diff --git a/ChangeLog.rst b/ChangeLog.rst
index 0c2c3be4..2b0cbb9f 100644
--- a/ChangeLog.rst
+++ b/ChangeLog.rst
@@ -4,6 +4,29 @@ This project adheres to `Semantic Versioning <http://semver.org/spec/v2.0.0.html
 v0.x.x - 20xx-xx-xx
 -------------------
 
+Breaking
+~~~~~
+
+- [breaking] The hidden ``TabulatedShapeFamily`` class has been removed, with functionality moved to ``TabulatedGSDShapeFamily``.
+
+Added
+~~~~~
+
+- ``TabulatedGSDShapeFamilies`` are now iterable, allowing easier access to shapes.
+- New ``UniformPrismFamily``, ``UniformAntiprismFamily``, ``UniformPyramidFamily``, and ``UniformDipyramidFamily``
+- New documentation to assist users initialize common geometries.
+
+Changed
+~~~~~~~
+
+- The data in ``DOI_SHAPE_REPOSITORIES`` for source :cite:`Damasceno2012` is now sorted to match the order described in the paper.
+
+Deprecated
+~~~~~~~~~~
+
+- The ``PrismAntiprismFamily`` and ``PyramidDipyramidFamily`` have been deprecated in favor of the new families added above, which are faster, more consistent, and present a simplified interface.
+  The deprecated code was retained for backwards compatibility, but is no longer included in the documentation.
+
 v0.8.0 - 2024-02-21
 -------------------
 
diff --git a/coxeter/families/__init__.py b/coxeter/families/__init__.py
index 074cc6a0..0d6d1968 100644
--- a/coxeter/families/__init__.py
+++ b/coxeter/families/__init__.py
@@ -4,17 +4,66 @@
 """Provide tools for generating shapes.
 
 Shape families are coxeter's way of providing well-defined methods for
-generating classes of shapes according to some set of rules. The basic
-interface is defined by the :class:`~.ShapeFamily`, which is a functor that is
-called to generate a shape. The :class:`~.TabulatedShapeFamily` group of
-subclasses enable the generation of shape families according to some
-tabulated set of data, while other families are defined by some set of
-(discrete or continuous) parameters that are used to construct a shape
-analytically.
-
-The `DOI_SHAPE_REPOSITORIES` variable provides convenient access to the shape families
-associated with different scientific publications. This dataset is useful for
+generating classes of shapes according to some set of rules. The
+:class:`~.TabulatedGSDShapeFamily` group of subclasses enable the generation of shape
+families according to some tabulated set of data, while other families are defined by
+some set of parameters that are used to construct a shape analytically. Discrete
+families -- those that contain a fixed number of individual shapes -- may be iterated
+over.
+
+
+Example:
+
+    >>> from coxeter.families import PlatonicFamily
+    >>> for name, shape in PlatonicFamily:
+    >>>    print(name, shape.num_faces)
+    ... (Cube, 6)
+    ... (Dodecahedron, 12)
+    ... (Icosahedron, 20)
+    ... (Octahedron, 8)
+    ... (Tetrahedron, 4)
+
+    >>> cube = PlatonicFamily.get_shape("Cube")
+    >>> cube.num_faces
+    ... 6
+
+
+For continuous families of shapes, one must instead provide the required parameters.
+
+
+Example:
+
+    >>> from coxeter.families import Family423
+    >>> cube = Family423.get_shape(a=1.0, c=3.0) # These values yield a Platonic cube
+    >>> cube.num_faces
+    ... 6
+
+The `DOI_SHAPE_REPOSITORIES` variable provides convenient access to the shape family or
+families associated with different scientific publications. This dataset is useful for
 reproducing the exact set of shapes from publications.
+
+For convenience, shapes included in the paper *10.1126/science.1220869* may be accessed
+as a single family. These are indexed in a three character format consistent with the
+supplementary information of that publication.
+
+
+Example:
+
+    >>> from coxeter.families import DOI_SHAPE_REPOSITORIES
+    >>> DOI_SHAPE_REPOSITORIES["10.1103/PhysRevX.4.011024"]
+    ... [Family323Plus, Family423, Family523]
+
+    >>> science_family = DOI_SHAPE_REPOSITORIES["10.1126/science.1220869"][0]
+    >>> for code, shape in science_family:
+    >>>     print(code, shape.num_vertices)
+    ... (P01, 4)  # Tetrahedron
+    ... (P02, 8)  # Octahedron
+    ... (P03, 6)  # Cube
+    ... (P04, 20) # Icosahedron
+    ... (P05, 12) # Dodecahedron
+    ... (A01, 14) # Cuboctahedron
+    ... ...
+
 """
 
 from .common import (
@@ -25,6 +74,10 @@
     PrismAntiprismFamily,
     PyramidDipyramidFamily,
     RegularNGonFamily,
+    UniformAntiprismFamily,
+    UniformDipyramidFamily,
+    UniformPrismFamily,
+    UniformPyramidFamily,
 )
 from .doi_data_repositories import _doi_shape_collection_factory, _KeyedDefaultDict
 from .plane_shape_families import (
@@ -34,7 +87,7 @@
     TruncatedTetrahedronFamily,
 )
 from .shape_family import ShapeFamily
-from .tabulated_shape_family import TabulatedGSDShapeFamily, TabulatedShapeFamily
+from .tabulated_shape_family import TabulatedGSDShapeFamily
 
 # Note for devs: we want this object to be documented in the public API. The Sphinx
 # method for documenting a module-level constant is placing the docstring directly below
@@ -61,6 +114,10 @@
     "Family423",
     "Family523",
     "PlatonicFamily",
+    "UniformAntiprismFamily",
+    "UniformDipyramidFamily",
+    "UniformPrismFamily",
+    "UniformPyramidFamily",
     "ArchimedeanFamily",
     "CatalanFamily",
     "JohnsonFamily",
@@ -68,7 +125,6 @@
     "PyramidDipyramidFamily",
     "RegularNGonFamily",
     "ShapeFamily",
-    "TabulatedShapeFamily",
     "TabulatedGSDShapeFamily",
     "TruncatedTetrahedronFamily",
 ]
diff --git a/coxeter/families/common.py b/coxeter/families/common.py
index 10782d9c..4a41caad 100644
--- a/coxeter/families/common.py
+++ b/coxeter/families/common.py
@@ -4,15 +4,71 @@
 """Certain common shape families that can be analytically generated."""
 
