积极 AI Logo 积极 AI

八面体截平面演示

八面体截平面演示
几何画板及绘图内容加载中，请稍等……
2015-12-21 07:25
多边形立体几何几何作图
①本范例演示八面体与多个截平面的交线及其形成的几何图形；②涉及的核心数学概念包括平面、逻辑推理、四边形、方差、等腰三角形、几何构造；③作图要点提炼自构造摘要，使用了Intersect（交点）、Point（点）、Mirror（镜像）、Circle（圆）、AngularBisector（角平分线）、Octahedron（八面体）、Line（直线）、Segment（线段）、Polygon（多边形）、Plane（平面）、IntersectPath（路径交点）、Sphere（球体）、PointIn（点在对象内）、Midpoint（中点）、Ray（射线）、Rotate（旋转）、Star（星形）等GeoGebra命令/对象；④适合高中及以上学段学习立体几何、几何作图及空间想象能力。

GeoGebra 命令及参数

  1. Intersect(yAxis, zAxis) → O
  2. Point(xAxis) → A
  3. Mirror(A, O) → B
  4. Mirror(C, O) → D
  5. Mirror(E, O) → F
  6. Circle(O, x(A), zAxis) → c
  7. Circle(O, x(A), yAxis) → d
  8. Circle(O, x(A), xAxis) → e
  9. AngularBisector(A, O, C) → a
  10. AngularBisector(C, O, E) → b
  11. AngularBisector(E, O, A) → f
  12. Octahedron(A, C, F) → g, G, face7, face8, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, H, edge9, edge10, edge11, edge12, I, face1, face2, face3, face4, face5, face6
  13. Mirror(αAngle, O) → αAngle'
  14. Mirror(βAngle, O) → βAngle'
  15. Mirror(γAngle, O) → γAngle'
  16. Line(γAngle, yAxis) → h
  17. Line(γAngle', yAxis) → i
  18. Segment(γAngle', γAngle) → j
  19. Circle(γAngle, x(A), j) → k
  20. Intersect(h, k) → J, K
  21. Segment(K, J) → l
  22. Circle(γAngle', x(A), j) → p
  23. Intersect(i, p) → L, M
  24. Segment(J, L) → m
  25. Segment(L, M) → n
  26. Segment(M, K) → q
  27. Polygon(M, L, J, K) → poly1, m_1, l_1, j_1, k_1
  28. Segment(βAngle, βAngle') → r
  29. Line(βAngle', xAxis) → s
  30. Line(βAngle, xAxis) → t
  31. Circle(βAngle', x(A), r) → c_1
  32. Circle(βAngle, x(A), r) → d_1
  33. Intersect(s, c_1) → N, P
  34. Intersect(t, d_1) → Q, R
  35. Segment(N, P) → a_1
  36. Segment(P, R) → b_1
  37. Segment(R, Q) → e_1
  38. Segment(Q, N) → f_1
  39. Polygon(Q, R, P, N) → poly2, q_1, r_1, p_1, n_1
  40. Segment(αAngle, αAngle') → g_1
  41. Line(αAngle', zAxis) → h_1
  42. Line(αAngle, zAxis) → i_1
  43. Circle(αAngle', x(A), g_1) → s_1
  44. Circle(αAngle, x(A), g_1) → t_1
  45. Intersect(i_1, t_1) → S, T
  46. Intersect(h_1, s_1) → U, V
  47. Segment(U, S) → a_2
  48. Segment(S, T) → b_2
  49. Segment(T, V) → c_2
  50. Segment(V, U) → d_2
  51. Polygon(S, T, V, U) → poly3, s_2, t_2, v, u_1
  52. Plane(T, V, U) → o_1
  53. IntersectPath(o_1, face1) → f_2
  54. IntersectPath(o_1, face3) → g_2
  55. Intersect(o_1, face3) → W, Z
  56. IntersectPath(o_1, face2) → h_2
  57. Intersect(o_1, face2) → A_1, B_1
  58. IntersectPath(o_1, poly3) → i_2
  59. Intersect(o_1, poly3) → C_1
  60. IntersectPath(o_1, face8) → j_2
  61. Intersect(o_1, face8) → D_1, E_1
  62. IntersectPath(o_1, face7) → k_2
  63. Intersect(o_1, face7) → F_1, G_1
  64. IntersectPath(o_1, face4) → l_2
  65. Intersect(o_1, face4) → H_1, I_1
  66. IntersectPath(o_1, face5) → m_2
  67. Intersect(o_1, face5) → J_1, K_1
  68. IntersectPath(o_1, face6) → n_2
  69. Intersect(o_1, face6) → L_1, M_1
  70. Plane(P, N, Q) → v_1
  71. IntersectPath(v_1, face5) → p_2
  72. Intersect(v_1, face5) → N_1, O_1
  73. IntersectPath(v_1, face4) → q_2
  74. Intersect(v_1, face4) → P_1, Q_1
  75. IntersectPath(v_1, face7) → r_2
  76. Intersect(v_1, face7) → R_1, S_1
  77. IntersectPath(v_1, face2) → a_3
  78. Intersect(v_1, face2) → T_1, U_1
  79. IntersectPath(v_1, face8) → b_3
  80. Intersect(v_1, face8) → V_1, W_1
  81. IntersectPath(v_1, face3) → c_3
  82. Intersect(v_1, face3) → Z_1, A_2
  83. IntersectPath(v_1, face1) → d_3
  84. Intersect(v_1, face1) → B_2, C_2
  85. IntersectPath(v_1, face6) → e_3
  86. Intersect(v_1, face6) → D_2, E_2
  87. Plane(M, L, J) → w_1
  88. IntersectPath(w_1, face4) → f_3
