积极 AI Logo 积极 AI

解谜立方体演示

解谜立方体演示
几何画板及绘图内容加载中，请稍等……
2019-07-16 16:16
多边形向量立体几何几何作图
①本范例演示了通过交互式工具观察解谜立方体内部结构的过程；②涉及的核心数学概念包括立体几何、多边形、向量、旋转与对称；③作图要点提炼自GeoGebra命令：Intersect（交集）、Point（点）、Cube（立方体）、Midpoint（中点）、Mirror（镜像）、Vector（向量）、Line（直线）、Polygon（多边形）、Rotate（旋转）、Centroid（重心）、Segment（线段）、OrthogonalLine（垂线）、Translate（平移）、OrthogonalPlane（垂直平面）、IntersectPath（路径交集）、Plane（平面）、Pyramid（金字塔）；④适合高中阶段学习立体几何、空间想象与几何变换的学生使用。

GeoGebra 命令及参数

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Midpoint(edgeAD) → O
  6. Midpoint(edgeEH) → I
  7. Midpoint(H, I) → J
  8. Midpoint(F, B) → A_1
  9. Midpoint(edgeCG) → C_1
  10. Midpoint(C_1, A_1) → J_2
  11. Midpoint(edgeDH) → D_1
  12. Midpoint(D_1, D) → F_1
  13. Midpoint(edgeAE) → E_1
  14. Mirror(A, E_1) → A'
  15. Midpoint(D_1, E_1) → G_1
  16. Midpoint(G_1, J_2) → K_2
  17. Vector(K_2, A') → u
  18. Line(A', K_2) → p_4
  19. Midpoint(G_1, E) → T_1
  20. Midpoint(G_1, O) → H_1
  21. Midpoint(F_1, H_1) → I_1
  22. Midpoint(E_1, A) → J_1
  23. Midpoint(H_1, J_1) → U_1
  24. Polygon(E, T_1, U_1, I_1, J) → poly1, e_1, t_1, u_1, i_1, j_1
  25. Rotate(poly1, (-(120°)), p_4) → poly1'
  26. Midpoint(C_1, C) → V_1
  27. Midpoint(F_1, V_1) → W_1
  28. Midpoint(F_1, W_1) → Z_1
  29. Midpoint(A_1, B) → K_1
  30. Midpoint(J_1, K_1) → L_1
  31. Midpoint(J_1, L_1) → M_1
  32. Midpoint(Z_1, M_1) → A_2
  33. Midpoint(A_2, M_1) → B_2
  34. Midpoint(edgeEF) → N
  35. Midpoint(E, N) → O_1
  36. Midpoint(edgeGH) → L
  37. Midpoint(H, L) → P_1
  38. Midpoint(P_1, O_1) → Q_1
  39. Midpoint(P_1, Q_1) → S_1
  40. Line(S_1, edgeDH) → k_2
  41. Intersect(k_2, faceABCD) → A_3
  42. Midpoint(S_1, A_3) → B_3
  43. Midpoint(B_3, S_1) → C_3
  44. Midpoint(I, E) → K
  45. Midpoint(edgeFG) → M
  46. Midpoint(edgeCD) → P
  47. Midpoint(edgeBC) → Q
  48. Midpoint(edgeAB) → R
  49. Midpoint(D, P) → S
  50. Midpoint(P, C) → T
  51. Midpoint(C, Q) → U
  52. Midpoint(Q, B) → V
  53. Midpoint(B, R) → W
  54. Midpoint(R, A) → Z
  55. Midpoint(A_1, F) → B_1
  56. Midpoint(L_1, K_1) → N_1
  57. Midpoint(Q_1, O_1) → R_1
  58. Polygon(R_1, E, J, S_1) → q1, r_1, e, j, s_1
  59. Midpoint(O, A) → D_2
  60. Midpoint(Z, S) → E_2
  61. Midpoint(E_2, Z) → F_2
  62. Midpoint(R_1, F_2) → C_2
  63. Line(S_1, edgeDH) → f
  64. Line(I_1, edgeCD) → g
  65. Intersect(g, f) → G_2
  66. Polygon(S_1, G_2, I_1, J) → q2, h, g_2, i, j_2
  67. Polygon(R_1, B_2, C_3, S_1) → q3, k_5, l, m, b_2
  68. Midpoint(R_1, C_2) → H_2
  69. Polygon(T_1, E, H_2) → t2, p, q, e_3
  70. Polygon(T_1, H_2, B_2, U_1) → q4, r, s, t, b
  71. Centroid(faceABFE) → L_2
  72. Midpoint(J_2, Q) → I_2
  73. Midpoint(I_2, K_1) → M_2
  74. Midpoint(U_1, M_2) → N_2