 import os
+import warnings
+from functools import wraps
+from math import cos, sin, sqrt, tan
 
 import numpy as np
+from numpy import cbrt, pi
 
-from ..shapes import ConvexPolygon
+from ..shapes import ConvexPolygon, ConvexPolyhedron
 from .doi_data_repositories import _DATA_FOLDER
 from .shape_family import ShapeFamily
 from .tabulated_shape_family import TabulatedGSDShapeFamily
 
 
+# Allows us to monkeypatch an existing method with our choice of warning
+def _deprecated_method(func, deprecated="", replacement="", reason=""):
+    @wraps(func)
+    def wrapper(*args, **kwargs):
+        warnings.warn(
+            (f"{deprecated} has been deprecated in favor of {replacement}. {reason}"),
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        return func(*args, **kwargs)
+
+    return wrapper
+
+
+def sec(theta):
+    """Return the secant of an angle."""
+    return 1 / cos(theta)
+
+
+def cot(theta):
+    """Return the cotangent of an angle."""
+    return 1 / tan(theta)
+
+
+def _make_ngon(n, z=0, area=1, angle=0):
+    """Make a regular n-gon with a given area, z height, and rotation angle.
+
+    The initial vertex  lies on the :math:`x` axis by default, but can be rotated by
+    the angle parameter.
+
+    Args:
+        n (int): Number of vertices
+        z (int|float): z value for the polygon. Defaults to 0.
+        area (int|float|None, optional): Area of polygon. Defaults to 1.
+        angle (int|float, optional): Rotation angle, in radians. Defaults to 0.
+
+    Returns
+    -------
+        np.array: n-gon vertices
+    """
+    if n < 3:
+        raise ValueError("Cannot generate an n-gon with fewer than 3 vertices.")
+
+    theta = np.linspace(0, 2 * pi, num=n, endpoint=False) + angle
+    ngon_vertices = np.array([np.cos(theta), np.sin(theta), np.full_like(theta, z)]).T
+    if area is not None:
+        area_0 = 0.5 * n * sin(2 * pi / n)  # Area of the shape with circumradius = 1
+        ngon_vertices[:, :2] *= sqrt(area / area_0)  # Rescale coords to correct area
+
+    return ngon_vertices
+
+
 class RegularNGonFamily(ShapeFamily):
     """The family of convex regular polygons.
 
@@ -29,11 +85,11 @@ class RegularNGonFamily(ShapeFamily):
 
     @classmethod
     def get_shape(cls, n):
-        """Generate a unit area n-gon.
+        r"""Generate a unit area n-gon.
 
         Args:
             n (int):
-                The number of vertices (greater than or equal to 3).
+                The number of vertices (:math:`n \geq 3`).
 
         Returns
         -------
@@ -43,59 +99,218 @@ def get_shape(cls, n):
 
     @classmethod
     def make_vertices(cls, n):
-        """Generate vertices of a unit area n-gon.
+        r"""Generate vertices of a unit area n-gon.
 
         Args:
             n (int):
-                An integer greater than or equal to 3.
+                The number of vertices of the polygon (:math:`n \geq 3`).
 
         Returns
         -------
             :math:`(n, 3)` :class:`numpy.ndarray` of float: The vertices of the polygon.
         """
-        if n < 3:
-            raise ValueError("Cannot generate an n-gon with fewer than 3 vertices.")
-        r = 1  # The radius of the circle
-        theta = np.linspace(0, 2 * np.pi, num=n, endpoint=False)
-        pos = np.array([np.cos(theta), np.sin(theta)]).T
+        return _make_ngon(n, area=1, angle=0)
+
+
+class UniformPrismFamily(ShapeFamily):
+    """The infinite family of uniform right prisms with unit volume.
+
+    As with the :class:`~.RegularNGonFamily`, the initial vertex lies on the
+    :math:`x` axis.
+    """
+
+    @classmethod
+    def get_shape(cls, n):
+        r"""Generate a uniform right n-prism of unit volume.
+
+        Args:
+            n (int):
+                The number of vertices of the base polygons (:math:`n \geq 3`).
+
+        Returns
+        -------
+             :class:`~.ConvexPolyhedron`: The corresponding convex polyhedron.
+        """
+        return ConvexPolyhedron(cls.make_vertices(n))
+
+    @classmethod
+    def make_vertices(cls, n):
+        r"""Generate the vertices of a uniform right n-prism with unit volume.
+
+        Args:
+            n (int):
+                The number of vertices of the base polygons (:math:`n \geq 3`).
+
+        Returns
+        -------
+             :math:`(n*2, 3)` :class:`numpy.ndarray` of float:
+                 The vertices of the prism.
+        """
+        volume = 1
+        h = cbrt(volume * 4 / n * tan(pi / n))
+        area = volume / h  # Top and bottom face areas
+        vertices = np.concatenate(
+            [_make_ngon(n, z=-h / 2, area=area), _make_ngon(n, z=h / 2, area=area)]
+        )
+        return vertices
 
-        # First normalize to guarantee that the limiting case of an infinite
-        # number of vertices produces a circle of area r^2.
-        pos /= np.sqrt(np.pi) / r
 
-        # The area of an n-gon inscribed in a circle is given by:
-        # \frac{n r^2}{2} \sin(2\pi / n)
-        # The ratio of that n-gon area to its circumscribed circle area is:
-        a_circ_a_poly = np.pi / ((n / 2) * np.sin(2 * np.pi / n))
+class UniformAntiprismFamily(ShapeFamily):
+    r"""The infinite family of uniform right antiprisms with unit volume.
 
-        # Rescale the positions so that the final shape has area 1.
-        pos *= np.sqrt(a_circ_a_poly)
+    As with the :class:`~.RegularNGonFamily`, the initial vertex lies on the
+    :math:`x` axis. The bottom face of each antiprism is rotated :math:`\pi/n` radians
+    relative to the top face.
+    """
+
+    @classmethod
+    def get_shape(cls, n):
+        r"""Generate a uniform right n-antiprism of unit volume.
 
-        return pos
+        Args:
+            n (int):
+                The number of vertices of the base polygons (:math:`n \geq 3`).
 
