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4V-Triacon 八面体

4V-Triacon 八面体
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2016-05-06 09:00
多边形立体几何几何作图
①本范例演示了一个名为 4V-Triacon 的复杂八面体图形的构造与性质；②涉及的核心数学概念包括多边形构造、空间几何、对称性、旋转与镜像等；③作图要点提炼自 GeoGebra 命令：使用了 Mirror（镜像）、Polygon（多边形）、Pyramid（金字塔）、Segment（线段）、Midpoint（中点）、Intersect（交点）、Sphere（球体）、Ray（射线）、Rotate（旋转）等命令与对象；④适合高中及以上学段学习立体几何、空间想象能力及 GeoGebra 软件应用的学生。

GeoGebra 命令及参数

  1. Mirror(B, yAxis) → B'
  2. Mirror(A, yAxis) → A'
  3. Mirror(C, xAxis) → C'
  4. Polygon(A', A, B, B') → poly1, a', a_1, b, b'
  5. Pyramid(poly1, C) → c, faceAA'C, faceABC, faceBB'C, faceA'B'C, edgeA'C, edgeAC, edgeBC, edgeB'C
  6. Pyramid(poly1, C') → d, faceAA'C', faceABC', faceBB'C', faceA'B'C', edgeA'C', edgeAC', edgeBC', edgeB'C'
  7. Segment(A, C) → f
  8. Segment(C, B) → g
  9. Segment(B, A) → h
  10. Midpoint(h) → E
  11. Midpoint(f) → L
  12. Midpoint(g) → M
  13. Segment(A, E) → i
  14. Segment(E, B) → j
  15. Segment(B, M) → k
  16. Segment(M, C) → l
  17. Segment(C, L) → m
  18. Segment(L, A) → n
  19. Midpoint(n) → I
  20. Midpoint(m) → O
  21. Midpoint(l) → P
  22. Midpoint(k) → J
  23. Midpoint(j) → F
  24. Midpoint(i) → D
  25. Segment(C, E) → p
  26. Segment(L, B) → q
  27. Segment(M, A) → r
  28. Segment(M, O) → s
  29. Segment(M, F) → t
  30. Segment(L, P) → f_1
  31. Segment(L, D) → g_1
  32. Segment(E, I) → h_1
  33. Segment(E, J) → i_1
  34. Intersect(p, f_1) → N
  35. Intersect(p, q) → K
  36. Intersect(g_1, r) → G
  37. Intersect(t, i_1) → H
  38. Sphere(Z, (a * sqrt(2) / 2)) → u
  39. Ray(Z, O) → j_1
  40. Ray(Z, P) → k_1
  41. Ray(Z, N) → l_1
  42. Ray(Z, L) → m_1
  43. Ray(Z, M) → n_1
  44. Ray(Z, K) → p_1
  45. Ray(Z, I) → q_1
  46. Ray(Z, J) → r_1
  47. Ray(Z, G) → s_1
  48. Ray(Z, H) → t_1
  49. Ray(Z, D) → c_1
  50. Ray(Z, E) → d_1
  51. Ray(Z, F) → e_1
  52. Intersect(k_1, u) → Q, P'
  53. Intersect(j_1, u) → S, O'
  54. Intersect(l_1, u) → U, N'
  55. Intersect(n_1, u) → W, M'
  56. Intersect(e_1, u) → B_1, F'
  57. Intersect(t_1, u) → D_1, H'
  58. Intersect(p_1, u) → F_1, K'
  59. Intersect(m_1, u) → H_1, L'
  60. Intersect(c_1, u) → J_1, D'
  61. Intersect(d_1, u) → L_1, E'
  62. Intersect(s_1, u) → N_1, G'
  63. Intersect(q_1, u) → P_1, I'
  64. Intersect(r_1, u) → R_1, J'
  65. Intersect(edgeBC, edgeAC) → T_1
  66. Intersect(a_1, edgeAC) → U_1
  67. Intersect(edgeBC, b) → V_1
  68. Segment(T_1, O') → f_2
  69. Segment(O', L') → g_2
  70. Segment(L', I') → h_2
  71. Segment(I', U_1) → i_2
  72. Segment(U_1, D') → j_2
  73. Segment(D', E') → k_2
  74. Segment(E', F') → l_2
  75. Segment(F', V_1) → m_2
  76. Segment(V_1, J') → n_2
  77. Segment(J', M') → p_2
  78. Segment(M', P') → q_2
  79. Segment(P', T_1) → r_2
  80. Segment(P', N') → s_2
  81. Segment(N', O') → t_2
  82. Segment(N', T_1) → a_2
  83. Segment(L', K') → b_2
  84. Segment(K', H') → c_2
  85. Segment(H', V_1) → d_2
  86. Segment(N', K') → e_2
  87. Segment(K', E') → f_3