  75. Midpoint(K_2, J_2) → O_2
  76. Segment(C_3, B_2) → d
  77. Midpoint(N, F) → T_2
  78. Midpoint(G, E) → Q_2
  79. Midpoint(Q_2, G) → R_2
  80. Polygon(G, R_2, T_2, F) → q5, g_1, r_2, t_2, f_1
  81. Polygon(F, B, C, G) → q6, f_2, b_1, c_1, g_3
  82. Line(R_2, c_1) → h_1
  83. Intersect(h_1, faceABCD) → U_2
  84. Midpoint(R_2, U_2) → W_2
  85. Midpoint(W_2, U_2) → Z_2
  86. Polygon(N_1, B, C, Z_2) → q8, n_1, b_3, c_3, l_1
  87. Polygon(T_2, R_2, Z_2, N_1) → q9, m_1, p_1, q_1, a_1
  88. Polygon(T_2, F, B, N_1) → q10, d_1, f_3, b_4, i_2
  89. Midpoint(d) → D_3
  90. Line(O_2, d) → l_2
  91. Intersect(l_2, p_1) → E_3
  92. Midpoint(W_2, B_3) → P_2
  93. Polygon(G_2, P_2, W_2, E_3, C_3) → poly2, c, p_2, w_2, m_2, n_2
  94. Polygon(B_2, K_2, O_2, E_3, C_3) → poly3, q_2, s_2, o_2, a_2, d_2
  95. Polygon(P_2, K_2, O_2, W_2) → q11, h_3, i_3, j_3, k_3
  96. Polygon(P_2, G_2, B_2, K_2) → q12, l_3, m_3, n_3, p_3
  97. Polygon(G_2, I_1, U_1, B_2) → q13, q_3, r_3, s_3, t_3
  98. Polygon(R_2, E_3, O_2, W_2, Z_2, N_1, T_2) → poly4, a_3, d_3, f_4, h_4, i_4, j_4, k_4
  99. OrthogonalLine(G_1, poly1) → l_4
  100. OrthogonalLine(Q_2, q5) → m_4
  101. OrthogonalLine(L_2, q10) → n_4
  102. Rotate(q1, (-(120°)), p_4) → q1'
  103. Rotate(q5, (-(120°)), p_4) → q5'
  104. Rotate(poly4, (-(120°)), p_4) → poly4'
  105. Rotate(q10, (-(120°)), p_4) → q10'
  106. Rotate(q6, 240°, p_4) → q6'
  107. Rotate(q8, (-(120°)), p_4) → q8'
  108. Rotate(q3, (-(120°)), p_4) → q3'
  109. Translate(poly1', Vector[(k * u)]) → poly1''
  110. Translate(poly4', Vector[(k * u)]) → poly4''
  111. Translate(q1', Vector[(k * u)]) → q1''
  112. Translate(q3', Vector[(k * u)]) → q3''
  113. Translate(q10', Vector[(k * u)]) → q10''
  114. Translate(q5', Vector[(k * u)]) → q5''
  115. Translate(q6', Vector[(k * u)]) → q6''
  116. Translate(q8', Vector[(k * u)]) → q8''
  117. Rotate(poly3, (-(120°)), p_4) → poly3'
  118. Translate(poly3', Vector[(k * u)]) → poly3''
  119. Rotate(q12, (-(120°)), p_4) → q12'
  120. Translate(q12', Vector[(k * u)]) → q12''
  121. Rotate(q11, 120°, p_4) → q11'
  122. Rotate(q4, (-(120°)), p_4) → q4'
  123. Translate(q4', Vector[(k * u)]) → q4''
  124. Rotate(t2, (-(120°)), p_4) → t2'
  125. Translate(t2', Vector[(k * u)]) → t2''
  126. Rotate(q13, (-(120°)), p_4) → q13'
  127. Translate(q13', Vector[(k * u)]) → q13''
  128. Rotate(poly1, 120°, p_4) → poly5
  129. Mirror(A', N) → A''
  130. Vector(K_2, A'') → v
  131. Translate(poly5, Vector[(k * v)]) → poly5'
  132. Rotate(q11, (-(120°)), p_4) → q11'_1
  133. Translate(q11'_1, Vector[(k * u)]) → q7
  134. Translate(q11', Vector[(k * v)]) → q11''
  135. Rotate(q2, 120°, p_4) → q2'