+        Returns
+        -------
+             :class:`~.ConvexPolyhedron`: The corresponding convex polyhedron.
+        """
+        return ConvexPolyhedron(cls.make_vertices(n))
+
+    @classmethod
+    def make_vertices(cls, n):
+        r"""Generate the vertices of a uniform right n-antiprism with unit volume.
+
+        Args:
+            n (int):
+                The number of vertices of the base polygons (:math:`n \geq 3`).
+
+        Returns
+        -------
+             :math:`(n*2, 3)` :class:`numpy.ndarray` of float:
+                 The vertices of the antiprism.
+        """
+        volume = 1
+        s = cbrt(
+            24
+            * volume
+            / (n * (cot(pi / (2 * n)) + cot(pi / n)) * sqrt(4 - sec(pi / (2 * n)) ** 2))
+        )
+        area = n / 4 * (cot(pi / n)) * s**2
+
+        h = sqrt(1 - 0.25 * sec(pi / (2 * n)) ** 2) * s
+        vertices = np.concatenate(
+            [_make_ngon(n, -h / 2, area, angle=pi / n), _make_ngon(n, h / 2, area)]
+        )
+        return vertices
+
+
+class UniformPyramidFamily(ShapeFamily):
+    """The family of uniform right pyramids with unit volume.
+
+    As with the :class:`~.RegularNGonFamily`, the initial vertex of the base polygon
+    lies on the :math:`x` axis.
+    """
+
+    @classmethod
+    def get_shape(cls, n):
+        r"""Generate a uniform right n-pyramid of unit volume.
 
-PlatonicFamily = TabulatedGSDShapeFamily.from_json_file(
+        Args:
+            n (int):
+                The number of vertices of the base polygon (:math:`3 \leq n \leq 5`).
+
+        Returns
+        -------
+             :class:`~.ConvexPolyhedron`: The corresponding convex polyhedron.
+        """
+        return ConvexPolyhedron(cls.make_vertices(n))
+
+    @classmethod
+    def make_vertices(cls, n):
+        r"""Generate the vertices of a uniform right n-pyramid with unit volume.
+
+        Args:
+            n (int):
+                The number of vertices of the base polygon (:math:`3 \leq n \leq 5`).
+
+        Returns
+        -------
+             :math:`(n+1, 3)` :class:`numpy.ndarray` of float:
+                 The vertices of the pyramid.
+        """
+        volume = 1
+        h = cbrt((3 * volume * (4 - sin(pi / n) ** -2)) / (n * cot(pi / n)))
+        area = 3 * volume / h
+
+        # The centroid of a pyramid is 1/4 of the height offset from the base.
+        base = _make_ngon(n, z=-h / 4, area=area)
+        apex = [[0, 0, 3 * h / 4]]
+        vertices = np.concatenate([base, apex])
+        return vertices
+
+
+class UniformDipyramidFamily(ShapeFamily):
+    """The family of uniform right dipyramids with unit volume.
+
+    As with the :class:`~.RegularNGonFamily`, the initial vertex of the base polygon
+    lies on the :math:`x` axis.
+    """
+
+    @classmethod
+    def get_shape(cls, n):
+        r"""Generate a uniform right n-dipyramid of unit volume.
+
+        Args:
+            n (int):
+                The number of vertices of the base polygon (:math:`3 \leq n \leq 5`).
+
+        Returns
+        -------
+             :class:`~.ConvexPolyhedron`: The corresponding convex polyhedron.
+        """
+        return ConvexPolyhedron(cls.make_vertices(n))
+
+    @classmethod
+    def make_vertices(cls, n):
+        r"""Generate the vertices of a uniform right n-dipyramid with unit volume.
+
+        Args:
+            n (int):
+                The number of vertices of the base polygon (:math:`3 \leq n \leq 5`).
+
+        Returns
+        -------
+             :math:`(n+2, 3)` :class:`numpy.ndarray` of float:
+                 The vertices of the dipyramid.
+        """
+        volume = 1
+        # h = cbrt((3 * volume * (4 - sin(pi / n) ** -2)) / (n * cot(pi / n)))
+        # area = 3.0 * volume / h
+
+        h = cbrt((3 * volume * (4 - sin(pi / n) ** -2) / 2) / (n * cot(pi / n)))
+        area = 1.5 * volume / h
+
+        base = _make_ngon(n, z=0, area=area)
+        apexes = [[0, 0, h], [0, 0, -h]]
+        vertices = np.concatenate([base, apexes])
+        return vertices
+
+
+PlatonicFamily = TabulatedGSDShapeFamily._from_json_file(
     os.path.join(_DATA_FOLDER, "platonic.json"),
     classname="PlatonicFamily",
     docstring="""The family of Platonic solids (5 total).
 
-    Args:
-        name (str):
-                The name of the Platonic solid.
-
     Options are "Cube", "Dodecahedron", "Icosahedron", "Octahedron", and "Tetrahedron".
 """,
 )
 
-ArchimedeanFamily = TabulatedGSDShapeFamily.from_json_file(
+ArchimedeanFamily = TabulatedGSDShapeFamily._from_json_file(
     os.path.join(_DATA_FOLDER, "archimedean.json"),
     classname="ArchimedeanFamily",
     docstring="""The family of Archimedean solids (13 total).
 
-    Args:
-        name (str):
-                The name of the Archimedean solid.
-
     Options are "Cuboctahedron", "Icosidodecahedron", "Truncated Tetrahedron",
     "Truncated Octahedron", "Truncated Cube", "Truncated Icosahedron", "Truncated
     Dodecahedron", "Rhombicuboctahedron", "Rhombicosidodecahedron", "Truncated \
@@ -104,16 +319,12 @@ def make_vertices(cls, n):
 """,
 )
 
-CatalanFamily = TabulatedGSDShapeFamily.from_json_file(
+CatalanFamily = TabulatedGSDShapeFamily._from_json_file(
     os.path.join(_DATA_FOLDER, "catalan.json"),
     classname="CatalanFamily",
     docstring="""The family of Catalan solids, also known as Archimedean duals \
     (13 total).
 
-    Args:
-        name (str):
-                The name of the Catalan solid.
-
     Options are "Deltoidal Hexecontahedron", "Deltoidal Icositetrahedron", "Disdyakis \
     Dodecahedron", "Disdyakis Triacontahedron", "Pentagonal Hexecontahedron",
     "Pentagonal Icositetrahedron", "Pentakis Dodecahedron", "Rhombic Dodecahedron",
@@ -122,47 +333,44 @@ def make_vertices(cls, n):
 """,
 )
 
-JohnsonFamily = TabulatedGSDShapeFamily.from_json_file(
+JohnsonFamily = TabulatedGSDShapeFamily._from_json_file(
     os.path.join(_DATA_FOLDER, "johnson.json"),
     classname="JohnsonFamily",
     docstring="""The family of Johnson solids, as enumerated in \
     :cite:`Johnson1966` (92 total).
 
