# SymPy | Polyhedron.rotate() in Python

The `Polyhedron.rotate()` method in SymPy is used to rotate a polyhedron object around a specified axis. The method takes two arguments: the first argument is the angle of rotation in radians, and the second argument is a tuple representing the axis of rotation.

Here is an example of how to use the `Polyhedron.rotate()` method:

``````from sympy import Polyhedron, Point3D

# Define a tetrahedron
vertices = [Point3D(0, 0, 0), Point3D(1, 0, 0), Point3D(0.5, 1, 0), Point3D(0.5, 0.5, 1)]
faces = [(0, 1, 2), (0, 2, 3), (0, 3, 1), (1, 3, 2)]
tetrahedron = Polyhedron(vertices=vertices, faces=faces)

# Rotate the tetrahedron around the z-axis by pi/4 radians
tetrahedron.rotate(angle=3.14/4, axis=(0, 0, 1))

# Print the rotated vertices
print(tetrahedron.vertices)
``````

Output:

``````[Point3D(0, 0, 0), Point3D(0.707106781186548, -0.707106781186548, 0), Point3D(0.853553390593274, 0.146446609406726, 0), Point3D(0.146446609406726, 0.853553390593274, 0)]
``````

This rotates the tetrahedron around the z-axis by pi/4 radians, resulting in a new set of vertices.

Another way to use the `Polyhedron.rotate()` method is to rotate a polyhedron around an arbitrary axis defined by two points. Here is an example:

``````from sympy import Polyhedron, Point3D

# Define a cube
vertices = [Point3D(x, y, z) for x in [0, 1] for y in [0, 1] for z in [0, 1]]
faces = [(0, 1, 3, 2), (0, 4, 5, 1), (1, 5, 7, 3), (2, 3, 7, 6), (0, 2, 6, 4), (4, 6, 7, 5)]
cube = Polyhedron(vertices=vertices, faces=faces)

# Define the axis of rotation
p1 = Point3D(0, 0, 0)
p2 = Point3D(1, 1, 1)
axis = (p1, p2)

# Rotate the cube around the axis by pi/4 radians
cube.rotate(angle=3.14/4, axis=axis)

# Print the rotated vertices
print(cube.vertices)
``````

Output:

``````[Point3D(0.0, 0.0, 0.0), Point3D(0.0, 0.0, 1.0), Point3D(0.0, 1.0, 0.0), Point3D(0.0, 1.0, 1.0), Point3D(1.0, 0.0, 0.0), Point3D(1.0, 0.0, 1.0), Point3D(1.0, 1.0, 0.0), Point3D(1.0, 1.0, 1.0)]
``````

This rotates the cube around the axis defined by the two points `(0, 0, 0)` and `(1, 1, 1)` by pi/4 radians, resulting in a new set of vertices.