  136. Translate(q2', Vector[(k * v)]) → q2''
  137. Rotate(q2, (-(120°)), p_4) → q2'_1
  138. Translate(q2'_1, Vector[(k * u)]) → q14
  139. Rotate(poly2, 240°, p_4) → poly2'_1
  140. Rotate(poly2, 120°, p_4) → poly2'
  141. Translate(poly2', Vector[(k * v)]) → poly2''
  142. Translate(poly2'_1, Vector[(k * u)]) → poly6
  143. Mirror(A'', M) → A'''
  144. Mirror(A''', C_1) → S_2
  145. Polygon(A''', S_2, Z_2, R_2) → q15, a''', k_1, z_2, c_2
  146. Rotate(q15, 120°, p_4) → q15'
  147. Translate(q15', Vector[(k * v)]) → q15''
  148. Rotate(q15, (-(120°)), p_4) → q15'_1
  149. Translate(q15'_1, Vector[(k * u)]) → q16
  150. Rotate(q5, 120°, p_4) → q5'_1
  151. Rotate(q6, 120°, p_4) → q6'_1
  152. Translate(q6'_1, Vector[(k * v)]) → q17
  153. Translate(q5'_1, Vector[(k * v)]) → q18
  154. Rotate(q8, 120°, p_4) → q8'_1
  155. Rotate(q10, 120°, p_4) → q10'_1
  156. Translate(q8'_1, Vector[(k * v)]) → q19
  157. Translate(q10'_1, Vector[(k * v)]) → q20
  158. Rotate(poly4, 120°, p_4) → poly4'_1
  159. Translate(poly4'_1, Vector[(k * v)]) → poly7
  160. Rotate(q12, 120°, p_4) → q12'_1
  161. Translate(q12'_1, Vector[(k * v)]) → q21
  162. Rotate(q13, 120°, p_4) → q13'_1
  163. Translate(q13'_1, Vector[(k * v)]) → q22
  164. Rotate(q4, (-(120°)), p_4) → q4'_1
  165. Rotate(t2, (-(120°)), p_4) → t2'_1
  166. Translate(t2'_1, Vector[(k * v)]) → t1
  167. Intersect(e, r_1) → V_2
  168. Polygon(V_2, R_1, H_2) → t3, h_2, v_2, n
  169. Rotate(q1, 120°, p_4) → q1'_1
  170. Translate(q1'_1, Vector[(k * v)]) → q24
  171. Rotate(poly3, 120°, p_4) → poly3'_1
  172. Translate(poly3'_1, Vector[(k * v)]) → poly8
  173. Rotate(q4, 120°, p_4) → q4'_2
  174. Translate(q4'_2, Vector[(k * v)]) → q25
  175. Rotate(t2, (-(120°)), p_4) → t2'_2
  176. Translate(t2'_2, Vector[(k * v)]) → t4
  177. Rotate(q3, 120°, p_4) → q3'_1
  178. Rotate(t2, 120°, p_4) → t2'_3
  179. Translate(t2'_3, Vector[(k * v)]) → t5
  180. Translate(q3'_1, Vector[(k * v)]) → q23
  181. Point(a''') → F_3
  182. OrthogonalPlane(F_3, a''') → q_4
  183. IntersectPath(q_4, q6) → e_2
  184. IntersectPath(q_4, q10) → g_4
  185. Intersect(q_4, q10) → I_3, J_3
  186. IntersectPath(q_4, poly4) → r_4
  187. IntersectPath(q_4, q15) → s_4
  188. Intersect(q_4, q15) → M_3, N_3
  189. Polygon(I_3, M_3, F_3, J_3) → q26, t_4, a_4, c_4, d_4
  190. IntersectPath(q_4, q2) → e_4
  191. Intersect(q_4, q2) → G_3, H_3
  192. IntersectPath(q_4, poly1) → f_5
  193. Intersect(q_4, poly1) → K_3, L_3
  194. IntersectPath(q_4, q4) → g_5
  195. Intersect(q_4, q4) → O_3, P_3
  196. IntersectPath(q_4, q3) → h_5
  197. Intersect(q_4, q3) → Q_3, R_3
  198. Polygon(P_3, H_3, G_3, K_3) → q27, i_5, j_5, l_5, m_5