  88. Segment(U_1, G') → g_3
  89. Segment(G', K') → h_3
  90. Segment(K', M') → i_3
  91. Segment(M', H') → j_3
  92. Segment(H', F') → k_3
  93. Segment(L', G') → l_3
  94. Segment(G', D') → m_3
  95. Segment(E', G') → n_3
  96. Segment(G', I') → p_3
  97. Segment(E', H') → q_3
  98. Segment(H', J') → r_3
  99. Segment(L', N') → s_3
  100. Segment(N', M') → t_3
  101. Rotate(N', 90°, zAxis) → N''
  102. Rotate(P', 90°, zAxis) → P''
  103. Rotate(K', 90°, zAxis) → K''
  104. Rotate(M', 90°, zAxis) → M''
  105. Rotate(J', 90°, zAxis) → J''
  106. Rotate(V_1, 90°, zAxis) → R
  107. Rotate(F', 90°, zAxis) → F''
  108. Rotate(H', 90°, zAxis) → H''
  109. Rotate(E', 90°, zAxis) → E''
  110. Rotate(D', 90°, zAxis) → D''
  111. Rotate(G', 90°, zAxis) → G''
  112. Rotate(N'', 90°, zAxis) → N'''
  113. Rotate(P'', 90°, zAxis) → P'''
  114. Rotate(M'', 90°, zAxis) → M'''
  115. Rotate(J'', 90°, zAxis) → J'''
  116. Rotate(R, 90°, zAxis) → R'
  117. Rotate(H'', 90°, zAxis) → H'''
  118. Rotate(F'', 90°, zAxis) → F'''
  119. Rotate(K'', 90°, zAxis) → K'''
  120. Rotate(E'', 90°, zAxis) → E'''
  121. Rotate(D'', 90°, zAxis) → D'''
  122. Rotate(G'', 90°, zAxis) → G'''
  123. Segment(T_1, P'') → a_3
  124. Segment(P'', M'') → b_3
  125. Segment(M'', J'') → c_3
  126. Segment(J'', R) → d_3
  127. Segment(T_1, P''') → e_3
  128. Segment(P''', M''') → f_4
  129. Segment(M''', J''') → g_4
  130. Segment(J''', R') → h_4
  131. Rotate(N''', 90°, zAxis) → T
  132. Rotate(K''', 90°, zAxis) → V
  133. Rotate(G''', 90°, zAxis) → A_1
  134. Rotate(D''', 90°, zAxis) → C_1
  135. Rotate(E''', 90°, zAxis) → E_1
  136. Rotate(H''', 90°, zAxis) → G_1
  137. Rotate(F''', 90°, zAxis) → I_1
  138. Segment(P', N'') → i_4
  139. Segment(N'', T_1) → j_4
  140. Segment(N'', P'') → k_4
  141. Segment(P'', N''') → l_4
  142. Segment(N''', P''') → m_4
  143. Segment(N''', T_1) → n_4
  144. Segment(P''', T) → p_4
  145. Segment(T, O') → q_4
  146. Segment(T, T_1) → r_4
  147. Segment(M', K'') → s_4
  148. Segment(K'', M'') → t_4
  149. Segment(M'', N'') → a_4
  150. Segment(N'', M') → b_4
  151. Segment(N'', K'') → c_4
  152. Segment(K'', E'') → d_4
  153. Segment(J', G'') → e_4
  154. Segment(G'', V_1) → f_5
  155. Segment(V_1, D'') → g_5
  156. Segment(D'', E'') → h_5
  157. Segment(E'', F'') → i_5
  158. Segment(F'', R) → j_5
  159. Segment(G'', D'') → k_5
  160. Segment(G'', M') → l_5
  161. Segment(G'', K'') → m_5
  162. Segment(G'', E'') → n_5
  163. Segment(K'', H'') → p_5
  164. Segment(H'', E'') → q_5
  165. Segment(H'', F'') → r_5
  166. Segment(H'', R) → s_5
  167. Segment(J'', H'') → t_5
  168. Segment(H'', M'') → a_5
  169. Segment(N''', K''') → b_5
  170. Segment(K''', E''') → c_5
  171. Segment(E''', D''') → d_5
  172. Segment(R, D''') → e_5
  173. Segment(E''', F''') → f_6
  174. Segment(F''', R') → g_6
  175. Segment(J'', G''') → h_6
  176. Segment(G''', M'') → i_6
  177. Segment(G''', R) → j_6
