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五立方体组合 by Idan Tal

五立方体组合 by Idan Tal
几何画板及绘图内容加载中，请稍等……
2019-03-30 18:21
立体几何变换几何作图
该范例展示了五立方体组合的几何构造。它涉及立方体、立体几何和几何作图的核心概念。通过使用GeoGebra命令如Intersect、Point、Circle、Rotate等，可以动态地展示立方体的旋转和组合。适合高中及以上学生或教师用于立体几何的教学与研究。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c, 1 - v) → C
  5. Rotate(C, 72°, A) → C'
  6. Angle(C, A, C') → α
  7. Rotate(C, 144°, A) → D
  8. Dodecahedron(C, C', D) → a, E, N, O, P, Q, R, S, T, U, faceCC'DEF, faceCFJPK, F, faceCC'GLK, faceC'DHMG, faceDEINH, faceEFJOI, faceJOTUP, faceKLQUP, faceGLQRM, faceHMRSN, faceINSTO, faceQRSTU, G, edgeCF, edgeCC', edgeC'D, edgeDE, edgeEF, edgeCK, edgeFJ, edgeJP, edgeKP, edgeKL, H, edgeGL, edgeC'G, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, edgeEI, edgeIO, edgeJO, I, edgeOT, edgeTU, edgePU, edgeQU, edgeLQ, edgeQR, edgeMR, edgeRS, edgeNS, edgeST, J, K, L, M
  9. Polygon(L, U, S, M) → q1, l, u, s, m
  10. Polygon(S, U, J, I) → q2, s_1, u_1, j, i
  11. Polygon(M, S, I, D) → q3, m_1, s_2, i_1, d
  12. Polygon(L, M, D, C) → q4, l_1, m_2, d_1, c_1
  13. Polygon(J, U, L, C) → q5, j_1, u_2, l_2, c_2
  14. Polygon(I, J, C, D) → q6, i_2, j_2, c_3, d_2
  15. Polygon(Q, M, N, T) → q7, q, m_3, n, t
  16. Polygon(T, J, E, N) → q8, t_1, j_3, e, n_1
  17. Polygon(J, T, Q, K) → q9, j_4, t_2, q_1, k
  18. Polygon(K, Q, M, C') → q10, k_1, q_2, m_4, c'
  19. Polygon(C', M, N, E) → q11, f, m_5, n_2, e_1
  20. Polygon(J, K, C', E) → q12, j_5, k_2, g, e_2
  21. Polygon(R, T, I, H) → q13, r, t_3, i_3, h
  22. Polygon(R, L, P, T) → q14, r_1, l_3, p, t_4
  23. Polygon(T, P, F, I) → q15, t_5, p_1, f_1, i_4
  24. Polygon(P, L, C', F) → q16, p_2, l_4, b, f_2
  25. Polygon(L, R, H, C') → q17, l_5, r_2, h_1, g_1
  26. Polygon(H, I, F, C') → q18, h_2, i_5, f_3, a_1
  27. Polygon(U, R, N, O) → q19, u_3, r_3, n_3, o
  28. Polygon(R, N, D, G) → q20, r_4, n_4, d_3, g_2
  29. Polygon(O, U, K, F) → q22, o_1, u_5, k_4, f_4
  30. Polygon(D, N, O, F) → q23, d_4, n_5, o_2, f_5
  31. Polygon(D, F, K, G) → q24, d_5, f_6, k_5, g_4
  32. Polygon(Q, S, H, G) → q25, q_3, s_3, h_3, g_5
  33. Polygon(S, O, E, H) → q26, s_4, o_3, e_3, h_4
  34. Polygon(O, S, Q, P) → q27, o_4, s_5, q_4, p_3
  35. Polygon(P, Q, G, C) → q28, p_4, q_5, g_6, c_4
  36. Polygon(E, O, P, C) → q29, e_4, o_5, p_5, c_5
  37. Polygon(C, G, H, E) → q30, c_6, g_7, h_5, e_5
  38. Intersect(q1, q10) → V, W, Z, A_1, B_1
  39. Intersect(q_2, l_5) → C_1
  40. Intersect(l_5, q_5) → D_1
  41. Intersect(l_1, q_5) → E_1
  42. Intersect(k_5, g_1) → I_1
  43. Intersect(k_5, l_2) → J_1
  44. Intersect(l_2, k_2) → K_1
  45. Intersect(c_6, k_2) → L_1
  46. Intersect(c_6, g_1) → M_1
  47. Intersect(j_5, f_2) → H_1
  48. Intersect(j_5, p_5) → N_1
  49. Intersect(f_6, p_5) → O_1
  50. Intersect(j_2, f_6) → P_1
  51. Intersect(f_2, j_2) → Q_1
  52. Intersect(o_1, j_4) → R_1
  53. Intersect(t_5, o_1) → S_1
  54. Intersect(j_1, t_5) → T_1
  55. Intersect(o_5, j_4) → U_1
  56. Intersect(j_1, o_5) → V_1
  57. Intersect(s_5, t_2) → W_1
  58. Intersect(s_1, t_2) → Z_1
  59. Intersect(s_1, t_4) → A_2
  60. Intersect(t_4, s_5) → B_2
  61. Intersect(n_5, i_4) → E_2
  62. Intersect(o_4, i_4) → F_2
  63. Intersect(o_4, n_1) → G_2
  64. Intersect(s_2, n_1) → H_2
  65. Intersect(s_2, n_5) → I_2
  66. Intersect(r_2, m_1) → J_2
  67. Intersect(r_4, m_1) → K_2
  68. Intersect(h_4, r_4) → L_2
  69. Intersect(h_4, m_5) → M_2
  70. Intersect(m_5, r_2) → N_2
  71. Intersect(u_2, p_4) → O_2
  72. Intersect(p_4, u_5) → P_2
  73. Intersect(u_5, p_2) → Q_2
  74. Intersect(p_2, k_1) → R_2
  75. Intersect(g_7, m_2) → S_2
  76. Intersect(a_1, g_4) → T_2
  77. Intersect(n_2, h_2) → U_2
  78. Intersect(h_2, d_4) → V_2
  79. Intersect(h_5, d_4) → W_2
  80. Intersect(d_2, h_5) → Z_2
  81. Intersect(d_2, n_2) → A_3
  82. Intersect(f_3, e_5) → B_3
  83. Intersect(d_5, e_5) → C_3
  84. Intersect(d_5, c_3) → D_3
  85. Intersect(g, c_3) → E_3
  86. Intersect(f_3, c_3) → F_3
  87. Intersect(d_5, g) → G_3
  88. Intersect(f, g_7) → H_3
  89. Intersect(g_4, f) → I_3
  90. Intersect(a_1, m_2) → J_3
  91. Intersect(i_2, e_4) → K_3
  92. Intersect(o_2, i_2) → L_3
  93. Intersect(o_2, e_2) → M_3
  94. Intersect(e_2, i_5) → N_3
  95. Intersect(e_4, i_5) → O_3
  96. PointIn(q6) → Q_3
  97. Polygon(U, R, G, K) → q21, u_4, r_5, g_3, k_3
  98. Rotate(C, 144°, A) → C'_1