3D アニメーション　点と点を直線で繋げたい

こんにちは。
現在jupyter notebookにて
下記のような3次元座標空間の中で3つの点が動くプログラムを組んでいるのですが
point1とpoint2
point2とpoint3を繋ぐ線を引きたいと考えております。


%matplotlib notebook
%matplotlib nbagg
import mpl_toolkits.mplot3d as plt3d
from mpl_toolkits.mplot3d import Axes3D 
import matplotlib.pyplot as plt 
import matplotlib.animation as animation
from IPython.display import HTML
import numpy as np



def init():
    ax.set_xlim(-10,10)
    ax.set_ylim(-10,10)
    ax.set_zlim(-10,10)
    ax.set_xlabel("x")
    ax.set_ylabel("y")
    ax.set_zlabel("z")
    ax.set_aspect('equal')

    return lines1,lines2,lines3



x1,y1,z1 = [],[],[]
x2,y2,z2 = [],[],[]
x3,y3,z3 = [],[],[]

x1=[1,8,3,6,3,6,4]
y1=[9,1,5,3,7,3,8]
z1=[0,2,5,7,1,0,5]

x2=[-1,-8,-3,-6,-3,-6,-4]
y2=[-9,-1,-5,-3,-7,-3,-8]
z2=[1,3,1,2,4,2,4]

x3=[6,8,3,0,7,1,2]
y3=[1,5,6,4,7,0,8]
z3=[2,2,4,4,0,0,7]

def update_lines(num,data1,data2,data3,lines1,lines2,lines3,points1,points2, points3):
    for dat1,dat2,dat3,line1,line2,line3,point1,point2, point3 in zip(data1,data2,data3,lines1,lines2,lines3,points1,points2, points3):
        point1.set_data(dat1[0:2, num+1])
        point1.set_3d_properties(dat1[2, num+10])
        point2.set_data(dat2[0:2, num+1])
        point2.set_3d_properties(dat2[2, num+10])
        point3.set_data(dat3[0:2, num+1])
        point3.set_3d_properties(dat3[2, num+10])

    return lines1,lines2,lines3,

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

t = np.linspace(-3, 2, 30)
z = np.linspace(-3, 2, 30)
r = np.linspace(-3, 2, 30)

x1, y1, z1 = x1, y1, z1
x2, y2, z2 = x2, y2, z2
x3, y3, z3 = x3, y3, z3

data1 = np.array([[x1,y1,z1]])
data2 = np.array([[x2,y2,z2]])
data3 = np.array([[x3,y3,z3]])

lines1=[ax.plot(dat[0, 0:1], dat[1, 0:1], dat[2, 0:1] )[0] for dat in data1]
lines2=[ax.plot(dat[0, 0:1], dat[1, 0:1], dat[2, 0:1] )[0] for dat in data2]
lines3=[ax.plot(dat[0, 0:1], dat[1, 0:1], dat[2, 0:1] )[0] for dat in data3]

points1=[ax.plot(dat[0, 0:1], dat[1, 0:1], dat[2, 0:1], 'o-')[0] for dat in data1]
points2=[ax.plot(dat[0, 0:1], dat[1, 0:1], dat[2, 0:1], 'o-')[0] for dat in data2]
points3=[ax.plot(dat[0, 0:1], dat[1, 0:1], dat[2, 0:1], 'o-')[0] for dat in data3]

line_ani = animation.FuncAnimation(fig, update_lines, 172, fargs=(data1,data2,data3,lines1,lines2,lines3, points1,points2,points3),
                                   interval=10, init_func=init, blit=True, repeat=True,)