  178. Segment(G''', D''') → k_6
  179. Segment(G''', E''') → l_6
  180. Segment(G''', K''') → m_6
  181. Segment(K''', M'') → n_6
  182. Segment(M'', N''') → p_6
  183. Segment(N''', M''') → q_6
  184. Segment(M''', K''') → r_6
  185. Segment(K''', H''') → s_6
  186. Segment(H''', R') → t_6
  187. Segment(J''', H''') → a_6
  188. Segment(H''', F''') → b_6
  189. Segment(E''', H''') → c_6
  190. Segment(H''', M''') → d_6
  191. Segment(R', C_1) → e_6
  192. Segment(C_1, E_1) → f_7
  193. Segment(E_1, I_1) → g_7
  194. Segment(I_1, U_1) → h_7
  195. Segment(I', G_1) → i_7
  196. Segment(G_1, U_1) → j_7
  197. Segment(G_1, I_1) → k_7
  198. Segment(R', A_1) → l_7
  199. Segment(A_1, J''') → m_7
  200. Segment(A_1, C_1) → n_7
  201. Segment(A_1, E_1) → p_7
  202. Segment(E_1, G_1) → q_7
  203. Segment(V, E_1) → r_7
  204. Segment(V, T) → s_7
  205. Segment(M''', T) → t_7
  206. Segment(T, L') → a_7
  207. Segment(L', V) → b_7
  208. Segment(M''', V) → c_7
  209. Segment(V, A_1) → d_7
  210. Segment(M''', A_1) → e_7
  211. Segment(V, G_1) → f_8
  212. Segment(G_1, L') → g_8
  213. Mirror(T_1, xOyPlane) → K_1
  214. Mirror(O', xOyPlane) → O''
  215. Mirror(N', xOyPlane) → N''_1
  216. Mirror(P', xOyPlane) → P''_1
  217. Mirror(L', xOyPlane) → L''
  218. Mirror(K', xOyPlane) → K''_1
  219. Mirror(M', xOyPlane) → M''_1
  220. Mirror(I', xOyPlane) → I''
  221. Mirror(G', xOyPlane) → G''_1
  222. Mirror(H', xOyPlane) → H''_1
  223. Mirror(J', xOyPlane) → J''_1
  224. Rotate(I'', (-(90°)), zAxis) → I'''
  225. Rotate(G''_1, (-(90°)), zAxis) → M_1
  226. Rotate(L'', (-(90°)), zAxis) → L'''
  227. Rotate(K''_1, (-(90°)), zAxis) → O_1
  228. Rotate(O'', (-(90°)), zAxis) → O'''
  229. Rotate(N''_1, (-(90°)), zAxis) → Q_1
  230. Rotate(M''_1, (-(90°)), zAxis) → W_1
  231. Rotate(J''_1, (-(90°)), zAxis) → Z_1
  232. Rotate(H''_1, (-(90°)), zAxis) → A_2
  233. Segment(I'', L'') → h_8
  234. Segment(L'', O'') → i_8
  235. Segment(O'', K_1) → j_8
  236. Segment(J''_1, M''_1) → k_8
  237. Segment(M''_1, P''_1) → l_8
  238. Segment(P''_1, K_1) → m_8
  239. Segment(I''', L''') → n_8
  240. Segment(L''', O''') → p_8
  241. Segment(O''', K_1) → q_8
  242. Rotate(A_2, (-(90°)), zAxis) → B_2
  243. Rotate(O_1, (-(90°)), zAxis) → C_2
  244. Rotate(Q_1, (-(90°)), zAxis) → D_2
  245. Rotate(O''', (-(90°)), zAxis) → E_2
  246. Rotate(L''', (-(90°)), zAxis) → F_2
  247. Rotate(I''', (-(90°)), zAxis) → G_2
  248. Rotate(M_1, (-(90°)), zAxis) → H_2
  249. Rotate(I''', (-(90°)), zAxis) → I_2
  250. Segment(G_2, F_2) → r_8
  251. Segment(F_2, E_2) → s_8
  252. Segment(E_2, K_1) → t_8
  253. Rotate(H_2, (-(90°)), zAxis) → K_2
  254. Rotate(C_2, (-(90°)), zAxis) → L_2
  255. Rotate(B_2, (-(90°)), zAxis) → M_2
  256. Rotate(D_2, (-(90°)), zAxis) → N_2
  257. Segment(N''_1, P''_1) → a_8
  258. Segment(P''_1, N_2) → b_8
  259. Segment(N_2, E_2) → c_8
  260. Segment(E_2, D_2) → d_8
  261. Segment(D_2, O''') → e_8
  262. Segment(O''', Q_1) → f_9
