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魔方模型

魔方模型
几何画板及绘图内容加载中，请稍等……
2018-09-09 16:06
多边形向量立体几何几何作图
①本范例演示了魔方（Rubik's Cube）的几何构造与展示；②涉及的核心数学概念包括立体几何、多边形、向量与变换；③作图要点提炼自GeoGebra命令：使用Cube命令创建立方体，结合If条件判断，通过create、testtext、button2等对象实现交互式展示，并定义Point、faceA、edgeB等几何元素构建魔方结构；④适合高中及以上学段学习立体几何、空间想象与几何作图的学生，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Cube(Point1111, Point2111, Point3111) → cube111, A, faceAEDPoint3111, faceBCDE, edgeAPoint1111, edgePoint1111Point2111, edgePoint2111Point3111, edgeAPoint3111, edgeBPoint1111, edgeAE, edgeBE, edgeBC, B, edgeCPoint2111, edgeCD, edgeDPoint3111, edgeDE, C, D, E, faceAPoint1111Point2111Point3111, faceAEBPoint1111, faceBCPoint2111Point1111, faceCDPoint3111Point2111
  2. Cube(Point1112, Point2112, Point3112) → cube112, F, faceFJIPoint3112, faceGHIJ, edgeFPoint1112, edgePoint1112Point2112, edgePoint2112Point3112, edgeFPoint3112, edgeGPoint1112, edgeFJ, edgeGJ, edgeGH, G, edgeHPoint2112, edgeHI, edgeIPoint3112, edgeIJ, H, I, J, faceFPoint1112Point2112Point3112, faceFJGPoint1112, faceGHPoint2112Point1112, faceHIPoint3112Point2112
  3. Cube(Point1113, Point2113, Point3113) → cube113, K, faceKONPoint3113, faceLMNO, edgeKPoint1113, edgePoint1113Point2113, edgePoint2113Point3113, edgeKPoint3113, edgeLPoint1113, edgeKO, edgeLO, edgeLM, L, edgeMPoint2113, edgeMN, edgeNPoint3113, edgeNO, M, N, O, faceKPoint1113Point2113Point3113, faceKOLPoint1113, faceLMPoint2113Point1113, faceMNPoint3113Point2113
  4. Cube(Point1121, Point2121, Point3121) → cube121, P, facePPoint3121ST, faceQRST, edgePPoint1121, edgePoint1121Point2121, edgePoint2121Point3121, edgePPoint3121, edgePoint1121Q, edgePT, edgeQT, edgeQR, Q, edgePoint2121R, edgeRS, edgePoint3121S, edgeST, R, S, T, facePPoint1121Point2121Point3121, facePPoint1121QT, facePoint1121Point2121RQ, facePoint2121Point3121SR
  5. Cube(Point1122, Point2122, Point3122) → cube122, U, face2, face3, edgePoint1122U, edgePoint1122Point2122, edgePoint2122Point3122, edgePoint3122U, edgePoint1122V, edge1, edge2, edgeVW, V, edgePoint2122W, edgeWZ, edgePoint3122Z, edge3, W, Z, A_1, facePoint1122Point2122Point3122U, face1, facePoint1122Point2122WV, facePoint2122Point3122ZW
  6. Cube(Point1123, Point2123, Point3123) → cube123, B_1, face8, face9, edge4, edgePoint1123Point2123, edgePoint2123Point3123, edge7, edge5, edge9, edge11, edge10, C_1, edge6, edge12, edge8, edge13, D_1, E_1, F_1, face4, face6, face5, face7
  7. Cube(Point1131, Point2131, Point3131) → cube131, G_1, face14, face15, edge14, edgePoint1131Point2131, edgePoint2131Point3131, edge17, edge15, edge19, edge21, edge20, H_1, edge16, edge22, edge18, edge23, I_1, J_1, K_1, face10, face12, face11, face13
  8. Cube(Point1132, Point2132, Point3132) → cube132, L_1, face20, face21, edge24, edgePoint1132Point2132, edgePoint2132Point3132, edge27, edge25, edge29, edge31, edge30, M_1, edge26, edge32, edge28, edge33, N_1, O_1, P_1, face16, face18, face17, face19
  9. Cube(Point1133, Point2133, Point3133) → cube133, Q_1, face26, face27, edge34, edgePoint1133Point2133, edgePoint2133Point3133, edge37, edge35, edge39, edge41, edge40, R_1, edge36, edge42, edge38, edge43, S_1, T_1, U_1, face22, face24, face23, face25