-    Args:
-        name (str):
-                The name of the Johnson solid.
-
-    A full list of Johnson solids is available in :cite:`Johnson1966`. In general, shape
-    names should have the first character of each word capitalized, with spaces between
-    words (e.g. "Elongated Triangular Cupola"). Pyramids and dipyramids are named from
-    their base polygon (e.g. "Square Pyramid" or "Elongated Pentagonal Dipyramid").
+    A full list of Johnson solids is available in :cite:`Johnson1966`, and in the
+    ``names`` property. In general, shape names should have the first character of
+    each word capitalized, with spaces between words (e.g. "Elongated Triangular
+    Cupola"). Pyramids and dipyramids are named from their base polygon (e.g. "Square
+    Pyramid" or "Elongated Pentagonal Dipyramid").
 """,
 )
 
-PyramidDipyramidFamily = TabulatedGSDShapeFamily.from_json_file(
+PyramidDipyramidFamily = TabulatedGSDShapeFamily._from_json_file(
     os.path.join(_DATA_FOLDER, "pyramid_dipyramid.json"),
     classname="PyramidDipyramidFamily",
     docstring="""The family of regular equilateral pyramids and dipyramids (6 total).
 
-    Args:
-        name (str):
-                The name of the pyramid or dipyramid.
-
     Options for pyramids are "Triangular Pyramid", "Square Pyramid", and
     "Pentagonal Pyramid". Options for dipyramids are "Triangular Dipyramid",
     "Square Dipyramid", and "Pentagonal Dipyramid".
 """,
 )
 
-PrismAntiprismFamily = TabulatedGSDShapeFamily.from_json_file(
+PrismAntiprismFamily = TabulatedGSDShapeFamily._from_json_file(
     os.path.join(_DATA_FOLDER, "prism_antiprism.json"),
     classname="PrismAntiprismFamily",
     docstring="""The family of uniform n-prisms and n-antiprisms with n∈[3,10] \
     (16 total).
 
-    Args:
-        name (str):
-                The name of the prism or antiprism.
+
+    .. warning::
+
+        This class has been deprecated in favor of the :class:`~.UniformPrismFamily`
+        and :class:`~.UniformAntiprismFamily`, as the new classes have a simplified API
+        and support the entire infinite shape family. Please transfer existing code to
+        use the new classes.
 
