立方体六个孔的几何构造

GeoGebra 命令及参数

1. CurveCartesian(cos(t), 2, sin(t), t, 0, (2 * pi)) → a
2. CurveCartesian((2 * cos(t)), 2, (2 * sin(t)), t, 0, (2 * pi)) → b
3. Surface(((1 - u) * a(t)) + (u * b(t)), u, 0, 1, t, 0, (4 * pi)) → c
4. CurveCartesian(cos(t), -2, sin(t), t, 0, (2 * pi)) → d
5. CurveCartesian((2 * cos(t)), -2, (2 * sin(t)), t, 0, (2 * pi)) → e
6. Surface(((1 - u) * d(t)) + (u * e(t)), u, 0, 1, t, 0, (4 * pi)) → f
7. CurveCartesian(cos(t), sin(t), 2, t, 0, (2 * pi)) → g
8. CurveCartesian((2 * cos(t)), (2 * sin(t)), 2, t, 0, (2 * pi)) → h
9. Surface(((1 - u) * g(t)) + (u * h(t)), u, 0, 1, t, 0, (4 * pi)) → i
10. CurveCartesian(cos(t), sin(t), -2, t, 0, (2 * pi)) → j
11. CurveCartesian((2 * cos(t)), (2 * sin(t)), -2, t, 0, (2 * pi)) → k
12. Surface(((1 - u) * j(t)) + (u * k(t)), u, 0, 1, t, 0, (4 * pi)) → l
13. CurveCartesian(2, cos(t), sin(t), t, 0, (2 * pi)) → m
14. CurveCartesian(2, (2 * cos(t)), (2 * sin(t)), t, 0, (2 * pi)) → n
15. Surface(((1 - u) * m(t)) + (u * n(t)), u, 0, 1, t, 0, (4 * pi)) → o
16. CurveCartesian(-2, cos(t), sin(t), t, 0, (2 * pi)) → p
17. CurveCartesian(-2, (2 * cos(t)), (2 * sin(t)), t, 0, (2 * pi)) → q
18. Surface(((1 - u) * p(t)) + (u * q(t)), u, 0, 1, t, 0, (4 * pi)) → r
19. Midpoint(A, C) → I
20. Midpoint(A, B) → J
21. Polygon(A, I, J) → t1, j_1, a_1, i_1
22. Rotate(t1, 90°, zAxis) → t1'
23. Rotate(t1, 180°, zAxis) → t1'_{1}
24. Rotate(t1, 270°, zAxis) → t1'_{2}
25. Rotate(t1, -90°, xAxis) → t1'_{3}
26. Rotate(t1'_{3}, 90°, yAxis) → t2
27. Rotate(t2, 90°, yAxis) → t2'
28. Rotate(t2, 180°, yAxis) → t2'_{1}
29. Rotate(t2, 90°, zAxis) → t2'_{2}
30. Rotate(t2'_{2}, -90°, xAxis) → t3
31. Rotate(t2'_{2}, -180°, xAxis) → t4
32. Rotate(t2'_{2}, -270°, xAxis) → t5
33. Mirror(t4, eq1) → t4'
34. Mirror(t3, eq1) → t3'
35. Mirror(t2'_{2}, eq1) → t6
36. Mirror(t5, eq1) → t5'
37. Mirror(t2'_{1}, s) → t7
38. Mirror(t2', s) → t2''
39. Mirror(t2, s) → t2'_{3}
40. Mirror(t1'_{3}, s) → t8
41. Mirror(t1'_{1}, t) → t9
42. Mirror(t1'_{2}, t) → t10
43. Mirror(t1, t) → t1'_{4}
44. Mirror(t1', t) → t1''
45. Segment(D, B) → f_1
46. Segment(B, A) → g_1
47. Segment(A, C) → h_1
48. Segment(C, D) → k_1
49. Segment(B, F) → l_1
50. Segment(D, H) → m_1
51. Segment(H, F) → n_1
52. Segment(F, E) → p_1
53. Segment(E, A) → q_1
54. Segment(E, G) → r_1
55. Segment(G, C) → s_1
56. Segment(G, H) → t_1
57. CurveCartesian(cos(t), 2, sin(t), t, 0, (2 * pi)) → u