Python/matplotlib : plotting a 3d cube, a sphere and a vector?

I search how to plot something with less instruction as possible with matplotlib but I don't find any help for this in the documentation.

I want to plot the following things:

  • a wireframe cube centered in 0 with a side length of 2
  • a "wireframe" sphere centered in 0 with a radius of 1
  • a point at coordinates [0, 0, 0]
  • a vector that starts at this point and goes to [1, 1, 1]

How to do that?

It is a little complicated, but you can draw all the objects by the following code:

    from mpl_toolkits.mplot3d import Axes3D
    import matplotlib.pyplot as plt
    import numpy as np
    from itertools import product, combinations

    fig = plt.figure()
    ax = fig.gca(projection='3d')

    # draw cube
    r = [-1, 1]
    for s, e in combinations(np.array(list(product(r, r, r))), 2):
        if np.sum(np.abs(s-e)) == r[1]-r[0]:
            ax.plot3D(*zip(s, e), color="b")

    # draw sphere
    u, v = np.mgrid[0:2*np.pi:20j, 0:np.pi:10j]
    x = np.cos(u)*np.sin(v)
    y = np.sin(u)*np.sin(v)
    z = np.cos(v)
    ax.plot_wireframe(x, y, z, color="r")

    # draw a point
    ax.scatter([0], [0], [0], color="g", s=100)

    # draw a vector
    from matplotlib.patches import FancyArrowPatch
    from mpl_toolkits.mplot3d import proj3d

    class Arrow3D(FancyArrowPatch):

        def __init__(self, xs, ys, zs, *args, **kwargs):
            FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
            self._verts3d = xs, ys, zs

        def draw(self, renderer):
            xs3d, ys3d, zs3d = self._verts3d
            xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
            self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
            FancyArrowPatch.draw(self, renderer)

    a = Arrow3D([0, 1], [0, 1], [0, 1], mutation_scale=20,
                lw=1, arrowstyle="-|>", color="k")