     Options for prisms are  \
     "Triangular Prism", "Square Prism", "Pentagonal Prism", "Hexagonal Prism", \
@@ -173,3 +381,22 @@ def make_vertices(cls, n):
     and "Decagonal Antiprism".
 """,
 )
+
+PrismAntiprismFamily.get_shape = _deprecated_method(
+    PrismAntiprismFamily.get_shape,
+    deprecated="PrismAntiprismFamily",
+    replacement="UniformPrismFamily and UniformAntiprismFamily",
+    reason=(
+        "These alternate classes have a simplified interface and support the "
+        "entire infinite family of geometries."
+    ),
+)
+PyramidDipyramidFamily.get_shape = _deprecated_method(
+    PyramidDipyramidFamily.get_shape,
+    deprecated="PyramidDipyramidFamily",
+    replacement="UniformPyramidFamily and UniformDipyramidFamily",
+    reason=(
+        "These alternate classes have a simplified interface and better match the "
+        "naming conventions of coxeter."
+    ),
+)
diff --git a/coxeter/families/data/_previous_science1220869.json b/coxeter/families/data/_previous_science1220869.json
new file mode 100644
index 00000000..134a825c
--- /dev/null
+++ b/coxeter/families/data/_previous_science1220869.json
@@ -0,0 +1,20027 @@
+{
+    "1": {
+        "type": "ConvexPolyhedron",
+        "vertices": [
+            [
+                -0.947214,
+                -0.58541,
+                -0.425325
+            ],
+            [
+                -0.5,
+                -0.309017,
+                0.425325
+            ],
+            [
+                -0.5,
+                0.309017,
+                -0.425325
+            ],
+            [
+                -0.0527864,
+                0.58541,
+                0.425325
+            ],
+            [
+                0.0527864,
+                -0.58541,
+                -0.425325
+            ],
+            [
+                0.5,
+                -0.309017,
+                0.425325
+            ],
+            [
+                0.5,
+                0.309017,
+                -0.425325
+            ],
+            [
+                0.947214,
+                0.58541,
+                0.425325
+            ]
+        ],
+        "name": "Acute Golden Rhombohedron",
+        "short_name": "O19",
+        "alternative_name": null,
+        "comment": null
+    },
+    "2": {
+        "type": "ConvexPolyhedron",
+        "vertices": [
+            [
+                -0.5,
+                -0.5,
+                -0.420448208
+            ],
+            [
+                -0.5,
+                0.5,
+                -0.420448208
+            ],
+            [
+                0.0,
+                -0.707106781,
+                0.420448208
+            ],
+            [
+                0.0,
+                0.707106781,
+                0.420448208
+            ],
+            [
+                0.5,
+                -0.5,
+                -0.420448208
+            ],
+            [
+                0.5,
+                0.5,
+                -0.420448208
+            ],
+            [
+                -0.707106781,
+                0.0,
+                0.420448208
+            ],
+            [
+                0.707106781,
+                0.0,
+                0.420448208
+            ]
+        ],
+        "name": "Square Antiprism",
+        "short_name": "O08",
+        "alternative_name": null,
+        "comment": "edge length=8"
+    },
+    "3": {
+        "type": "ConvexPolyhedron",
+        "vertices": [
+            [
+                -0.850650808,
+                0.0,
+                -0.425325404
+            ],
+            [
+                0.850650808,
+                0.0,
+                0.425325404
+            ],
+            [
+                -0.68819096,
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diff --git a/coxeter/families/data/science1220869.json b/coxeter/families/data/science1220869.json
index 134a825c..42b95acf 100644
--- a/coxeter/families/data/science1220869.json
+++ b/coxeter/families/data/science1220869.json
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+                -0.872673738
             ],
             [
-                1.96417,
-                0.809017,
-                1.27598
+                2.2847,
+                0.934172,
+                0.127322262
             ],
             [
-                0.850651,
+                2.41202,
                 0.0,
-                2.32744
-            ],
-            [
-                -2.22703,
-                -1.0,
-                0.425325
-            ],
-            [
-                -2.22703,
-                1.0,
-                0.425325
+                -0.539344738
             ],
             [
-                -0.850651,
+                2.41202,
                 0.0,
-                -2.32744
-            ],
-            [
-                -0.525731,
-                -1.61803,
-                -1.80171
-            ],
-            [
-                -0.525731,
-                1.61803,
-                -1.80171
-            ],
-            [
-                0.525731,
-                -1.61803,
-                1.80171
-            ],
-            [
-                0.525731,
-                1.61803,
-                1.80171
+                0.460655562
             ]
         ],
-        "name": "Truncated Icosahedron",
-        "short_name": "A06",
+        "name": "Rhombic Enneacontahedron",
+        "short_name": "O17",
         "alternative_name": null,
         "comment": null
     },
-    "143": {
+    "O18": {
         "type": "ConvexPolyhedron",
         "vertices": [
             [
-                -1.5,
-                -0.5,
-                0.0
-            ],
-            [
-                -1.5,
-                0.5,
-                0.0
-            ],
-            [
-                -1.0,
-                -1.0,
-                -0.707107
-            ],
-            [
-                -1.0,
-                -1.0,
-                0.707107
-            ],
-            [
-                -1.0,
-                1.0,
-                -0.707107
+                -0.947214,
+                0.0854102,
+                0.262866
             ],
             [
-                -1.0,
-                1.0,
-                0.707107
+                -0.5,
+                -0.809017,
+                0.262866
             ],
             [
                 -0.5,
-                -1.5,
-                0.0
+                0.809017,
+                -0.262866
             ],
             [
-                -0.5,
-                -0.5,
-                -1.41421
+                -0.0527864,
+                -0.0854102,
+                -0.262866
             ],
             [
-                -0.5,
-                -0.5,
-                1.41421
+                0.0527864,
+                0.0854102,
+                0.262866
             ],
             [
-                -0.5,
                 0.5,
-                -1.41421
+                -0.809017,
+                0.262866
             ],
             [
-                -0.5,
                 0.5,
-                1.41421
+                0.809017,
+                -0.262866
             ],
             [
-                -0.5,
-                1.5,
-                0.0
-            ],
+                0.947214,
+                -0.0854102,
+                -0.262866
+            ]
+        ],
+        "name": "Obtuse Golden Rhombohedron",
+        "short_name": "O18",
+        "alternative_name": null,
+        "comment": null
+    },
+    "O19": {
+        "type": "ConvexPolyhedron",
+        "vertices": [
             [
-                0.5,
-                -1.5,
-                0.0
+                -0.947214,
+                -0.58541,
+                -0.425325
             ],
             [
-                0.5,
                 -0.5,
-                -1.41421
+                -0.309017,
+                0.425325
             ],
             [
-                0.5,
                 -0.5,
-                1.41421
+                0.309017,
+                -0.425325
             ],
             [
-                0.5,
-                0.5,
-                -1.41421
+                -0.0527864,
+                0.58541,
+                0.425325
             ],
             [
-                0.5,
-                0.5,
-                1.41421
+                0.0527864,
+                -0.58541,
+                -0.425325
             ],
             [
                 0.5,
-                1.5,
-                0.0
-            ],
-            [
-                1.0,
-                -1.0,
-                -0.707107
-            ],
-            [
-                1.0,
-                -1.0,
-                0.707107
-            ],
-            [
-                1.0,
-                1.0,
-                -0.707107
-            ],
-            [
-                1.0,
-                1.0,
-                0.707107
+                -0.309017,
+                0.425325
             ],
             [
-                1.5,
-                -0.5,
-                0.0
+                0.5,
+                0.309017,
+                -0.425325
             ],
             [
-                1.5,
-                0.5,
-                0.0
+                0.947214,
+                0.58541,
+                0.425325
             ]
         ],
-        "name": "Truncated Octahedron",
-        "short_name": "A04",
+        "name": "Acute Golden Rhombohedron",
+        "short_name": "O19",
         "alternative_name": null,
         "comment": null
     },
-    "144": {
+    "O20": {
         "type": "ConvexPolyhedron",
         "vertices": [
             [
-                0,
-                -1,
-                -0.612372
+                0.0,
+                -1.7769,
+                0.961343
             ],
             [
-                0,
-                1,
-                -0.612372
+                0.0,
+                1.7769,
+                -0.961343
             ],
             [
-                -0.57735,
-                -1,
-                0.204124
+                0.0,
+                -1.09819,
+                1.69574
             ],
             [
-                -0.57735,
-                1,
-                0.204124
+                0.0,
+                1.09819,
+                -1.69574
             ],
             [
-                -0.288675,
-                -0.5,
-                1.02062
+                -1.53884,
+                -0.888451,
+                -0.961343
             ],
             [
-                -0.288675,
-                0.5,
-                1.02062
+                -1.53884,
+                0.888451,
+                0.961343
             ],
             [
-                0.57735,
-                0,
-                1.02062
+                1.53884,
+                -0.888451,
+                -0.961343
             ],
             [
-                1.1547,
-                0,
-                0.204124
+                1.53884,
+                0.888451,
+                0.961343
             ],
             [
-                -0.866025,
-                -0.5,
-                -0.612372
+                -0.951057,
+                -0.549093,
+                -1.69574
             ],
             [
-                -0.866025,
-                0.5,
-                -0.612372
+                -0.951057,
+                0.549093,
+                1.69574
             ],
             [
-                0.866025,
-                -0.5,
-                -0.612372
+                0.951057,
+                -0.549093,
+                -1.69574
             ],
             [
-                0.866025,
-                0.5,
-                -0.612372
+                0.951057,
+                0.549093,
+                1.69574
             ]
         ],
-        "name": "Truncated Tetrahedron",
-        "short_name": "A03",
+        "name": "Duerers Solid",
+        "short_name": "O20",
         "alternative_name": null,
         "comment": null
     },
-    "145": {
+    "O21": {
         "type": "ConvexPolyhedron",
         "vertices": [
             [
-                -1.9,
-                -0.3,
+                -0.866025,
+                -0.866025,
                 -0.5
             ],
             [
-                -1.833333,
-                0.1666667,
-                -0.833333
-            ],
-            [
-                -1.7,
-                -0.9,
+                -0.866025,
+                -0.866025,
                 0.5
             ],
             [
-                -1.5,
-                -1.1,
-                0.7
-            ],
-            [
-                -1.5,
-                0.1,
-                -1.3
-            ],
-            [
-                -1.3,
-                -0.1,
-                -1.5
-            ],
-            [
-                -1.166667,
-                -1.166667,
-                1.166667
-            ],
-            [
-                -1.1,
-                -0.7,
-                1.5
-            ],
-            [
-                -0.9,
-                -0.5,
-                1.7
-            ],
-            [
-                -0.833333,
-                -0.166667,
-                -1.833333
+                -0.866025,
+                0.0,
+                -1.0
             ],
             [
-                -0.7,
-                -1.5,
-                1.1
+                -0.866025,
+                0.0,
+                1.0
             ],
             [
-                -0.5,
-                -1.7,
-                0.9
+                -0.866025,
+                0.866025,
+                -0.5
             ],
             [
-                -0.5,
-                0.3,
-                -1.9
+                -0.866025,
+                0.866025,
+                0.5
             ],
             [
-                -0.3,
-                0.5,
-                1.9
+                0.0,
+                -0.866025,
+                -1.0
             ],
             [
-                -0.166667,
-                1.833333,
-                0.8333333
+                0.0,
+                -0.866025,
+                1.0
             ],
             [
-                -0.1,
-                1.5,
-                1.3
+                0.0,
+                0.0,
+                -1.5
             ],
             [
-                0.1,
-                1.3,
+                0.0,
+                0.0,
                 1.5
             ],
             [
-                0.1666667,
-                0.8333333,
-                1.833333
+                0.0,
+                0.866025,
+                -1.0
             ],
             [
-                0.3,
-                1.9,
-                0.5
+                0.0,
+                0.866025,
+                1.0
             ],
             [
-                0.5,
-                -1.9,
-                0.3
+                0.866025,
+                -0.866025,
+                -0.5
             ],
             [
-                0.5,
-                0.9,
-                -1.7
+                0.866025,
+                -0.866025,
+                0.5
             ],
             [
-                0.7,
-                1.1,
-                -1.5
+                0.866025,
+                0.0,
+                -1.0
             ],
             [
-                0.8333333,
-                -1.833333,
-                -0.166667
+                0.866025,
+                0.0,
+                1.0
             ],
             [
-                0.9,
-                1.7,
+                0.866025,
+                0.866025,
                 -0.5
             ],
             [
-                1.1,
-                1.5,
-                -0.7
-            ],
-            [
-                1.166667,
-                1.166667,
-                -1.166667
-            ],
-            [
-                1.3,
-                -1.5,
-                -0.1
-            ],
+                0.866025,
+                0.866025,
+                0.5
+            ]
+        ],
+        "name": "Elongated Dodecahedron",
+        "short_name": "O21",
+        "alternative_name": null,
+        "comment": null
+    },
+    "O22": {
+        "type": "ConvexPolyhedron",
+        "vertices": [
             [
-                1.5,
-                -1.3,
-                0.1
+                0.0,
+                0.0,
+                1.1447142425533319
             ],
             [
-                1.5,
-                0.7,
-                -1.1
+                0.0,
+                -1.1447142425533319,
+                0.0
             ],
             [
-                1.7,
-                0.5,
-                -0.9
+                0.0,
+                1.1447142425533319,
+                0.0
             ],
             [
-                1.833333,
-                -0.833333,
-                0.1666667
+                -1.1447142425533319,
+                0.0,
+                0.0
             ],
             [
-                1.9,
-                -0.5,
-                -0.3
+                1.1447142425533319,
+                0.0,
+                0.0
             ]
         ],
         "name": "Square Pyramid",
         "short_name": "O22",
         "alternative_name": null,
-        "comment": "height/edge length=1/2"
+        "comment": "height/edge length=1/2",
+        "source": "pyramid_dipyramid.json"
     }
 }
diff --git a/coxeter/families/doi_data_repositories.py b/coxeter/families/doi_data_repositories.py
index 5517213e..f0c25423 100644
--- a/coxeter/families/doi_data_repositories.py
+++ b/coxeter/families/doi_data_repositories.py
@@ -49,7 +49,7 @@ def _doi_shape_collection_factory(doi):
     if doi in _DOI_TO_FILE:
         for fn in _DOI_TO_FILE[doi]:
             families.append(
-                TabulatedGSDShapeFamily.from_json_file(os.path.join(_DATA_FOLDER, fn))
+                TabulatedGSDShapeFamily._from_json_file(os.path.join(_DATA_FOLDER, fn))
             )
     if doi in _DOI_TO_FAMILY:
         for family_type in _DOI_TO_FAMILY[doi]:
diff --git a/coxeter/families/shape_family.py b/coxeter/families/shape_family.py
index 1d131391..f7d8c8ba 100644
--- a/coxeter/families/shape_family.py
+++ b/coxeter/families/shape_family.py
@@ -30,9 +30,9 @@ class ShapeFamily(ABC):
     roughly like ``family.get_shape(n=6)``.
     """
 
