import plotly
import plotly.express as px
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

fig = px.scatter_3d(x=xs, y=ys, z=zs, 
    size=np.ones_like(xs)*0.5)
fig.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)
# 由于存在舍入誤差，所以得到的邊的數(shù)值可能不唯一
ix, jx = np.where((dMat-np.min(dMat))<0.01)

edges = []
for k in range(len(ix)):
    edges.append(pts[ix[k]].tolist() + [k])
    edges.append(pts[jx[k]].tolist() + [k])

edges = np.array(edges)

fig = px.line_3d(edges, x=0, y=1, z=2, color=3)
fig.show()

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

edges = [pts[[i,j]] for i,j in zip(ix, jx)]
from itertools import combinations
faces = [es for es in combinations(edges, 3) 
    if isFace(*es)]

ptFace = [np.unique(np.vstack(f),axis=0) for f in faces]
ptFace = np.vstack(ptFace)    

import plotly.figure_factory as ff
simplices = np.arange(len(ptFace)).reshape(-1,3)
fig = ff.create_trisurf(x=ptFace[:,0], 
    y=ptFace[:,1], z=ptFace[:,2],
    simplices=simplices)
fig.show()