Polyhedron

Qualified name: manim.mobject.three\_d.polyhedra.Polyhedron

class Polyhedron(vertex_coords, faces_list, faces_config={}, graph_config={})

Bases: VGroup

An abstract polyhedra class.

In this implementation, polyhedra are defined with a list of vertex coordinates in space, and a list of faces. This implementation mirrors that of a standard polyhedral data format (OFF, object file format).

Parameters

• vertex_coords (list[list[float] | np.ndarray]) – A list of coordinates of the corresponding vertices in the polyhedron. Each coordinate will correspond to a vertex. The vertices are indexed with the usual indexing of Python.

• faces_list (list[list[int]]) – A list of faces. Each face is a sublist containing the indices of the vertices that form the corners of that face.

• faces_config (dict[str, str | int | float | bool]) – Configuration for the polygons representing the faces of the polyhedron.

• graph_config (dict[str, str | int | float | bool]) – Configuration for the graph containing the vertices and edges of the polyhedron.

Examples

To understand how to create a custom polyhedra, let’s use the example of a rather simple one - a square pyramid.

Example: SquarePyramidScene

from manim import *

class SquarePyramidScene(ThreeDScene):
    def construct(self):
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        vertex_coords = [
            [1, 1, 0],
            [1, -1, 0],
            [-1, -1, 0],
            [-1, 1, 0],
            [0, 0, 2]
        ]
        faces_list = [
            [0, 1, 4],
            [1, 2, 4],
            [2, 3, 4],
            [3, 0, 4],
            [0, 1, 2, 3]
        ]
        pyramid = Polyhedron(vertex_coords, faces_list)
        self.add(pyramid)

In defining the polyhedron above, we first defined the coordinates of the vertices. These are the corners of the square base, given as the first four coordinates in the vertex list, and the apex, the last coordinate in the list.

Next, we define the faces of the polyhedron. The triangular surfaces of the pyramid are polygons with two adjacent vertices in the base and the vertex at the apex as corners. We thus define these surfaces in the first four elements of our face list. The last element defines the base of the pyramid.

The graph and faces of polyhedra can also be accessed and modified directly, after instantiation. They are stored in the graph and faces attributes respectively.

Example: PolyhedronSubMobjects

from manim import *

class PolyhedronSubMobjects(ThreeDScene):
    def construct(self):
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        octahedron = Octahedron(edge_length = 3)
        octahedron.graph[0].set_color(RED)
        octahedron.faces[2].set_color(YELLOW)
        self.add(octahedron)

Methods

create_faces	Creates VGroup of faces from a list of face coordinates.
extract_face_coords	Extracts the coordinates of the vertices in the graph.
get_edges	Creates list of cyclic pairwise tuples.
update_faces

Attributes

animate	Used to animate the application of any method of self.
animation_overrides
color
depth	The depth of the mobject.
fill_color	If there are multiple colors (for gradient) this returns the first one
height	The height of the mobject.
n_points_per_curve
sheen_factor
stroke_color
width	The width of the mobject.

create_faces(face_coords)

Creates VGroup of faces from a list of face coordinates.

Parameters

face_coords (list[list[list | np.ndarray]]) –

Return type

VGroup

extract_face_coords()

Extracts the coordinates of the vertices in the graph. Used for updating faces.

Return type

list[list[np.ndarray]]

get_edges(faces_list)

Creates list of cyclic pairwise tuples.

Parameters

faces_list (list[list[int]]) –

Return type

list[tuple[int, int]]