多面体的对偶性

GeoGebra 命令及参数

1. Point(Circle[(((1 - sqrt(5)) * A) + ((3 + sqrt(5)) * B)) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
2. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, ABCDE, AEIOJ, E, ABFKJ, BCGLF, CDHMG, DEINH, INSTO, JKPTO, FKPQL, GLQRM, HMRSN, PQRST, F, AE, AB, BC, CD, DE, AJ, EI, IO, JO, JK, G, FK, BF, FL, GL, CG, GM, HM, DH, HN, IN, H, NS, ST, OT, PT, KP, PQ, LQ, QR, MR, RS, I, J, K, L
3. Midpoint(IN) → U
4. Midpoint(I, L) → V
5. Line(V, U) → c
6. Midpoint(NS) → W
7. Midpoint(IO) → Z
8. Line(V, W) → d
9. Line(V, Z) → e
10. OrthogonalPlane(W, d) → f
11. OrthogonalPlane(U, c) → g
12. OrthogonalPlane(Z, e) → h
13. IntersectPath(h, f) → i
14. IntersectPath(f, g) → j
15. Intersect(j, i) → A_1
16. Line(V, I) → k
17. Rotate(A_1, 120°, k) → B_1
18. Rotate(B_1, 120°, k) → C_1
19. Icosahedron(A_1, C_1, B_1) → l, D_1, t1, t2, t5, t4, t3, t9, t10, t6, t7, t8, E_1, t13, t14, t19, t16, t18, t20, t17, t15, t12, t11, F_1, arete1, arete2, arete6, arete4, arete8, arete5, arete19, arete3, arete13, arete10, G_1, arete12, arete14, arete11, arete16, arete7, arete9, arete17, arete20, arete18, arete25, H_1, arete26, arete27, arete30, arete21, arete28, arete24, arete29, arete23, arete22, arete15, I_1, J_1, K_1, L_1
20. Polygon(T, A_1, O, D_1) → poly1, t, a_1, o, d_1
21. Polygon(A_1, T, G_1, S) → poly2, a_2, t_1, g_1, s
22. Polygon(A_1, S, F_1, N) → poly3, a_3, s_1, f_1, n
23. Polygon(A_1, O, C_1, I) → poly4, a_4, o_1, c_1, i_1
24. Polygon(A_1, N, B_1, I) → poly5, a_5, n_1, b_1, i_2
25. Polygon(T, D_1, P, G_1) → poly6, t_2, d_2, p, g_2
26. Polygon(R, G_1, S, F_1) → poly7, r, g_3, s_2, f_2
27. Polygon(F_1, H, B_1, N) → poly8, f_3, h_1, b_2, n_2
28. Polygon(B_1, I, C_1, E) → poly9, b_3, i_3, c_2, e_1
29. Polygon(C_1, J, D_1, O) → poly10, c_3, j_1, d_3, o_2
30. Polygon(D_1, J, H_1, K) → poly11, d_4, j_2, h_2, k_1
31. Polygon(D_1, K, J_1, P) → poly12, d_5, k_2, j_3, p_1
32. Polygon(J_1, Q, G_1, P) → poly13, j_4, q, g_4, p_2
33. Polygon(G_1, Q, L_1, R) → poly14, g_5, q_1, l_1, r_1
34. Polygon(L_1, M, F_1, R) → poly15, l_2, m, f_4, r_2
35. Polygon(F_1, M, I_1, H) → poly16, f_5, m_1, i_4, h_3
36. Polygon(D, B_1, H, I_1) → poly17, d_6, b_4, h_4, i_5
37. Polygon(D, E_1, E, B_1) → poly18, d_7, e_2, e_3, b_5
38. Polygon(E, C_1, A, E_1) → poly19, e_4, c_4, a_6, e_5
39. Polygon(C_1, J, H_1, A) → poly20, c_5, j_5, h_5, a_7
40. Polygon(H_1, F, J_1, K) → poly21, h_6, f_6, j_6, k_3
41. Polygon(F, K_1, L, J_1) → poly22, f_7, k_4, l_3, j_7
42. Polygon(J_1, L, L_1, Q) → poly23, j_8, l_4, l_5, q_2
43. Polygon(L_1, G, K_1, L) → poly24, l_6, g_6, k_5, l_7
44. Polygon(L_1, G, I_1, M) → poly25, l_8, g_7, i_6, m_2
45. Polygon(E_1, C, I_1, D) → poly26, e_6, c_6, i_7, d_8
46. Polygon(C, I_1, G, K_1) → poly27, c_7, i_8, g_8, k_6
47. Polygon(C, K_1, B, E_1) → poly28, c_8, k_7, b_6, e_7
48. Polygon(B, H_1, A, E_1) → poly29, b_7, h_7, a_8, e_8
49. Polygon(B, K_1, F, H_1) → poly30, b_8, k_8, f_8, h_8
50. Distance(V, U) → u
51. Sphere(V, (v / 5 * u)) → b