立方体三等分谜题

GeoGebra 命令及参数

1. Sphere(A, a) → b
2. PointIn(b) → D
3. Segment(A, D) → c
4. OrthogonalPlane(D, c) → d
5. Sphere(D, a) → e
6. IntersectPath(d, e) → f
7. Point(f) → E
8. Plane(A, D, E) → g
9. Sphere(E, a) → h
10. IntersectPath(g, h) → k
11. Line(E, c) → i
12. Intersect(i, k) → F, G
13. Polygon(A, D, E, G) → poly1, a_1, d_1, e_1, g_1
14. OrthogonalPlane(A, i) → j
15. IntersectPath(j, b) → p
16. OrthogonalLine(A, g) → l
17. Intersect(l, p) → H, I
18. Pyramid(poly1, I) → m, faceADI, faceDEI, faceEGI, faceAGI, edgeAI, edgeDI, edgeEI, edgeGI
19. Line(I, Segment[A, G]) → n
20. Point(n) → B
21. OrthogonalPlane(B, n) → o
22. Circle(B, a, j) → q
23. IntersectPath(j, o) → r
24. Line(B, Segment[A, D]) → b_1
25. Point(q) → C
26. Line(B, C) → s
27. Sphere(B, a) → t
28. Intersect(b_1, t) → J, K
29. Plane(B, C, K) → u
30. Line(C, b_1) → c_1
31. Line(K, s) → f_1
32. Intersect(f_1, c_1) → L
33. Polygon(B, C, L, K) → poly2, b_2, c_2, l_1, k_1
34. OrthogonalLine(B, u) → h_1
35. Intersect(h_1, q) → M, N
36. Pyramid(poly2, N) → v, faceBCN, faceCLN, faceKLN, faceBKN, edgeBN, edgeCN, edgeLN, edgeKN
37. OrthogonalLine(I, j) → i_1
38. Point(i_1) → O
39. Sphere(O, a) → w
40. Plane(I, A, D) → j_1
41. IntersectPath(j_1, w) → q_1
42. Point(q_1) → P
43. Segment(O, P) → m_1
44. Line(O, Segment[A, G]) → n_1
45. Intersect(n_1, w) → Q, R
46. Line(R, Segment[O, P]) → p_1
47. Line(P, n_1) → r_1
48. Intersect(p_1, r_1) → S
49. Polygon(O, P, S, R) → poly3, o_1, p_2, s_1, r_2
50. Plane(O, R, S) → t_1
51. OrthogonalLine(O, t_1) → a_2
52. Intersect(a_2, w) → T, U
53. Pyramid(poly3, T) → u_1, faceOPT, facePST, faceRST, faceORT, edgeOT, edgePT, edgeST, edgeRT