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截锥二十面体 by Guillermo Bautista

截锥二十面体 by Guillermo Bautista
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2019-12-11 23:38
圆多边形立体几何几何作图
①本范例演示了截锥二十面体的三维图形及其性质；②涉及的核心数学概念包括立体几何、多边形、圆、线段等；③作图要点提炼自构造摘要，使用了Polygon（多边形）、Icosahedron（二十面体）、Circle（圆）、Midpoint（中点）、Intersect（交点）、Segment（线段）、Mirror（镜像）等GeoGebra命令；④适合高中及以上学段学习立体几何、几何作图的学生或教师使用。

GeoGebra 命令及参数

  1. Polygon(A, B, 3, xOyPlane) → poly1, f, g, h, C
  2. Icosahedron(poly1, true) → a, D, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, faceEHK, E, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, edgeAF, F, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, edgeBH, edgeDH, edgeBE, edgeEH, G, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, edgeIK, edgeIL, edgeKL, edgeFL, H, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Circle(B, t, xOyPlane) → c
  4. Circle(A, t, xOyPlane) → d
  5. Circle(C, t, xOyPlane) → e
  6. Midpoint(E, C) → R
  7. Circle(B, t, xOyPlane) → k
  8. Circle(C, t, xOyPlane) → p
  9. Intersect(f, k, 2) → M
  10. Intersect(g, p, 2) → N
  11. Intersect(h, p, 1) → O
  12. Intersect(g, k, 1) → P
  13. Circle(A, t, xOyPlane) → q
  14. Intersect(f, q, 1) → Q
  15. Intersect(h, q, 2) → S
  16. Midpoint(edgeAF) → T
  17. Midpoint(edgeFI) → U
  18. Midpoint(edgeEI) → V
  19. Midpoint(edgeBE) → W
  20. Segment(U, C) → i
  21. Segment(T, C) → j
  22. Mirror(O, j) → O'
  23. Mirror(O', i) → O''
  24. Segment(V, C) → l
  25. Mirror(O'', l) → O'''
  26. Midpoint(edgeBD) → Z
  27. Midpoint(edgeDG) → A_1
  28. Segment(Z, A) → m
  29. Segment(A, A_1) → n
  30. Mirror(Q, m) → Q'
  31. Mirror(Q', n) → Q''
  32. Midpoint(edgeFG) → B_1
  33. Segment(A, B_1) → r
  34. Mirror(Q'', r) → Q'''
  35. Segment(B, R) → s
  36. Midpoint(edgeEH) → C_1
  37. Midpoint(edgeDH) → D_1
  38. Segment(C_1, B) → f_1
  39. Segment(D_1, B) → g_1
  40. Mirror(P, s) → P'
  41. Mirror(P', f_1) → P''
  42. Mirror(P'', g_1) → P'''
  43. Mirror(P', W) → P''_1
  44. Midpoint(edgeCE) → E_1
  45. Mirror(O''', E_1) → F_1
  46. Midpoint(edgeCI) → G_1
  47. Mirror(O'', G_1) → O'''_1
  48. Midpoint(edgeCF) → H_1
  49. Mirror(O', H_1) → O''_1
  50. Mirror(Q''', T) → I_1
  51. Segment(I, H_1) → h_1
  52. Mirror(O'''_1, h_1) → J_1
  53. Mirror(J_1, U) → K_1
  54. Segment(E, G_1) → i_1
  55. Mirror(F_1, i_1) → L_1
  56. Mirror(L_1, V) → M_1
  57. Midpoint(edgeAD) → N_1
  58. Mirror(Q', N_1) → Q''_1
  59. Mirror(P''', Z) → O_1
  60. Midpoint(edgeBH) → P_1
  61. Mirror(P'', P_1) → P'''_1
  62. Segment(D, P_1) → j_1
  63. Mirror(O_1, j_1) → Q_1
  64. Mirror(P''', j_1) → R_1
  65. Segment(H, W) → k_1
  66. Mirror(P'''_1, k_1) → S_1
  67. Mirror(P'', k_1) → P'''_2
  68. Midpoint(edgeFL) → T_1
  69. Segment(I, T_1) → l_1
  70. Mirror(J_1, l_1) → U_1
  71. Mirror(K_1, l_1) → V_1
  72. Midpoint(edgeIL) → W_1
  73. Segment(W_1, F) → m_1
  74. Mirror(J_1, m_1) → Z_1
  75. Mirror(K_1, m_1) → A_2
  76. Segment(L, B_1) → n_1
  77. Mirror(Z_1, n_1) → B_2
  78. Mirror(A_2, n_1) → C_2
  79. Segment(T_1, G) → p_1
  80. Mirror(C_2, p_1) → D_2
  81. Mirror(B_2, p_1) → E_2
  82. Segment(B_1, A) → q_1
  83. Mirror(I_1, q_1) → F_2
  84. Segment(G, N_1) → r_1
  85. Mirror(F_2, r_1) → G_2
  86. Mirror(Q'', r_1) → Q'''_1
  87. Midpoint(edgeKL) → H_2
  88. Segment(H_2, I) → s_1
  89. Mirror(U_1, s_1) → J_2
  90. Mirror(V_1, s_1) → K_2
  91. Segment(W_1, K) → t_1
