            with endpoints included on every axis.
         """
-        if self._cached_box is None:
-            from .cad import make_box  # noqa: PLC0415
+        import pyvista as pv  # noqa: PLC0415
+
+        if isinstance(resolution, int):
+            nx, ny, nz = resolution, resolution, resolution
+        elif isinstance(resolution, (tuple, list)) and len(resolution) == _DIM:
+            nx, ny, nz = (int(r) for r in resolution)
+        elif isinstance(resolution, np.ndarray) and resolution.shape == (_DIM,):
+            nx, ny, nz = (int(r) for r in resolution.tolist())
+        else:
+            err_msg = f"resolution must be an int or Sequence of length {_DIM}"
+            raise ValueError(err_msg)
 
-            self._cached_box = make_box(tuple(self.dim), tuple(self.center))
-        return self._cached_box
+        xi = np.linspace(self.min_point[0], self.max_point[0], nx)
+        yi = np.linspace(self.min_point[1], self.max_point[1], ny)
+        zi = np.linspace(self.min_point[2], self.max_point[2], nz)
+        x, y, z = np.meshgrid(xi, yi, zi, indexing="ij")
+        return pv.StructuredGrid(x, y, z)
 
-    @box.setter
-    def box(self, value: CadShape) -> None:
-        self._cached_box = value
+    def __repr__(self: Rve) -> str:
+        return (
+            f"Rve(center={tuple(self.center.tolist())}, "
+            f"dim={tuple(self.dim.tolist())}, pbc={self.pbc})"
+        )
 
     @classmethod
     def from_min_max(
         cls: type[Rve],
         min_point: Vector3DType = (-0.5, -0.5, -0.5),
         max_point: Vector3DType = (0.5, 0.5, 0.5),
+        pbc: bool | tuple[bool, bool, bool] | Sequence[bool] = (True, True, True),
     ) -> Rve:
         """Generate a Rve from min and max corner points.
 
         :param min_point: ``(x_min, y_min, z_min)`` corner of the RVE
         :param max_point: ``(x_max, y_max, z_max)`` corner of the RVE
+        :param pbc: periodic-boundary-condition flags (see ``__init__``)
         """
         lo = np.asarray(min_point, dtype=float)
         hi = np.asarray(max_point, dtype=float)
-        return cls(center=tuple(0.5 * (lo + hi)), dim=tuple(np.abs(hi - lo)))
+        return cls(
+            center=tuple(0.5 * (lo + hi)),
+            dim=tuple(np.abs(hi - lo)),
+            pbc=pbc,
+        )
diff --git a/tests/test_rve.py b/tests/test_rve.py
index 63dbdbf6..21397342 100644
--- a/tests/test_rve.py
+++ b/tests/test_rve.py
@@ -1,7 +1,10 @@
 """Tests for Rve class."""
 
+import dataclasses
+
 import numpy as np
 import pytest
+import pyvista as pv
 
 from microgen import Rve
 
@@ -80,3 +83,84 @@ def test_rve_from_min_max_must_return_expected_rve() -> None:
     rve = Rve.from_min_max(min_point=(-1, 0, -3), max_point=(0, 2, 3))
     assert np.all(rve.center == [-0.5, 1, 0])
     assert np.all(rve.dim == [1, 2, 6])
+
+
+def test_rve_pbc_default_is_fully_periodic() -> None:
+    """``pbc`` defaults to ``(True, True, True)``."""
+    assert Rve().pbc == (True, True, True)
+
+
+def test_rve_pbc_scalar_broadcasts_to_all_axes() -> None:
+    """A single bool is broadcast to all three axes."""
+    assert Rve(pbc=False).pbc == (False, False, False)
+    assert Rve(pbc=True).pbc == (True, True, True)
+
+
+def test_rve_pbc_accepts_per_axis_tuple() -> None:
+    """A length-3 sequence sets each axis independently."""
+    assert Rve(pbc=(True, False, True)).pbc == (True, False, True)
+    assert Rve(pbc=[False, False, True]).pbc == (False, False, True)
+
+
+def test_rve_invalid_pbc_raises() -> None:
+    """``pbc`` of wrong length or type raises ``ValueError``."""
+    with pytest.raises(ValueError, match="pbc must be a bool"):
+        Rve(pbc=(True, False))  # type: ignore[arg-type]
+    with pytest.raises(ValueError, match="pbc must be a bool"):
+        Rve(pbc=1.5)  # type: ignore[arg-type]
+
+
+def test_rve_is_frozen() -> None:
+    """Reassigning ``center``/``dim``/``pbc`` after construction raises FrozenInstanceError."""
+    rve = Rve(dim=2)
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        rve.center = np.array([1.0, 2.0, 3.0])  # type: ignore[misc]
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        rve.dim = np.array([3.0, 3.0, 3.0])  # type: ignore[misc]
+    with pytest.raises(dataclasses.FrozenInstanceError):
+        rve.pbc = (False, False, False)  # type: ignore[misc]
+
+
+def test_rve_min_max_points_are_consistent() -> None:
+    """``min_point`` / ``max_point`` are derived from center ± 0.5·dim."""
+    rve = Rve(center=(1.0, 2.0, 3.0), dim=(2.0, 4.0, 6.0))
+    assert np.allclose(rve.min_point, [0.0, 0.0, 0.0])
+    assert np.allclose(rve.max_point, [2.0, 4.0, 6.0])
+
+
+def test_rve_grid_with_scalar_resolution() -> None:
+    """``Rve.grid(n)`` returns a StructuredGrid spanning the cell with n^3 points."""
+    rve = Rve(center=(0.0, 0.0, 0.0), dim=(2.0, 4.0, 6.0))
+    grid = rve.grid(5)
+    assert isinstance(grid, pv.StructuredGrid)
+    assert grid.dimensions == (5, 5, 5)
+    pts = np.asarray(grid.points)
+    assert np.isclose(pts[:, 0].min(), -1.0)
+    assert np.isclose(pts[:, 0].max(), 1.0)
+    assert np.isclose(pts[:, 1].min(), -2.0)
+    assert np.isclose(pts[:, 1].max(), 2.0)
+    assert np.isclose(pts[:, 2].min(), -3.0)
+    assert np.isclose(pts[:, 2].max(), 3.0)
+
+
+def test_rve_grid_with_per_axis_resolution() -> None:
+    """``Rve.grid((nx, ny, nz))`` honors per-axis resolution."""
+    rve = Rve(center=(0.0, 0.0, 0.0), dim=1.0)
+    grid = rve.grid((3, 4, 5))
+    assert grid.dimensions == (3, 4, 5)
+
+
+def test_rve_grid_invalid_resolution_raises() -> None:
+    """Wrong-length resolution raises ``ValueError``."""
+    rve = Rve()
+    with pytest.raises(ValueError, match="resolution must be an int"):
+        rve.grid((3, 4))  # type: ignore[arg-type]
+
+
+def test_rve_repr_round_trips_inputs() -> None:
+    """``repr(rve)`` contains the canonical ``center``/``dim``/``pbc`` triple."""
+    rve = Rve(center=(1.0, 2.0, 3.0), dim=(2.0, 2.0, 2.0), pbc=(True, False, True))
+    text = repr(rve)
+    assert "center=(1.0, 2.0, 3.0)" in text
+    assert "dim=(2.0, 2.0, 2.0)" in text
+    assert "pbc=(True, False, True)" in text