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Baravelle 五边形十二面体基础

Baravelle 五边形十二面体基础
几何画板及绘图内容加载中，请稍等……
2019-03-06 20:42
多边形解析几何立体几何几何作图
本范例演示了如何通过交互式元素构建 Baravelle 五边形，并展示其作为十二面体基础的几何特性。涉及的核心数学概念包括多边形构造、相似变换、坐标几何和几何变换。作图要点主要运用了 GeoGebra 的 Intersect（交点）、Polygon（多边形）、Point（点）、Distance（距离）、Circle（圆）等命令和对象。适合高中及以上学段，用于学习立体几何和几何作图。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  3. Point(f) → F
  4. Distance(A, F) → AF
  5. Distance(A, B) → AB
  6. Circle(B, AF) → c
  7. Circle(C, AF) → d
  8. Circle(D, AF) → e
  9. Circle(E, AF) → k
  10. Intersect(c, g, 1) → G
  11. Intersect(d, h, 1) → H
  12. Intersect(e, i, 1) → I
  13. Intersect(k, j, 1) → J
  14. Polygon(F, B, G) → t1, g_1, f_1, b
  15. Polygon(G, C, H) → t2, h_1, g_2, c_1
  16. Polygon(H, D, I) → t3, i_1, h_2, d_1
  17. Polygon(I, E, J) → t4, j_1, i_2, e_1
  18. Polygon(J, A, F) → t5, f_2, j_2, a
  19. Circle(J, (r * a)) → p
  20. Intersect(p, a, 1) → K
  21. Circle(I, (r * a)) → q
  22. Circle(H, (r * a)) → s
  23. Circle(G, (r * a)) → t
  24. Circle(F, (r * a)) → k_1
  25. Intersect(q, e_1, 1) → L
  26. Intersect(k_1, b, 1) → P
  27. Intersect(s, d_1, 1) → Q
  28. Intersect(t, c_1, 1) → M
  29. Polygon(K, L, J) → t6, j_3, k_2, l
  30. Polygon(L, Q, I) → t7, i_3, l_1, q_1
  31. Polygon(Q, M, H) → t8, h_3, q_2, m
  32. Polygon(M, P, G) → t9, g_3, m_1, p_1
  33. Polygon(K, P, F) → t10, f_3, k_3, p_2
  34. Circle(K, (r * f_3)) → r_1
  35. Circle(L, (r * f_3)) → s_1
  36. Circle(Q, (r * f_3)) → t_1
  37. Circle(M, (r * f_3)) → c_2
  38. Circle(P, (r * f_3)) → d_2
  39. Intersect(r_1, f_3, 1) → N
  40. Intersect(s_1, j_3, 1) → O
  41. Intersect(t_1, i_3, 1) → R
  42. Intersect(c_2, h_3, 1) → S
  43. Intersect(d_2, g_3, 1) → T
  44. Polygon(N, K, O) → t11, o, n, k_4
  45. Polygon(O, L, R) → t12, r_2, o_1, l_2
  46. Polygon(R, Q, S) → t13, s_2, r_3, q_3
  47. Polygon(S, M, T) → t14, t_2, s_3, m_2
  48. Polygon(T, P, N) → t15, n_1, t_3, p_3
  49. Circle(N, (r * p_3)) → e_2
  50. Circle(O, (r * p_3)) → c_3
  51. Circle(R, (r * p_3)) → d_3
  52. Circle(S, (r * p_3)) → e_3
  53. Circle(T, (r * p_3)) → c_4
  54. Intersect(d_3, l_2, 1) → W
  55. Intersect(c_3, k_4, 1) → Z
  56. Polygon(O, Z, W) → t16, w, o_2, z_1
  57. Intersect(e_3, q_3, 1) → U
  58. Polygon(W, U, R) → t17, r_4, w_1, u
  59. Intersect(c_4, m_2, 1) → A_1
  60. Intersect(e_2, p_3, 1) → B_1
  61. Polygon(Z, B_1, N) → t18, n_2, z_2, b_1
  62. Polygon(U, S, A_1) → t19, a_1, u_1, s_4
  63. Polygon(A_1, B_1, T) → t20, t_4, a_2, b_2
  64. Circle(Z, (r * n_2)) → d_4
  65. Circle(W, (r * n_2)) → e_4
  66. Circle(U, (r * n_2)) → f_4
  67. Circle(A_1, (r * n_2)) → g_4
  68. Circle(B_1, (r * n_2)) → h_4
  69. Intersect(d_4, n_2, 1) → V
  70. Intersect(e_4, o_2, 1) → C_1
  71. Intersect(f_4, r_4, 1) → D_1
  72. Intersect(g_4, s_4, 1) → E_1
  73. Intersect(h_4, t_4) → F_1,
