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立方体变为八面体

立方体变为八面体
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2017-08-15 23:54
立体几何变换几何作图
这个范例演示了如何通过几何变换将立方体转化为八面体。核心数学概念包括立体几何中的变换。使用了Sphere, Segment, Intersect, Polygon, Midpoint, Line, Distance等命令。适合高中几何课程使用。

GeoGebra 命令及参数

  1. Sphere(A, B) → a
  2. Segment(G, E) → b
  3. Segment(E, D) → c
  4. Segment(D, F) → d
  5. Segment(F, G) → e
  6. Segment(G, K) → f
  7. Segment(E, I) → g
  8. Segment(D, H) → h
  9. Segment(J, F) → i
  10. Segment(J, H) → j
  11. Segment(H, I) → k
  12. Segment(I, K) → l
  13. Segment(K, J) → m
  14. Intersect(c, a) → C, L
  15. Intersect(h, a) → M, N
  16. Intersect(g, a) → O, P
  17. Intersect(k, a) → Q, R
  18. Intersect(d, a) → S, T
  19. Intersect(i, a) → U, V
  20. Intersect(j, a) → W, Z
  21. Intersect(e, a) → A_1, B_1
  22. Intersect(m, a) → C_1, D_1
  23. Intersect(f, a) → E_1, F_1
  24. Intersect(b, a) → G_1, H_1
  25. Intersect(l, a) → I_1, J_1
  26. Polygon(T, V, A_1) → poly1, a_1, t, v
  27. Polygon(B_1, E_1, G_1) → poly2, g_1, b_1, e_1
  28. Polygon(O, H_1, C) → poly3, c_1, o, h_1
  29. Polygon(M, L, S) → poly4, s, m_1, l_1
  30. Polygon(Z, Q, N) → poly5, n, z_1, q
  31. Polygon(D_1, U, W) → poly6, w, d_1, u
  32. Polygon(C_1, J_1, F_1) → poly7, f_1, c_2, j_1
  33. Polygon(I_1, R, P) → poly8, p, i_1, r
  34. Polygon(J_1, I_1, P, O, H_1, G_1, E_1, F_1) → poly9, j_2, i_2, p_1, o_1, h_2, g_2, e_2, f_2
  35. Polygon(C, L, M, N, Q, R, P, O) → poly10, c_3, l_2, m_2, n_1, q_1, r_1, p_2, o_2
  36. Polygon(Z, N, M, S, T, V, U, W) → poly11, z_2, n_2, m_3, s_1, t_1, v_1, u_1, w_1
  37. Polygon(D_1, U, V, A_1, B_1, E_1, F_1, C_1) → poly12, d_2, u_2, v_2, a_2, b_2, e_3, f_3, c_4
  38. Polygon(B_1, A_1, T, S, L, C, H_1, G_1) → poly13, b_3, a_3, t_2, s_2, l_3, c_5, h_3, g_3
  39. Polygon(Q, Z, W, D_1, C_1, J_1, I_1, R) → poly14, q_2, z_3, w_2, d_3, c_6, j_3, i_3, r_2
  40. Midpoint(F, G) → K_1
  41. Midpoint(G, E) → L_1
  42. Midpoint(E, D) → M_1
  43. Midpoint(D, F) → N_1
  44. Midpoint(F, J) → O_1
  45. Midpoint(G, K) → P_1
  46. Midpoint(I, E) → Q_1
  47. Midpoint(D, H) → R_1
  48. Midpoint(H, J) → S_1
  49. Midpoint(J, K) → T_1
  50. Midpoint(K, I) → U_1
  51. Midpoint(I, H) → V_1
  52. Segment(Q_1, M_1) → k_2
  53. Segment(L_1, Q_1) → q_3
  54. Segment(L_1, M_1) → a_4
  55. Line(L_1, k_2) → k_1
  56. Segment(K_1, O_1) → k_3
  57. Line(N_1, k_3) → n_3
  58. Intersect(n_3, k_1) → W_1
  59. Line(M_1, W_1) → p_3
  60. Line(W_1, K_1) → r_3
  61. Segment(M_1, N_1) → s_3
  62. Line(R_1, s_3) → t_3
  63. Intersect(t_3, n_3) → Z_1