-    @classmethod
+    @property
     @abstractmethod
-    def get_shape(cls):
+    def get_shape(self):
         """Generate a shape.
 
         Subclasses must define this function to accept whatever parameters are
diff --git a/coxeter/families/tabulated_shape_family.py b/coxeter/families/tabulated_shape_family.py
index cdd0d387..2f683f1e 100644
--- a/coxeter/families/tabulated_shape_family.py
+++ b/coxeter/families/tabulated_shape_family.py
@@ -11,99 +11,50 @@
 appropriate formatting.
 """
 
-import copy
 import json
 
 from ..shape_getters import from_gsd_type_shapes
 from .shape_family import ShapeFamily
 
 
-class TabulatedShapeFamily(ShapeFamily):
-    """A shape family corresponding to a tabulated set of shapes.
+class TabulatedGSDShapeFamily(ShapeFamily):
+    """A tabulated shape family, used to generate families of named polyhedra.
 
-    Data can either be read from a file or provided in the form of a
-    dictionary. If a filename is provided, it must be a JSON file that can be
-    parsed into an appropriately formatted dictionary, namely a set of
-    key-value pairs such that the call operator of this class can generate
-    a :class:`~coxeter.shapes.Shape` from the dictionary. The raw parsed
-    JSON is accessible via the :attr:`~.data` attribute. Subclasses of this
-    class implement the call operator to define exactly how the dictionary
-    values are converted to a shape definition.
-    """
-
-    @classmethod
-    def from_mapping(cls, mapping, classname=None, docstring=None):
-        """Generate a subclass for a dataset from a mapping.
-
-        Notably, this method is a _class_ factory: rather than generating a new
-        instance, this method actually generates a new subclass. This design is
-        consistent with the usage :class:`~.ShapeFamily` subclasses by direct
-        interaction with the class (without instantiation).
+    The values of the dictionary used to construct this class must adhere to
+    the :ref:`GSD shape spec <gsd:shapes>`. Each mapping may contain additional
+    data, which is ignored when the class is called to actually produce
+    :class:`~coxeter.shapes.Shape` objects.
 
