交错四面体模型

GeoGebra 命令及参数

1. OrthogonalLine(A, xOyPlane) → f
2. Point(f) → D_1
3. Line(A, B) → g
4. Point(g) → V
5. Plane(D_1, V, A) → d_1
6. Point(g) → C
7. Midpoint(C, V) → C_1
8. Point(Circle[C, Distance[A, C], Segment[A, C]]) → F
9. Rotate(C, 45°, F) → C'
10. Point(Circle[C', Distance[F, C'], Segment[F, C']]) → P
11. Cube(F, C', P) → n, Q, facePQUT, faceRSTU, edgeFQ, edgeC'F, edgeC'P, edgePQ, edgeFR, edgeQU, edgeRU, edgeRS, R, edgeC'S, edgeST, edgePT, edgeTU, S, T, U, faceC'FQP, faceFQUR, faceC'FRS, faceC'PTS
12. Cube(A, C, F) → b, G, faceFGKJ, faceHIJK, edgeAG, edgeAC, edgeCF, edgeFG, edgeAH, edgeGK, edgeHK, edgeHI, H, edgeCI, edgeIJ, edgeFJ, edgeJK, I, J, K, faceACFG, faceAGKH, faceACIH, faceCFJI
13. Plane(A, F, J) → d
14. Line(A, F) → q
15. Point(q) → W
16. Midpoint(W, F) → F_1
17. Rotate(C, (2 * α), C_1, d_1) → C'_1
18. Sphere(C'_1, 1) → u_1
19. Rotate(R, (-α), F, d) → R'
20. Line(F, L) → t
21. OrthogonalLine(W, t, d) → g_1
22. Intersect(t, g_1) → A_1
23. Circle(A_1, 1, d) → q_1
24. Intersect(t, q_1) → I_1, J_1
25. Rotate(F, (-2 * α), F_1, d) → F'_1
26. Plane(C'_1, I_1, F'') → o_1
27. OrthogonalLine(C'_1, o_1) → t_1
28. Intersect(t_1, u_1) → K_1, L_1
29. OrthogonalLine(L_1, d_1) → g_2
30. Intersect(g_2, d_1) → M_1
31. OrthogonalLine(C, g, xOyPlane) → i
32. Circle(C, A, xOyPlane) → c
33. Intersect(i, c) → D, E
34. Polygon(A, C, E) → poly1, e, a, c_1
35. OrthogonalLine(F, q, xOyPlane) → h_1
36. Vector(E, A_1) → v
37. Rotate(Translate[Rotate[F, (-α), h_1], v], β, q) → F'
38. Plane(F'', F', F) → b_1
39. Angle(F'', F, F', b_1) → δ
40. Polygon(C, F, J) → poly2, j, c_2, f_1
41. Polygon(A, C, J) → poly3, j_1, a_1, c_3
42. Polygon(A, F, J) → poly4, j_2, a_2, f_2
43. Translate({poly1, poly2, poly3, poly4}, Vector[A, A]) → SkewTet
44. Translate(Rotate[SkewTet, (-α), h_1], v) → SkewTet'_1
45. OrthogonalLine(F, b_1) → k_1
46. OrthogonalLine(A_1, q, d) → i_1
47. Intersect(q, i_1) → B_1
48. Polygon(F, S, C') → poly5, c'_1, f_3, s
49. Intersect(g, c) → M, N
50. OrthogonalLine(M, g, xOyPlane) → l
51. OrthogonalLine(A, g, xOyPlane) → h
52. OrthogonalLine(F, h, xOyPlane) → m
53. Intersect(l, m) → O
54. Rotate(O, 45°, F) → O'
55. Polygon(S, F, O') → poly8, o'_2, s_2, f_5
56. Polygon(S, O', C') → poly7, c'_2, s_1, o'_1
57. Polygon(C', F, O') → poly6, o', c', f_4
58. Mirror(SkewTet, d) → SkewTet'
59. Sequence(Rotate[{SkewTet, SkewTet'}, (n * 90°), f], n, 0, 3, 1) → pos1
60. Circle(i, C) → k
61. Vector(E, W) → u
62. Translate({poly5, poly6, poly7, poly8}, u) → SkewTet2
63. Mirror(SkewTet2, d) → SkewTet2'
64. Sequence(Rotate[{SkewTet2, SkewTet2'}, (n * 90°), f], n, 0, 3, 1) → pos2
65. Translate(Q, u) → Q'
66. Plane(V, faceCFJI) → o
67. OrthogonalLine(Q', g, xOyPlane) → r
68. Intersect(r, g) → Z
69. Rotate(SkewTet2, 180°, r) → SkewTet3_1
70. Mirror(SkewTet3_1, d) → SkewTet3'_1
71. Rotate(SkewTet, (-(180°)), i) → SkewTet3'
72. Rotate(SkewTet', (-(180°)), m) → SkewTet3
73. Sequence(Rotate[{SkewTet3, SkewTet3'}, (n * 90°), f], n, 0, 3, 1) → pos3
74. Mirror(pos1, xOyPlane) → pos4
75. Circle(F, R, d) → p
76. Rotate(Rotate[SkewTet'_1, β, q], γ, k_1) → SkewTet01
77. Mirror(SkewTet01, d) → SkewTet01'
78. Vector(W, W) → w
79. Translate(SkewTet01, w) → SkewTet01'_1
80. Sequence(Rotate[{SkewTet01'_1, Mirror[SkewTet01'_1, d]}, (n * 90°), f], n, 0, 3, 1) → pos01
81. Rotate(Translate[Rotate[poly4, (-α), h_1], v], β, q) → poly9
82. Mirror(poly9, d) → poly9'
83. Point(pos01) → E_1
84. Circle(C_1, C, d_1) → e_1
85. Circle(F_1, F, d) → p_1
86. Intersect(h_1, m) → G_1
87. Segment(F, J) → l_1
88. Point(xAxis) → H_1
89. Segment(F'', I_1) → m_1
90. Segment(C'_1, F'') → n_1
91. Polygon(ZZZ, C'_1, F'') → poly10, h_2, k_2, l_2
92. Segment(C'_1, I_1) → r_1
93. Polygon(ZZZ, I_1, F'') → poly11, i_2, m_2, n_2
94. Polygon(F'', I_1, C'_1) → poly12, c'_4, f''_2, i_3
95. Polygon(ZZZ, C'_1, I_1) → poly13, p_2, q_2, r_2
96. Sequence(Rotate[{{poly10, poly11, poly12, poly13}, Mirror[{poly10, poly11, poly12, poly13}, d]}, (n * 90°), f], n, 0, 3, 1) → pos10
97. Distance(C'_1, F'_1) → distanceC'1F'1