How to calculate the midpoints of each triangle edges of an icosahedron

Am trying to compute the midpoints of each triangle edges of an icosahedron to get an icosphere which is the composion of an icosahedron subdivided in 6 or more levels. i tried to calculate the newly created vertices of each edges but some points wore missing. I tried to normalize each mid point but still the points woren't evenly spread out and some points wore missing.

import matplotlib.pyplot as pltimport numpy as npnum_points = 12indices = np.arange(0, num_points, dtype='float')r = 1vertices = [ [0.0, 0.0, -1.0], [0.0, 0.0, 1.0] ] # poles# icosahedronfor i in range(num_points):    theta = np.arctan(1 / 2) * (180 / np.pi) # angle 26 degrees    phi = np.deg2rad(i * 72)    if i >= (num_points / 2):        theta = -theta        phi = np.deg2rad(36 + i * 72)    x = r * np.cos(np.deg2rad(theta)) * np.cos(phi)    y = r * np.cos(np.deg2rad(theta)) * np.sin(phi)    z = r * np.sin(np.deg2rad(theta))    vertices.append([x, y, z])vertices = np.array(vertices)

Icosahedron:

# Triangle Subdivisionfor _ in range(2):    for j in range(0, len(vertices), 3):        v1 = vertices[j]        v2 = vertices[j + 1]          v3 = vertices[j + 2]        m1_2 = ((v1 + v2) / 2)        m2_3 = ((v2 + v3) / 2)        m1_3 = ((v1 + v3) / 2)        m1_2 /= np.linalg.norm(m1_2)        m2_3 /= np.linalg.norm(m2_3)        m1_3 /= np.linalg.norm(m1_3)        vertices = np.vstack([vertices, m1_2, m2_3, m1_3,])print(vertices)plt.figure().add_subplot(projection='3d').scatter(vertices[:, 0], vertices[:, 1], vertices[:, 2])plt.show()

icosphere attempt:

I used this as reference to create an icosahedronhttps://www.songho.ca/opengl/gl_sphere.htmland what am expecting to achive is this:

Geodesic polyhedro:

I tried debugging the subdivision of each edges and it performed well:

import numpy as npimport matplotlib.pyplot as pltvertices = [[1, 1], [2, 3], [3, 1]]vertices = np.array(vertices)for j in range(2):    for i in range(0, len(vertices), 3):        v1 = vertices[i]        v2 = vertices[i + 1]        v3 = vertices[i + 2]        m1_2 = (v1 + v2) / 2        m1_3 = (v1 + v3) / 2        m2_3 = (v2 + v3) / 2        vertices = np.vstack([vertices, m1_2, m1_3, m2_3])plt.figure().add_subplot().scatter(vertices[:, 0], vertices[:, 1])plt.plot(vertices[:, 0], vertices[:, 1], '-ok')plt.show()

Midpoints of each edgeL