-        Args:
-            mapping (Mapping):
-                A dict-like object containing valid shape definitions.
-            classname (str, optional):
-                The name of the new class to use if provided (Default value: None).
-            docstring (str, optional):
-                The docstring to apply to the class.
+    Args:
+        data (Mapping):
+            A dictionary containing valid shape definitions.
+    """
 
-        Returns
-        -------
-            A subclass of this one associated with the the provided data.
-        """
+    def __init__(self, data):
+        self._data = data
+        self._shape_names = [*data.keys()]
+        self._shape_specs = [*data.values()]
 
-        class NewTabulatedShapeFamily(cls):
-            # Make a full copy to avoid modifying an input dictionary.
-            data = copy.deepcopy(mapping)
+    @property
+    def data(self):  # noqa: D102
+        return self._data
 
-        # TODO: Consider dynamically setting attributes like __name__.
+    @property
+    def names(self):
+        """A list of names for the shapes in the family, in alphabetical order."""
+        return self._shape_names
 
+    @classmethod
+    def _from_json_file(cls, filename, classname=None, docstring=None):
+        with open(filename) as f:
+            NewTabulatedShapeFamily = cls(data=json.load(f))  # noqa:  N806
         if classname is not None:
             NewTabulatedShapeFamily.__name__ = classname
         if docstring is not None:
             NewTabulatedShapeFamily.__doc__ = docstring
         return NewTabulatedShapeFamily
 
-    @classmethod
-    def from_json_file(cls, filename, *args, **kwargs):
-        r"""Generate a subclass for a dataset from a JSON file.
-
-        This method simply loads the JSON file into a dictionary and calls
-        :meth:`~.from_mapping`, see that docstring for more information.
-
-        Args:
-            filename (str):
-                A JSON file containing valid shape definitions.
-            \*args:
-                Passed on to :meth:`~.from_mapping`.
-            \*\*kwargs:
-                Passed on to :meth:`~.from_mapping`.
-
-        Returns
-        -------
-            A subclass of this one associated with the the provided data.
-        """
-        with open(filename) as f:
-            return cls.from_mapping(json.load(f), *args, **kwargs)
-
-
-class TabulatedGSDShapeFamily(TabulatedShapeFamily):
-    """A tabulated shape family defined by a GSD shape schema.
-
-    The values of the dictionary used to construct this class must adhere to
-    the :ref:`GSD shape spec <gsd:shapes>`. Each mapping may contain additional
-    data, which is ignored when the class is called to actually produce
-    :class:`~coxeter.shapes.Shape` objects.
-
-    Args:
-        filename_or_dict (str or Mapping):
-            A dictionary containing valid shape definitions or a JSON file that
-            can be read into such a dictionary.
-    """
-
-    @classmethod
-    def get_shape(cls, name):
+    def get_shape(self, name):
         """Use the class's data to produce a shape for the given name.
 
         Args:
@@ -112,6 +63,17 @@ def get_shape(cls, name):
 
         Returns
         -------
-            :class:`~coxeter.shapes.Shape`: The requested shape.
+            :class:`~.ConvexPolyhedron`: The requested shape.
+        """
+        return from_gsd_type_shapes(self.data[name])
+
+    def __iter__(self):
+        """Iterate over the names and geometries associated with the class.
+
+        Yields
+        ------
+            tuple[str, :class:`~.ConvexPolyhedron`]:
+                An iterator of shape names and the related polyhedron objects.
         """
-        return from_gsd_type_shapes(cls.data[name])
+        for key in self.names:
+            yield (key, self.get_shape(key))
diff --git a/doc/source/package-families.rst b/doc/source/package-families.rst
index 79594b74..b61050f7 100644
--- a/doc/source/package-families.rst
+++ b/doc/source/package-families.rst
@@ -6,3 +6,12 @@ Families Module
 .. automodule:: coxeter.families
    :members:
    :show-inheritance:
+
+.. autoclass:: PlatonicFamily()
+   :special-members: __iter__
+.. autoclass:: ArchimedeanFamily()
+   :special-members: __iter__
+.. autoclass:: CatalanFamily()
+   :special-members: __iter__
+.. autoclass:: JohnsonFamily()
+   :special-members: __iter__
diff --git a/tests/test_shape_families.py b/tests/test_shape_families.py
index c17aa04d..22098fcf 100644
--- a/tests/test_shape_families.py
+++ b/tests/test_shape_families.py
@@ -3,21 +3,36 @@
 
 import numpy as np
 import pytest
-from hypothesis import given
-from hypothesis.strategies import floats
+from hypothesis import given, settings
+from hypothesis.strategies import floats, integers
 
-from conftest import _catalan_shape_names
 from coxeter.families import (
     DOI_SHAPE_REPOSITORIES,
+    ArchimedeanFamily,
     CatalanFamily,
     Family323Plus,
     Family423,
     Family523,
+    JohnsonFamily,
+    PlatonicFamily,
+    PrismAntiprismFamily,
+    PyramidDipyramidFamily,
     RegularNGonFamily,
+    TabulatedGSDShapeFamily,
     TruncatedTetrahedronFamily,
+    UniformAntiprismFamily,
+    UniformDipyramidFamily,
+    UniformPrismFamily,
+    UniformPyramidFamily,
 )
+from coxeter.shapes import ConvexPolyhedron
 
+ATOL = 1e-15
 MIN_REALISTIC_PRECISION = 2e-6
+MAX_N_POLY = 102
+TEST_EXAMPLES = 32
+
+ScienceFamily = DOI_SHAPE_REPOSITORIES["10.1126/science.1220869"][0]
 
 
 def _test_parameters_outside_precision(params_list):
@@ -33,7 +48,8 @@ def is_close_to_shape_space_boundary(param):
     return any(is_close_to_shape_space_boundary(param) for param in params_list)
 
 
-@pytest.mark.parametrize("n", range(3, 100))
+@given(n=integers(3, MAX_N_POLY))
+@settings(max_examples=TEST_EXAMPLES)
 def test_regular_ngon(n):
     poly = RegularNGonFamily.get_shape(n)
     assert len(poly.vertices) == n
@@ -50,19 +66,54 @@ def test_regular_ngon(n):
     )
 