  89. Intersect(w_1, face4) → F_2, G_2
  90. IntersectPath(w_1, face3) → g_3
  91. Intersect(w_1, face3) → H_2, I_2
  92. IntersectPath(w_1, face6) → h_3
  93. Intersect(w_1, face6) → J_2, K_2
  94. IntersectPath(w_1, face7) → i_3
  95. Intersect(w_1, face7) → L_2, M_2
  96. IntersectPath(w_1, face8) → j_3
  97. Intersect(w_1, face8) → N_2, O_2
  98. IntersectPath(w_1, face5) → k_3
  99. Intersect(w_1, face5) → P_2, Q_2
  100. IntersectPath(w_1, face2) → l_3
  101. Intersect(w_1, face2) → R_2, S_2
  102. IntersectPath(w_1, face1) → m_3
  103. Intersect(w_1, face1) → T_2, U_2
  104. Sphere(O, (1.5 * x(A))) → c_1
  105. PointIn(c_1) → V_2
  106. PointIn(c_1) → W_2
  107. PointIn(c_1) → Z_2
  108. Plane(V_2, W_2, Z_2) → e_2
  109. IntersectPath(e_2, c_1) → p_3
  110. IntersectPath(e_2, face8) → n_3
  111. Intersect(e_2, face8) → A_3, B_3
  112. IntersectPath(e_2, g) → poly4, C_3, t_3, a_4, b_4, D_3, E_3, F_3, G_3, H_3, q_3, r_3, s_3
  113. IntersectPath(e_2, face4) → c_4
  114. Intersect(e_2, face4) → I_3, J_3
  115. IntersectPath(e_2, face3) → d_4
  116. Intersect(e_2, face3) → K_3, L_3
  117. IntersectPath(e_2, face5) → e_4
  118. IntersectPath(e_2, face7) → f_4
  119. Intersect(e_2, face7) → M_3, N_3
  120. IntersectPath(e_2, face6) → g_4
  121. Intersect(e_2, face6) → O_3, P_3
  122. IntersectPath(e_2, face1) → h_4
  123. Intersect(e_2, face1) → Q_3, R_3
  124. IntersectPath(e_2, face2) → i_4
  125. AngularBisector(C, A, G) → c_1
  126. AngularBisector(A, G, C) → j_4
  127. Intersect(j_4, c_1) → S_3
  128. Midpoint(G, C) → T_3
  129. Midpoint(S_3, T_3) → U_3
  130. Midpoint(U_3, T_3) → V_3
  131. Ray(O, S_3) → k_4
  132. Segment(S_3, V_3) → radStar
  133. Circle(S_3, radStar, k_4) → p_4
  134. Rotate(V_3, 60°, k_4) → W_3
  135. Rotate(W_3, 60°, k_4) → Z_3
  136. Rotate(Z_3, 60°, k_4) → A_4
  137. Rotate(A_4, 60°, k_4) → B_4
  138. Rotate(B_4, 60°, k_4) → C_4
  139. Segment(A_4, V_3) → Star12
  140. Segment(B_4, W_3) → Star13
  141. Segment(Z_3, C_4) → Star11
  142. Star(A, G, D, O) → Star41, Star42, Star43
  143. Midpoint(B, D) → D_4
  144. Plane(F, D_4, G) → o_2
  145. Mirror(Star42, o_2) → Star23
  146. Mirror(Star43, o_2) → Star22
  147. Mirror(Star41, o_2) → Star21
  148. Midpoint(D, A) → E_4
  149. Plane(F, E_4, G) → u_2
  150. Mirror(A_4, u_2) → F_4
  151. Mirror(V_3, u_2) → G_4
  152. Segment(F_4, G_4) → Star32
  153. Mirror(Z_3, u_2) → H_4
  154. Mirror(C_4, u_2) → I_4
  155. Segment(H_4, I_4) → Star33
  156. Mirror(B_4, u_2) → J_4
  157. Mirror(W_3, u_2) → K_4
  158. Segment(J_4, K_4) → Star31
  159. Midpoint(F, D) → L_4
  160. Midpoint(C, G) → M_4
  161. Plane(L_4, D_4, M_4) → v_2
  162. Mirror(Star41, v_2) → Star61
  163. Mirror(Star43, v_2) → Star62
  164. Mirror(Star42, v_2) → Star63
  165. Midpoint(F, A) → N_4
  166. Midpoint(B, G) → O_4
  167. Plane(N_4, E_4, O_4) → w_2
  168. Mirror(A_4, w_2) → P_4
  169. Mirror(V_3, w_2) → Q_4
  170. Segment(P_4, Q_4) → Star72
  171. Mirror(B_4, w_2) → R_4
  172. Mirror(W_3, w_2) → S_4
  173. Segment(R_4, S_4) → Star71
  174. Mirror(Z_3, w_2) → T_4
  175. Mirror(C_4, w_2) → U_4
  176. Segment(T_4, U_4) → Star73
  177. Plane(F, E_4, G) → o_3
  178. Mirror(R_4, o_3) → V_4
  179. Mirror(S_4, o_3) → W_4
  180. Segment(V_4, W_4) → Star51
  181. Mirror(T_4, o_3) → Z_4
  182. Mirror(U_4, o_3) → A_5
  183. Segment(Z_4, A_5) → Star52
  184. Mirror(P_4, o_3) → B_5
  185. Mirror(Q_4, o_3) → C_5
  186. Segment(B_5, C_5) → Star53
  187. Plane(F, D_4, G) → u_3
  188. Mirror(Star61, u_3) → Star81
  189. Mirror(Star62, u_3) → Star83
  190. Mirror(Star63, u_3) → Star82