  74. Polygon(V, C_1, Z) → t21, z_3, v, c_5
  75. Polygon(C_1, D_1, W) → t22, w_2, c_6, d_5
  76. Polygon(D_1, U, E_1) → t23, e_5, d_6, u_2
  77. Polygon(E_1, A_1, F_1) → t24, f_5, e_6, a_3
  78. Polygon(V, F_1, B_1) → t25, b_3, v_1, f_6
  79. Circle(F_1, (r * a_3)) → p_4
  80. Circle(V, (r * a_3)) → q_4
  81. Circle(C_1, (r * a_3)) → g_5
  82. Circle(D_1, (r * a_3)) → h_5
  83. Circle(E_1, (r * a_3)) → k_5
  84. Intersect(q_4, b_3, 1) → G_1
  85. Intersect(g_5, z_3, 1) → H_1
  86. Intersect(h_5, w_2, 1) → I_1
  87. Intersect(k_5, u_2, 1) → J_1
  88. Intersect(p_4, a_3, 1) → K_1
  89. Polygon(G_1, H_1, V) → t26, v_2, g_6, h_6
  90. Polygon(H_1, I_1, C_1) → t27, c_7, h_7, i_4
  91. Polygon(I_1, D_1, J_1) → t28, j_4, i_5, d_7
  92. Polygon(J_1, K_1, E_1) → t29, e_7, j_5, k_6
  93. Polygon(K_1, G_1, F_1) → t30, f_7, k_7, g_7
  94. Circle(H_1, (r * v_2)) → p_5
  95. Circle(I_1, (r * v_2)) → q_5
  96. Circle(J_1, (r * v_2)) → r_5
  97. Circle(K_1, (r * v_2)) → s_5
  98. Circle(G_1, (r * v_2)) → t_5
  99. Intersect(p_5, v_2, 1) → L_1
  100. Intersect(q_5, c_7, 1) → M_1
  101. Intersect(r_5, d_7, 1) → N_1
  102. Intersect(s_5, e_7, 1) → O_1
  103. Intersect(t_5, f_7, 1) → P_1
  104. Polygon(L_1, P_1, G_1) → t31, g_8, l_3, p_6
  105. Polygon(H_1, L_1, M_1) → t32, m_3, h_8, l_4
  106. Polygon(M_1, I_1, N_1) → t33, n_3, m_4, i_6
  107. Polygon(N_1, J_1, O_1) → t34, o_3, n_4, j_6
  108. Polygon(O_1, K_1, P_1) → t35, p_7, o_4, k_8
  109. Circle(L_1, (r * g_8)) → q_6
  110. Circle(M_1, (r * g_8)) → r_6
  111. Circle(N_1, (r * g_8)) → s_6
  112. Circle(O_1, (r * g_8)) → t_6
  113. Circle(P_1, (r * g_8)) → q_7
  114. Intersect(r_6, h_8, 1) → Q_1
  115. Intersect(q_6, g_8, 1) → R_1
  116. Intersect(q_7, k_8, 1) → S_1
  117. Intersect(t_6, j_6, 1) → T_1
  118. Intersect(s_6, i_6, 1) → U_1
  119. Polygon(L_1, Q_1, R_1) → t36, r_7, l_5, q_8
  120. Polygon(Q_1, U_1, M_1) → t37, m_5, q_9, u_3
  121. Polygon(U_1, N_1, T_1) → t38, t_7, u_4, n_5
  122. Polygon(T_1, S_1, O_1) → t39, o_5, t_8, s_7
  123. Polygon(R_1, S_1, P_1) → t40, p_8, r_8, s_8
  124. Circle(Q_1, (r * l_5)) → c_8
  125. Intersect(c_8, l_5, 1) → V_1
  126. Circle(R_1, (r * l_5)) → d_8
  127. Circle(S_1, (r * l_5)) → e_8
  128. Circle(T_1, (r * l_5)) → f_8
  129. Circle(U_1, (r * l_5)) → c_9
  130. Intersect(d_8, p_8, 1) → W_1
  131. Intersect(e_8, o_5, 1) → Z_1
  132. Intersect(f_8, n_5, 1) → A_2
  133. Intersect(c_9, m_5, 1) → B_2
  134. Polygon(W_1, V_1, R_1) → t41, r_9, w_3, v_3
  135. Polygon(V_1, B_2, Q_1) → t42, q_{10}, v_4, b_4
  136. Polygon(B_2, U_1, A_2) → t43, a_4, b_5, u_5
  137. Polygon(A_2, T_1, Z_1) → t44, z_4, a_5, t_9
  138. Polygon(W_1, Z_1, S_1) → t45, s_9, w_4, z_5

AI 绘图提示语参考

画一个巴瓦雷拉五边形作为十二面体的基础，首先绘制坐标轴的交点，然后构建五边形，接着以五边形顶点为中心绘制圆，并求交点得到新的顶点，依次构建多个五边形，最后将这些五边形组合成一个立体图形，展示其作为十二面体基础的几何关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。