  92. Mirror(K_2, t_1) → I_2
  93. Mirror(J_2, t_1) → L_2
  94. Segment(K, V) → a_1
  95. Mirror(J_2, a_1) → M_2
  96. Mirror(K_2, a_1) → N_2
  97. Segment(K, C_1) → b_1
  98. Mirror(N_2, b_1) → O_2
  99. Mirror(M_2, b_1) → P_2
  100. Midpoint(edgeHJ) → Q_2
  101. Segment(Q_2, D) → c_1
  102. Mirror(Q_1, c_1) → R_2
  103. Mirror(R_1, c_1) → S_2
  104. Segment(J, D_1) → d_1
  105. Mirror(S_2, d_1) → T_2
  106. Mirror(R_2, d_1) → U_2
  107. Segment(A_1, J) → e_1
  108. Mirror(S_2, e_1) → V_2
  109. Mirror(R_2, e_1) → W_2
  110. Midpoint(edgeGJ) → Z_2
  111. Segment(L, Z_2) → f_2
  112. Mirror(B_2, f_2) → A_3
  113. Mirror(C_2, f_2) → B_3
  114. Segment(H_2, J) → g_2
  115. Mirror(B_3, g_2) → C_3
  116. Mirror(A_3, g_2) → D_3
  117. Polygon(V_2, S_2, T_2, C_3, B_3) → poly2, v_2, s_2, t_2, c_3, b_3
  118. Polygon(V_1, Z_1, B_2, A_3, L_2) → poly3, v_1, z_1, b_2, a_3, l_2
  119. Polygon(M_1, O'''_1, J_1, U_1, J_2) → poly4, h_2, o'''_1, i_2, u_1, j_2
  120. Polygon(D_2, F_2, G_2, W_2, C_2) → poly6, d_2, n_2, p_2, w_2, c_2
  121. Polygon(Q'''_1, R_2, Q_1, O_1, Q''_1) → poly7, q'''_1, r_2, q_2, o_1, q''_1
  122. Polygon(O_2, N_2, K_2, I_2, D_3) → poly8, o_2, f_3, g_3, h_3, d_3
  123. Polygon(L_1, F_1, P''_1, P'''_2, M_2) → poly9, i_3, j_3, p''_1, p'''_2, k_3
  124. Polygon(Q'', Q', Q, S, Q''') → poly10, q'', q', q_3, s_3, q'''
  125. Segment(A, B) → l_3
  126. Segment(B, C) → m_3
  127. Segment(C, A) → n_3
  128. Polygon(P_2, S_1, P'''_1, R_1, U_2) → poly11, p_3, r_3, p'''_1, t_3, u_2
  129. Polygon(O''', N, O, O', O'') → poly12, o''', n_4, o, o', o''
  130. Polygon(P, P', P'', P''', M) → poly13, p_4, p', p'', p''', m_4
  131. Polygon(A_3, B_2, C_2, W_2, V_2, B_3) → poly14, e_3, f_4, g_4, h_4, i_4, j_4
  132. Polygon(V_2, W_2, G_2, Q'''_1, R_2, S_2) → poly15, k_4, l_4, q_4, r_4, s_4, t_4
  133. Polygon(S_2, T_2, U_2, R_1, Q_1, R_2) → poly16, a_4, b_4, c_4, d_4, e_4, f_5
  134. Polygon(C_3, T_2, U_2, P_2, O_2, D_3) → poly17, g_5, h_5, i_5, j_5, k_5, l_5
  135. Polygon(Q_1, O_1, P''', P'', P'''_1, R_1) → poly18, m_5, n_5, p_5, q_5, r_5, s_5
  136. Polygon(L_2, A_3, B_3, C_3, D_3, I_2) → poly19, t_5, a_5, b_5, c_5, d_5, e_5
  137. Polygon(P_2, S_1, P'''_2, M_2, N_2, O_2) → poly20, f_6, g_6, h_6, i_6, j_6, k_6
  138. Polygon(P'''_1, S_1, P'''_2, P''_1, P', P'') → poly21, l_6, m_6, n_6, p_6, q_6, r_6
  139. Polygon(N_2, M_2, L_1, M_1, J_2, K_2) → poly22, s_6, t_6, a_6, b_6, c_6, d_6
  140. Polygon(K_2, J_2, U_1, V_1, L_2, I_2) → poly23, e_6, f_7, g_7, h_7, i_7, j_7
  141. Polygon(U_1, J_1, K_1, A_2, Z_1, V_1) → poly24, k_7, l_7, m_7, n_7, p_7, q_7
  142. Polygon(G_2, F_2, Q'', Q', Q''_1, Q'''_1) → poly27, j_8, k_8, l_8, m_8, n_8, p_8
  143. Polygon(P''_1, P', P, N, O''', F_1) → poly28, q_8, r_8, p_9, n_9, s_8, t_8
  144. Polygon(J_1, O'''_1, O'', O', O''_1, K_1) → poly29, a_8, b_8, c_8, d_8, e_8, f_9
  145. Polygon(O''_1, O', O, S, Q''', I_1) → poly30, g_9, h_9, o_3, s_9, i_9, j_9
  146. Polygon(O, N, P, M, Q, S) → poly31, o_4, n_{10}, p_{10}, m_9, q_9, s_{10}
  147. Polygon(Q''_1, Q', Q, M, P''', O_1) → poly32, k_9, l_9, q_{10}, m_{10}, r_9, t_9
  148. Midpoint(edgeFG) → E_3
  149. Mirror(D_2, E_3) → F_3
  150. Polygon(A_2, F_3, I_1, O''_1, K_1) → poly5, a_2, k_2, m_2, o''_1, e_2
  151. Polygon(F_3, I_1, Q''', Q'', F_2, D_2) → poly25, r_7, s_7, t_7, a_7, b_7, c_7
  152. Polygon(Z_1, A_2, F_3, D_2, C_2, B_2) → poly26, d_7, e_7, f_8, g_8, h_8, i_8