Python绘制正二十面体图形示例

import numpy as np
from itertools import product
G = (np.sqrt(5)-1)/2
def getVertex():
    pt2 =  [(a,b) for a,b in product([1,-1], [G, -G])]
    pts =  [(a,b,0) for a,b in pt2]
    pts += [(0,a,b) for a,b in pt2]
    pts += [(b,0,a) for a,b in pt2]
    return np.array(pts)

xs, ys zs = getVertex().T
ax = plt.subplot(projection='3d')
ax.scatter(xs, ys, zs)
plt.show()

def getDisMat(pts):
    N = len(pts)
    dMat = np.ones([N,N])*np.inf
    for i in range(N):
        for j in range(i):
            dMat[i,j] = np.linalg.norm([pts[i]-pts[j]])
    return dMat

pts = getVertex()
dMat = getDisMat(pts)
# 由于存在舍入误差，所以得到的边的数值可能不唯一
ix, jx = np.where((dMat-np.min(dMat))<0.01)

edges = [pts[[i,j]] for i,j in zip(ix, jx)]

ax = plt.subplot(projection='3d')
for pt in edges:
    ax.plot(*pt.T)

plt.show()

def isFace(e1, e2, e3):
    pts = np.vstack([e1, e2, e3])
    pts = np.unique(pts, axis=0)
    return len(pts)==3

from itertools import combinations
faces = [es for es in combinations(edges, 3) 
    if isFace(*es)]

ax = plt.subplot(projection='3d')
for f in faces:
    pt = np.unique(np.vstack(f), axis=0)
    try:
        ax.plot_trisurf(*pt.T)
    except:
        pass

plt.show()

# 将角度转弧度后再求余弦
cos = lambda th : np.cos(np.deg2rad(th))
sin = lambda th : np.sin(np.deg2rad(th))

# 即 Rx(th) => Matrix
Rx = lambda th : np.array([
    [1, 0,       0],
    [0, cos(th), -sin(th)],
    [0, sin(th), cos(th)]])
Ry = lambda th : np.array([
    [cos(th),  0, sin(th)],
    [0      ,  1, 0],
    [-sin(th), 0, cos(th)]
])

ax = plt.subplot(projection='3d')
for f in faces:
    pt = np.unique(np.vstack(f), axis=0)
    pt = Rx(1)@Ry(1)@pt.T
    ax.plot_trisurf(*pt)

for pt in edges:
    pt = Rx(1)@Ry(1)@pt.T
    ax.plot(*pt, lw=2, color='blue')

plt.show()