Yoshimoto Cube Net (制作8个)

Yoshimoto Cube Net (制作8个)
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2017-07-03 00:39
①本范例演示如何通过展开图制作8个Yoshimoto Cube;②涉及的核心数学概念包括立体几何、多边形构造、几何作图;③作图要点:使用Segment、Point、Line、Circle、Intersect、OrthogonalLine等GeoGebra命令进行点线圆的交点和垂线构造;④适合高中立体几何教学或几何作图练习。

GeoGebra 命令及参数

  1. Segment(B, C) → a
  2. Segment(C, D) → b
  3. Segment(D, E) → c
  4. Point(a) → F
  5. Segment(E, F) → d
  6. Segment(B, G) → e
  7. Point(b) → H
  8. Segment(G, H) → f
  9. Line(I, xAxis) → g
  10. Point(g) → J
  11. Circle(F, Segment[I, C]) → h
  12. Point(yAxis) → K
  13. Segment(K, L) → i
  14. Point(yAxis) → M
  15. Segment(M, N) → j
  16. Intersect(h, j, 1) → O
  17. Intersect(h, i, 1) → P
  18. Circle(B, Radius[h]) → k
  19. Circle(E, Radius[k]) → p
  20. Intersect(p, i, 2) → Q
  21. OrthogonalLine(I, g) → l
  22. Intersect(k, l, 2) → R
  23. Segment(O, B) → m
  24. Segment(O, F) → n
  25. Segment(F, P) → q
  26. Segment(P, C) → r
  27. Segment(C, I) → s
  28. Segment(I, H) → t
  29. Segment(H, J) → a_1
  30. Segment(J, D) → b_1
  31. Segment(D, Q) → c_1
  32. Segment(Q, E) → d_1
  33. Segment(B, R) → e_1
  34. Segment(R, G) → f_1
  35. Intersect(d, f) → S
  36. Line(L, c_1) → g_1
  37. Line(L, d_1) → h_1
  38. Line(N, f) → i_1
  39. Line(M, m) → j_1
  40. Line(M, n) → k_1
  41. Line(T, e_1) → l_1
  42. Line(T, f_1) → m_1
  43. Line(U, q) → n_1
  44. Line(U, r) → p_1
  45. Point(xAxis) → W
  46. Point(xAxis) → Z
  47. Line(V, d) → q_1
  48. Line(Z, b_1) → r_1
  49. Line(Z, a_1) → s_1
  50. Line(W, t) → t_1
  51. Line(W, s) → a_2
  52. Point(l_1) → A_1
  53. Segment(B, A_1) → b_2
  54. Point(l_1) → B_1
  55. Segment(R, B_1) → c_2
  56. Segment(A_1, B_1) → d_2
  57. Point(m_1) → C_1
  58. Segment(R, C_1) → e_2
  59. Point(m_1) → D_1
  60. Segment(G, D_1) → f_2
  61. Segment(C_1, D_1) → g_2
  62. Intersect(h_1, i_1) → E_1
  63. Segment(G, E_1) → h_2
  64. Point(i_1) → F_1
  65. Segment(S, F_1) → i_2
  66. Point(q_1) → G_1
  67. Segment(S, G_1) → j_2
  68. Segment(F_1, E_1) → k_2
  69. Intersect(m_1, q_1) → H_1
  70. Segment(E, H_1) → l_2
  71. Segment(G_1, H_1) → m_2
  72. Point(h_1) → I_1
  73. Segment(E, I_1) → n_2
  74. Point(h_1) → J_1
  75. Segment(Q, J_1) → p_2
  76. Segment(I_1, J_1) → q_2
  77. Point(g_1) → K_1
  78. Segment(D, K_1) → r_2
  79. Point(g_1) → L_1
  80. Segment(Q, L_1) → s_2
  81. Segment(K_1, L_1) → t_2
  82. Point(r_1) → M_1
  83. Segment(D, M_1) → a_3
  84. Point(r_1) → N_1
  85. Segment(J, N_1) → b_3
  86. Segment(N_1, M_1) → c_3
  87. Intersect(s_1, t_1) → O_1
  88. Segment(H, O_1) → d_3
  89. Intersect(p_1, t_1) → P_1
  90. Point(s_1) → Q_1
  91. Segment(J, Q_1) → f_3
  92. Segment(Q_1, O_1) → g_3
  93. Segment(O_1, P_1) → h_3
  94. Point(a_2) → R_1
  95. Segment(I, R_1) → i_3
  96. Point(a_2) → S_1
  97. Segment(R_1, S_1) → j_3
  98. Segment(S_1, C) → k_3
  99. Point(p_1) → T_1
  100. Segment(C, T_1) → l_3
  101. Point(p_1) → U_1
  102. Segment(T_1, U_1) → m_3
  103. Segment(U_1, P) → n_3
  104. Point(n_1) → V_1
  105. Segment(P, V_1) → p_3
  106. Intersect(k_1, n_1) → W_1
  107. Segment(V_1, W_1) → q_3
  108. Segment(W_1, F) → r_3
  109. Point(k_1) → Z_1
  110. Segment(W_1, Z_1) → s_3
  111. Segment(Z_1, O) → t_3
  112. Point(j_1) → A_2
  113. Segment(O, A_2) → a_4
  114. Point(j_1) → B_2
  115. Segment(A_2, B_2) → b_4
  116. Segment(B_2, B) → c_4
  117. Intersect(s, t) → C_2
  118. Point(h_3) → D_2
  119. Segment(C_2, D_2) → e_3
  120. Intersect(d_3, g_3) → E_2
  121. Segment(D_2, E_2) → d_4

AI 绘图提示语参考

绘制一个由六个正方形组成的展开图,这些正方形通过边相连形成网状结构,模拟一个立方体的展开。首先画出两条平行线段作为基准,然后在这两条线段上分别绘制四个正方形,接着连接这些正方形的边,形成网状结构,最后调整角度和位置,使其看起来像一个立方体的展开图。
以上提示语为根据原始绘图命令整理而来,仅供参考。