 
-def test_shape_repos():
-    family = DOI_SHAPE_REPOSITORIES["10.1126/science.1220869"][0]
-    for shape in _catalan_shape_names:
-        for key in family.data:
-            if family.data[key]["name"] == shape:
-                break
-        else:
-            raise AssertionError(f"Could not find {shape} in the dataset.")
-        reference_poly = CatalanFamily.get_shape(shape)
-        test_poly = family.get_shape(key)
-        test_poly.merge_faces(1e-3)
-        assert reference_poly.num_vertices == test_poly.num_vertices
-        assert reference_poly.num_faces == test_poly.num_faces
+@pytest.mark.parametrize(
+    "family",
+    [PlatonicFamily, ArchimedeanFamily, CatalanFamily, JohnsonFamily, ScienceFamily],
+    ids=[
+        "PlatonicFamily",
+        "ArchimedeanFamily",
+        "CatalanFamily",
+        "JohnsonFamily",
+        "ScienceFamily",
+    ],
+)
+def test_named_family(family):
+    def test_type(family):
+        assert isinstance(family, TabulatedGSDShapeFamily)
+
+    def test_iteration(family):
+        for name, shape in family:
+            assert isinstance(shape, ConvexPolyhedron)
+            np.testing.assert_allclose(family.get_shape(name).vertices, shape.vertices)
+
+    def test_names(family):
+        for name in family.names:
+            family.get_shape(name)
+
+    test_type(family)
+    test_iteration(family)
+    test_names(family)
+
+
+def test_science_family():
+    reference_mapping = {
+        "P": PlatonicFamily,
+        "A": ArchimedeanFamily,
+        "C": CatalanFamily,
+        "J": JohnsonFamily,
+        "O": None,
+    }
+    for name, shape in ScienceFamily:
+        reference = reference_mapping[name[0]]
+        if reference is not None:
+            try:
+                np.testing.assert_allclose(
+                    reference.get_shape(ScienceFamily.data[name]["name"]).vertices,
+                    shape.vertices,
+                )
+            except KeyError as e:
+                if name[0] != "J":
+                    raise KeyError from e
 
 
 def test_shape323():
@@ -162,3 +213,84 @@ def test_truncated_tetrahedron_intermediates(t):
     if _test_parameters_outside_precision([t]) or np.abs(np.round(t, 15) - t) < 2e-16:
         return
     TruncatedTetrahedronFamily.get_shape(t)
+
+
+@given(n=integers(3, MAX_N_POLY))
+@settings(max_examples=TEST_EXAMPLES)
+def test_uniform_prisms(n):
+    vertices = UniformPrismFamily.make_vertices(n=n)
+    shape = UniformPrismFamily.get_shape(n=n)
+
+    np.testing.assert_allclose(shape.centroid, 0.0, atol=ATOL)
+    np.testing.assert_allclose(shape.volume, 1.0, atol=ATOL)
+    np.testing.assert_allclose(shape.edge_lengths, shape.edge_lengths.mean(), atol=ATOL)
+    np.testing.assert_allclose(vertices, shape.vertices)
+
+
+@given(n=integers(3, MAX_N_POLY))
+@settings(max_examples=TEST_EXAMPLES)
+def test_uniform_antiprisms(n):
+    vertices = UniformAntiprismFamily.make_vertices(n=n)
+    shape = UniformAntiprismFamily.get_shape(n=n)
+
+    np.testing.assert_allclose(shape.centroid, 0.0, atol=ATOL)
+    np.testing.assert_allclose(shape.volume, 1.0, atol=ATOL)
+    np.testing.assert_allclose(shape.edge_lengths, shape.edge_lengths.mean(), atol=ATOL)
+    np.testing.assert_allclose(vertices, shape.vertices)
+
+
+@pytest.mark.parametrize("n", [3, 4, 5])
+def test_uniform_pyramids(n):
+    vertices = UniformPyramidFamily.make_vertices(n=n)
+    shape = UniformPyramidFamily.get_shape(n=n)
+
+    np.testing.assert_allclose(shape.centroid, 0.0, atol=ATOL)
+    np.testing.assert_allclose(shape.volume, 1.0, atol=ATOL)
+    np.testing.assert_allclose(shape.edge_lengths, shape.edge_lengths.mean(), atol=ATOL)
+    np.testing.assert_allclose(vertices, shape.vertices)
+
+
+@pytest.mark.parametrize("n", [3, 4, 5])
+def test_uniform_dipyramids(n):
+    vertices = UniformDipyramidFamily.make_vertices(n=n)
+    shape = UniformDipyramidFamily.get_shape(n=n)
+
+    np.testing.assert_allclose(shape.centroid, 0.0, atol=ATOL)
+    np.testing.assert_allclose(shape.volume, 1.0, atol=ATOL)
+    np.testing.assert_allclose(shape.edge_lengths, shape.edge_lengths.mean(), atol=ATOL)
+    np.testing.assert_allclose(vertices, shape.vertices)
+
+
+def test_new_prism_antiprism():
+    for i, nameshape in enumerate(PrismAntiprismFamily):
+        name, shape = nameshape
+
+        if "Anti" in name:
+            n = i + 3  # count + min_n
+            comparative_shape = UniformAntiprismFamily.get_shape(n)
+        else:
+            n = (i + 3) - 8  # count + min_n + n_prism
+            comparative_shape = UniformPrismFamily.get_shape(n)
+
+        np.testing.assert_allclose(shape.volume, comparative_shape.volume, atol=ATOL)
+        np.testing.assert_allclose(
+            shape.edge_lengths, comparative_shape.edge_lengths, atol=ATOL
+        )
+
+
+def test_new_pyramid_dipyramid():
+    for i, nameshape in enumerate(PyramidDipyramidFamily):
+        name, shape = nameshape
+
+        if "Di" in name:
+            n = i + 3  # count + min_n
+            comparative_shape = UniformDipyramidFamily.get_shape(n)
+        else:
+            n = (i + 3) - 3  # count + min_n + n_pyramid
+            comparative_shape = UniformPyramidFamily.get_shape(n)
+
+        np.testing.assert_allclose(comparative_shape.centroid, 0.0, atol=ATOL)
+        np.testing.assert_allclose(shape.volume, comparative_shape.volume, atol=ATOL)
+        np.testing.assert_allclose(
+            shape.edge_lengths, comparative_shape.edge_lengths, atol=ATOL
+        )