3D 座標架的製作
Author: 藍邦偉  老師

正二十面體

單位向量

單位點

座標軸

xy平面

x

y

z

α = 2.9551914894767988 rad (slider from 0 to 6.283185307179586, step 0.01*°)
β = 0.09250245035569947 rad (slider from 0 to 6.283185307179586, step 0.01*°)
L = 5 (slider from 1 to 10, step 1)
O = (49.17406903869823, 35.62586588162261)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-sin(α), cos(α) * cos(β))
Z_{unit}: O + (0, -sin(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
w = Vector(O, Z_{unit})
x_{Axis} = Vector(O - L * u, O + L * u)
y_{Axis} = Vector(O - L * v, O + L * v)
z_{Axis} = Vector(O - L * w, O + L * w)
多邊形1, d, e, f, g = Polygon(O + L * u + L * v, O - L * u + L * v, O - L * u - L * v, O + L * u - L * v)
h = false
i = false
j = false
k = false
A_１: O
b: O * (0 + v + 1.618 * u)
A: O + v + 1.618 * w
D: O - v + 1.618 * w
C: O + v - 1.618 * w
B: O - v - 1.618 * w
E: O + u + 1.618 * v
F: O - u - 1.618 * v
G: O + u - 1.618 * v
H: O - u + 1.618 * v
I: O + 1.618 * u + w
J: O - 1.618 * u - w
K: O + 1.618 * u - w
M: O - 1.618 * u + w
c = Segment(D, G)
m = Segment(D, I)
n = Segment(G, I)
p = Segment(I, K)
q = Segment(K, G)
r = Segment(A, I)
s = Segment(D, A)
t = Segment(A, E)
a_1 = Segment(E, I)
b_1 = Segment(K, E)
c_1 = Segment(A, H)
d_1 = Segment(H, E)
e_1 = Segment(E, C)
f_1 = Segment(C, H)
g_1 = Segment(K, C)
h_1 = Segment(A, M)
i_1 = Segment(H, M)
j_1 = Segment(J, M)
k_1 = Segment(J, H)
l_1 = Segment(J, C)
m_1 = Segment(M, D)
n_1 = Segment(D, F)
p_1 = Segment(M, F)
q_1 = Segment(F, G)
r_1 = Segment(F, B)
s_1 = Segment(F, J)
t_1 = Segment(J, B)
a_2 = Segment(G, B)
b_2 = Segment(B, K)
c_2 = Segment(B, C)
d_2 = Segment(A, C)
e_2 = Segment(D, B)
poly1, a_3, d_3, b_3, c_3 = Polygon(A, D, B, C)
poly2, e_3, g_2, f_2, h_2 = Polygon(E, G, F, H)
P_a, h_3, a_4, e_4 = Polygon(A, E, H)
P_b, e_5, a_5, i_3 = Polygon(A, I, E)
P_c, e_6, k_3, i_4 = Polygon(K, I, E)
P_d, e_7, k_4, c_4 = Polygon(K, C, E)
P_e, e_8, h_4, c_5 = Polygon(H, C, E)
P_f, j_3, h_5, c_6 = Polygon(H, C, J)
P_g, j_4, h_6, m_3 = Polygon(H, M, J)
P_h, a_6, h_7, m_4 = Polygon(H, M, A)
P_i, a_7, d_4, m_5 = Polygon(D, M, A)
P_j, a_8, d_5, i_5 = Polygon(D, I, A)
P_k, g_3, d_6, i_6 = Polygon(D, I, G)
P_l, g_4, k_5, i_7 = Polygon(K, I, G)
P_m, g_5, k_6, b_4 = Polygon(K, B, G)
P_n, c_7, k_7, b_5 = Polygon(K, B, C)
P_o, c_8, j_5, b_6 = Polygon(J, B, C)
P_p, a, l_2, n_2 = Polygon(B, J, F)
P_q, f_4, g_6, b_8 = Polygon(G, B, F)
P_r, f_5, g_7, d_7 = Polygon(G, D, F)
P_s, f_6, m_6, d_8 = Polygon(M, D, F)
P_t, f_7, m_7, j_7 = Polygon(M, J, F)