Platonic Solids

PyVista wraps the vtk.vtkPlatonicSolidSource filter as pyvista.PlatonicSolid().

import numpy as np

import pyvista as pv
from pyvista import examples

We can either use the generic PlatonicSolid() and specify the different kinds of solids to generate, or we can use the thin wrappers:

• pyvista.Tetrahedron()

• pyvista.Octahedron()

• pyvista.Dodecahedron()

• pyvista.Icosahedron()

• pyvista.Cube() (implemented via a different filter)

Let’s generate all the Platonic solids, along with the teapotahedron.

kinds = [
    'tetrahedron',
    'cube',
    'octahedron',
    'dodecahedron',
    'icosahedron',
]
centers = [
    (0, 1, 0),
    (0, 0, 0),
    (0, 2, 0),
    (-1, 0, 0),
    (-1, 2, 0),
]

solids = [pv.PlatonicSolid(kind, radius=0.4, center=center) for kind, center in zip(kinds, centers)]

# download and align teapotahedron
teapot = examples.download_teapot()
teapot.rotate_x(90, inplace=True)
teapot.rotate_z(-45, inplace=True)
teapot.scale(0.16, inplace=True)
teapot.points += np.array([-1, 1, 0]) - teapot.center
solids.append(teapot)

Now let’s plot them all.

Note

VTK has known issues when rendering shadows on certain window sizes. Be prepared to experiment with the window_size parameter. An initial window size of (1000, 1000) seems to work well, which can be manually resized without issue.

p = pv.Plotter(window_size=[1000, 1000])
for ind, solid in enumerate(solids):
    # only use smooth shading for the teapot
    smooth_shading = ind == len(solids) - 1
    p.add_mesh(
        solid,
        color='silver',
        smooth_shading=smooth_shading,
        specular=1.0,
        specular_power=10,
    )
p.view_vector((5.0, 2, 3))
p.add_floor('-z', lighting=True, color='lightblue', pad=1.0)
p.enable_shadows()
p.show()

The Platonic solids come with cell scalars that index each face of the solids.