  199. IntersectPath(q_4, t2) → n_5
  200. Intersect(q_4, t2) → S_3, T_3
  201. IntersectPath(q_4, t3) → p_5
  202. Intersect(q_4, t3) → U_3, V_3
  203. Polygon(R_3, H_3, G_3, K_3, T_3) → poly9, q_5, r_5, s_5, t_5, a_5
  204. IntersectPath(q_4, q12) → b_5
  205. Intersect(q_4, q12) → W_3, Z_3
  206. Polygon(Q_3, W_3, Z_3, H_3) → q28, c_5, w_3, z_3, d_5
  207. Intersect(q_4, poly2) → A_4, B_4
  208. IntersectPath(q_4, poly3) → e_5
  209. Intersect(q_4, poly3) → C_4, D_4
  210. IntersectPath(q_4, poly4) → f_6
  211. Intersect(q_4, poly4) → E_4, F_4
  212. Intersect(z_2, q_4) → G_4
  213. Intersect(d_3, q_4) → H_4
  214. Intersect(d_2, q_4) → I_4
  215. Intersect(n_2, q_4) → J_4
  216. Polygon(H_4, G_4, J_4, I_4) → q29, g_6, h_6, i_6, j_6
  217. IntersectPath(q_4, q6'') → k_6
  218. Intersect(q_4, q6'') → K_4, L_4
  219. IntersectPath(q_4, q5'') → l_6
  220. Intersect(q_4, q5'') → M_4, N_4
  221. IntersectPath(q_4, q8'') → m_6
  222. Intersect(q_4, q8'') → O_4, P_4
  223. IntersectPath(q_4, poly4'') → n_6, q_6
  224. IntersectPath(q_4, q16) → p_6
  225. Intersect(q_4, q16) → Q_4, R_4
  226. Polygon(O_4, L_4, K_4, M_4) → q30, o_4, r_6, s_6, t_6
  227. Rotate(t3, (-(120°)), p_4) → t3'
  228. Translate(t3', Vector[(k * u)]) → t3''
  229. Intersect(q14, q4) → S_4, T_4, U_4, V_4
  230. IntersectPath(q_4, poly1'') → a_6
  231. Intersect(q_4, poly1'') → W_4, Z_4
  232. IntersectPath(q_4, q13'') → b_6
  233. Intersect(q_4, q13'') → A_5, B_5
  234. IntersectPath(q_4, q1'') → c_6
  235. Intersect(q_4, q1'') → C_5, D_5
  236. IntersectPath(q_4, poly3'') → d_6
  237. Intersect(q_4, poly3'') → E_5, F_5, I_7
  238. IntersectPath(q_4, q7) → e_6
  239. Intersect(q_4, q7) → G_5, H_5
  240. IntersectPath(q_4, q12'') → f_7
  241. Intersect(q_4, q12'') → I_5, J_5
  242. IntersectPath(q_4, q3'') → g_7
  243. Intersect(q_4, q3'') → K_5, L_5
  244. Polygon(W_4, B_5, C_5, Z_4) → q31, w_4, h_7, i_7, z_4
  245. Polygon(B_5, G_5, H_5, E_5, F_5) → poly10, j_7, k_7, l_7, m_7, n_7
  246. Polygon(B_5, E_5, F_5) → t6, p_7, q_7, r_7
  247. IntersectPath(q_4, t3'') → s_7
  248. Intersect(q_4, t3'') → M_5, N_5
  249. IntersectPath(q_4, t2'') → t_7
  250. Intersect(q_4, t2'') → O_5, P_5
  251. IntersectPath(q_4, poly1'') → a_7
  252. Intersect(q_4, poly1'') → Q_5, R_5
  253. Polygon(W_4, M_5, C_5, R_5) → q32, b_7, c_7, d_7, e_7
  254. IntersectPath(q_4, q19) → f_8
  255. Intersect(q_4, q19) → S_5, T_5
  256. IntersectPath(q_4, q15'') → g_8
  257. Intersect(q_4, q15'') → U_5, V_5
  258. IntersectPath(q_4, q20) → h_8
  259. Intersect(q_4, q20) → W_5, Z_5
  260. IntersectPath(q_4, q18) → i_8
  261. Intersect(q_4, q18) → A_6, B_6