  263. Segment(Q_1, O'') → g_9
  264. Segment(O'', N''_1) → h_9
  265. Segment(N''_1, K_1) → i_9
  266. Segment(K_1, N_2) → j_9
  267. Segment(K_1, D_2) → k_9
  268. Segment(K_1, Q_1) → l_9
  269. Segment(K''_1, N''_1) → m_9
  270. Segment(D_2, C_2) → n_9
  271. Segment(Q_1, O_1) → p_9
  272. Segment(N_2, L_2) → q_9
  273. Segment(L'', Q_1) → r_9
  274. Segment(Q_1, L''') → s_9
  275. Segment(L''', D_2) → t_9
  276. Segment(F_2, D_2) → a_9
  277. Segment(F_2, N_2) → b_9
  278. Segment(L'', N''_1) → c_9
  279. Segment(N''_1, M''_1) → d_9
  280. Segment(M''_1, N_2) → e_9
  281. Segment(L'', K''_1) → f_{10}
  282. Segment(K''_1, M''_1) → g_{10}
  283. Segment(G''_1, K''_1) → h_{10}
  284. Segment(G''_1, I'') → j_{10}
  285. Segment(H''_1, J''_1) → k_{10}
  286. Segment(I'', A_2) → n_{10}
  287. Segment(J''_1, K_2) → p_{10}
  288. Segment(E', K''_1) → q_{10}
  289. Segment(E', H''_1) → r_{10}
  290. Segment(E', G''_1) → s_{10}
  291. Segment(F', H''_1) → t_{10}
  292. Segment(D', G''_1) → a_{10}
  293. Segment(U_1, I'') → b_{10}
  294. Segment(G''_1, U_1) → c_{10}
  295. Segment(U_1, A_2) → d_{10}
  296. Segment(I_1, A_2) → e_{10}
  297. Segment(V_1, J''_1) → f_{11}
  298. Segment(V_1, H''_1) → g_{11}
  299. Segment(V_1, K_2) → h_{11}
  300. Segment(K_2, D'') → i_{11}
  301. Segment(R, G_2) → j_{11}
  302. Segment(G_2, H_2) → k_{11}
  303. Segment(H_2, D''') → l_{11}
  304. Segment(G_2, M_2) → m_{11}
  305. Segment(F'', M_2) → n_{11}
  306. Segment(M_2, R) → p_{11}
  307. Segment(R, H_2) → q_{11}
  308. Segment(F''', B_2) → r_{11}
  309. Segment(B_2, I''') → s_{11}
  310. Segment(I''', M_1) → t_{11}
  311. Segment(M_1, C_1) → a_{11}
  312. Segment(R', I''') → b_{11}
  313. Segment(M_1, R') → c_{11}
  314. Segment(R', B_2) → d_{11}
  315. Segment(H''_1, K''_1) → i_{10}
  316. Segment(G''_1, L'') → l_{10}
  317. Segment(H''_1, M''_1) → m_{10}
  318. Segment(A_2, L'') → e_{11}
  319. Segment(O_1, L'') → f_{12}
  320. Segment(A_2, O_1) → g_{12}
  321. Segment(M_1, O_1) → h_{12}
  322. Segment(O_1, L''') → i_{12}
  323. Segment(H_2, C_2) → j_{12}
  324. Segment(C_2, L''') → k_{12}
  325. Segment(L''', M_1) → l_{12}
  326. Segment(B_2, L''') → m_{12}
  327. Segment(B_2, C_2) → n_{12}
  328. Segment(F_2, L_2) → p_{12}
  329. Segment(L_2, M''_1) → q_{12}
  330. Segment(L_2, K_2) → r_{12}
  331. Segment(L_2, M_2) → s_{12}
  332. Segment(F_2, C_2) → t_{12}
  333. Segment(H_2, F_2) → a_{12}
  334. Segment(F_2, M_2) → b_{12}
  335. Segment(K_2, M''_1) → c_{12}
  336. Segment(E'', L_2) → d_{12}
  337. Segment(K_2, E'') → e_{12}
  338. Segment(E'', M_2) → f_{13}
  339. Segment(E''', C_2) → g_{13}
  340. Segment(E''', B_2) → h_{13}
  341. Segment(E''', H_2) → i_{13}
  342. Segment(E_1, O_1) → j_{13}
  343. Segment(E_1, M_1) → k_{13}
  344. Segment(E_1, A_2) → l_{13}

AI 绘图提示语参考

画一个复杂的八面体，首先通过镜像和构造多边形创建基础结构，然后利用旋转和反射形成对称的几何体。接着，从基础结构出发，构建多个金字塔，并连接关键点形成网格。最后，围绕中心点绘制多个球体，并从中心点向各个关键点引出射线，完成整体造型。
以上提示语为根据原始绘图命令整理而来，仅供参考。