  64. Line(Z_1, O_1) → b_4
  65. Line(S_1, Z_1) → d_4
  66. Intersect(t_3, p_3) → A_2
  67. Line(Q_1, A_2) → e_4
  68. Line(A_2, V_1) → f_4
  69. Intersect(b_4, r_3) → B_2
  70. Intersect(e_4, k_1) → C_2
  71. Intersect(d_4, f_4) → D_2
  72. Segment(Z_1, B_2) → g_4
  73. Segment(B_2, C_2) → h_4
  74. Segment(C_2, A_2) → i_4
  75. Segment(A_2, Z_1) → j_4
  76. Segment(A_2, W_1) → k_4
  77. Segment(A_2, D_2) → l_4
  78. Segment(Z_1, W_1) → m_4
  79. Segment(Z_1, D_2) → n_4
  80. Segment(D_2, B_2) → p_4
  81. Segment(B_2, W_1) → q_4
  82. Segment(D_2, C_2) → r_4
  83. Segment(C_2, W_1) → s_4
  84. Sphere(A, B1) → o_3
  85. Intersect(m_4, o_3) → E_2, G_2
  86. Intersect(q_4, o_3) → H_2, I_2
  87. Intersect(s_4, o_3) → J_2, K_2
  88. Intersect(k_4, o_3) → L_2, M_2
  89. Intersect(n_4, o_3) → N_2, O_2
  90. Intersect(i_4, o_3) → P_2, Q_2
  91. Intersect(j_4, o_3) → R_2, S_2
  92. Intersect(p_4, g_4) → T_2
  93. Intersect(g_4, o_3) → U_2, V_2
  94. Intersect(h_4, o_3) → W_2, Z_2
  95. Intersect(p_4, o_3) → A_3, B_3
  96. Intersect(p_4, r_4) → C_3
  97. Intersect(r_4, o_3) → D_3, E_3
  98. Intersect(r_4, l_4) → F_3
  99. Intersect(l_4, o_3) → G_3, H_3
  100. Polygon(M_2, G_2, I_2, K_2) → poly15, m_5, g_5, i_5, k_5
  101. Polygon(S_2, N_2, U_2, E_2) → poly16, s_5, n_5, u_3, e_5
  102. Polygon(V_2, H_2, W_2, B_3) → poly17, v_3, h_5, w_3, b_5
  103. Polygon(E_3, Z_2, J_2, P_2) → poly18, e_6, z_4, j_5, p_5
  104. Polygon(G_3, Q_2, L_2, R_2) → poly19, g_6, q_5, l_5, r_5
  105. Polygon(H_3, D_3, A_3, O_2) → poly20, h_6, d_5, a_5, o_4
  106. Polygon(W_2, Z_2, J_2, K_2, I_2, H_2) → poly21, w_4, z_5, j_6, k_6, i_6, h_7
  107. Polygon(P_2, J_2, K_2, M_2, L_2, Q_2) → poly22, p_6, j_7, k_7, m_6, l_6, q_6
  108. Polygon(R_2, L_2, M_2, G_2, E_2, S_2) → poly23, r_6, l_7, m_7, g_7, e_7, s_6
  109. Polygon(U_2, E_2, G_2, I_2, H_2, V_2) → poly24, u_4, e_8, g_8, i_7, h_8, v_4
  110. Polygon(O_2, N_2, U_2, V_2, B_3, A_3) → poly25, o_5, n_6, u_5, v_5, b_6, a_6
  111. Polygon(D_3, A_3, B_3, W_2, Z_2, E_3) → poly26, d_6, a_7, b_7, w_5, z_6, e_9
  112. Polygon(H_3, D_3, E_3, P_2, Q_2, G_3) → poly27, h_9, d_7, e_{10}, p_7, q_7, g_9
  113. Polygon(O_2, H_3, G_3, R_2, S_2, N_2) → poly28, o_6, h_{10}, g_{10}, r_7, s_7, n_7
  114. Intersect(m_5, k_5) → F_2
  115. Intersect(m_7, g_8) → I_3
  116. Intersect(e_5, u_3) → J_3
  117. Distance(F_2, I_3) → distanceF2I3
  118. Distance(I_3, J_3) → distanceI3J3
  119. Intersect(v, s_1) → K_3
  120. Intersect(v, e) → L_3
  121. Intersect(l_1, d) → M_3
  122. Distance(M_3, K_3) → distanceM3K3
  123. Distance(K_3, L_3) → distanceK3L3