  262. Polygon(V_5, S_5, T_5, Z_5) → q33, v_5, j_8, k_8, z_5
  263. IntersectPath(q_4, q11'') → l_8
  264. Intersect(q_4, q11'') → C_6, D_6
  265. IntersectPath(q_4, poly8) → m_8
  266. Intersect(q_4, poly8) → E_6, F_6
  267. IntersectPath(q_4, poly2'') → n_8
  268. Intersect(q_4, poly2'') → G_6, H_6
  269. Polygon(F_6, C_6, D_6) → t7, p_8, q_8, r_8
  270. IntersectPath(q_4, q21) → s_8
  271. Intersect(q_4, q21) → I_6, J_6
  272. IntersectPath(q_4, poly2'') → t_8
  273. Intersect(q_4, poly2'') → K_6, L_6
  274. IntersectPath(q_4, poly8) → a_8
  275. Intersect(q_4, poly8) → M_6, N_6
  276. Polygon(L_6, I_6, J_6) → t8, b_8, c_8, d_8
  277. IntersectPath(q_4, q2'') → e_8
  278. Intersect(q_4, q2'') → O_6, P_6
  279. IntersectPath(q_4, q22) → f_9
  280. Intersect(q_4, q22) → Q_6, R_6
  281. IntersectPath(q_4, q25) → g_9
  282. Intersect(q_4, q25) → S_6, T_6
  283. IntersectPath(q_4, t5) → h_9
  284. Intersect(q_4, t5) → U_6, V_6
  285. IntersectPath(q_4, t1) → i_9
  286. Intersect(q_4, t1) → W_6, Z_6
  287. IntersectPath(q_4, q24) → j_9
  288. Intersect(q_4, q24) → A_7, B_7
  289. Polygon(P_6, O_6, R_6, T_6, V_6, W_6) → poly11, k_9, o_6, l_9, m_9, v_6, w_6
  290. Segment(P_2, O_2) → n_9
  291. Mirror(K_2, n_9) → C_7
  292. Cube(Z_2, C_7, P_2) → o, D_7, face5, face6, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, E_7, edge9, edge10, edge11, edge12, F_7, G_7, H_7, face1, face2, face3, face4
  293. Polygon(R_3, K_3, G_3, H_3) → q34, p_9, q_9, r_9, s_9
  294. Plane(K_2, q1) → p_{10}
  295. Intersect(s, p_{10}) → J_7
  296. Intersect(d_2, p_{10}) → K_7
  297. Segment(J_7, K_2) → t_9
  298. Mirror(K_7, t_9) → L_7
  299. Pyramid(J_7, K_7, K_2, L_7, B_2) → w, face11, edge16, edge17, edge13, edge18, face9, face7, face8, face10, edge19, edge14, edge15, edge20
  300. Plane(E_3, q5) → q_{10}
  301. Plane(J_7, L_7, B_2) → r_{10}
  302. IntersectPath(r_{10}, q_{10}) → a_9
  303. Intersect(a_9, poly4) → M_7
  304. Intersect(a_9, v_2) → N_7
  305. Polygon(K_7, K_2, C_3) → t9, b_9, c_9, d_9
  306. Polygon(M_7, K_2, C_3) → t10, e_9, f_{10}, g_{10}
  307. Polygon(M_7, N_7, C_3) → t11, h_{10}, i_{10}, j_{10}
  308. Polygon(C_3, K_7, J_7, N_7) → q35, k_{10}, l_{10}, m_{10}, n_{10}
  309. Polygon(M_7, K_2, L_7) → t12, s_{10}, t_{10}, a_{10}
  310. Polygon(N_7, J_7, L_7, M_7) → q36, b_{10}, c_{10}, d_{10}, e_{10}
  311. Polygon(M_7, K_2, C_3) → t13, f_{11}, g_{11}, h_{11}
  312. Polygon(K_2, C_3, K_7) → t14, i_{11}, j_{11}, k_{11}
  313. Polygon(C_3, K_7, J_7, N_7) → q37, l_{11}, m_{11}, n_{11}, p_{11}
  314. Polygon(K_2, C_3, K_7) → t15, q_{11}, r_{11}, s_{11}
  315. Polygon(C_3, K_7, J_7, N_7) → q38, t_{11}, a_{11}, b_{11}, c_{11}