  10. Cube(Point1211, Point2211, Point3211) → cube211, V_1, face32, face33, edge44, edgePoint1211Point2211, edgePoint2211Point3211, edge47, edge45, edge49, edge51, edge50, W_1, edge46, edge52, edge48, edge53, Z_1, A_2, B_2, face28, face30, face29, face31
  11. Cube(Point1212, Point2212, Point3212) → cube212, C_2, face38, face39, edge54, edgePoint1212Point2212, edgePoint2212Point3212, edge57, edge55, edge59, edge61, edge60, D_2, edge56, edge62, edge58, edge63, E_2, F_2, G_2, face34, face36, face35, face37
  12. Cube(Point1213, Point2213, Point3213) → cube213, H_2, face44, face45, edge64, edgePoint1213Point2213, edgePoint2213Point3213, edge67, edge65, edge69, edge71, edge70, I_2, edge66, edge72, edge68, edge73, J_2, K_2, L_2, face40, face42, face41, face43
  13. Cube(Point1221, Point2221, Point3221) → cube221, M_2, face50, face51, edge74, edgePoint1221Point2221, edgePoint2221Point3221, edge77, edge75, edge79, edge81, edge80, N_2, edge76, edge82, edge78, edge83, O_2, P_2, Q_2, face46, face48, face47, face49
  14. Cube(Point1223, Point2223, Point3223) → cube223, R_2, face56, face57, edge84, edgePoint1223Point2223, edgePoint2223Point3223, edge87, edge85, edge89, edge91, edge90, S_2, edge86, edge92, edge88, edge93, T_2, U_2, V_2, face52, face54, face53, face55
  15. Cube(Point1231, Point2231, Point3231) → cube231, W_2, face62, face63, edge94, edgePoint1231Point2231, edgePoint2231Point3231, edge97, edge95, edge99, edge101, edge100, Z_2, edge96, edge102, edge98, edge103, A_3, B_3, C_3, face58, face60, face59, face61
  16. Cube(Point1232, Point2232, Point3232) → cube232, D_3, face68, face69, edge104, edgePoint1232Point2232, edgePoint2232Point3232, edge107, edge105, edge109, edge111, edge110, E_3, edge106, edge112, edge108, edge113, F_3, G_3, H_3, face64, face66, face65, face67
  17. Cube(Point1233, Point2233, Point3233) → cube233, I_3, face74, face75, edge114, edgePoint1233Point2233, edgePoint2233Point3233, edge117, edge115, edge119, edge121, edge120, J_3, edge116, edge122, edge118, edge123, K_3, L_3, M_3, face70, face72, face71, face73
  18. Cube(Point1311, Point2311, Point3311) → cube311, N_3, face80, face81, edge124, edgePoint1311Point2311, edgePoint2311Point3311, edge127, edge125, edge129, edge131, edge130, O_3, edge126, edge132, edge128, edge133, P_3, Q_3, R_3, face76, face78, face77, face79
  19. Cube(Point1312, Point2312, Point3312) → cube312, S_3, face86, face87, edge134, edgePoint1312Point2312, edgePoint2312Point3312, edge137, edge135, edge139, edge141, edge140, T_3, edge136, edge142, edge138, edge143, U_3, V_3, W_3, face82, face84, face83, face85
  20. Cube(Point1313, Point2313, Point3313) → cube313, Z_3, face92, face93, edge144, edgePoint1313Point2313, edgePoint2313Point3313, edge147, edge145, edge149, edge151, edge150, A_4, edge146, edge152, edge148, edge153, B_4, C_4, D_4, face88, face90, face89, face91
  21. Cube(Point1321, Point2321, Point3321) → cube321, E_4, face98, face99, edge154, edgePoint1321Point2321, edgePoint2321Point3321, edge157, edge155, edge159, edge161, edge160, F_4, edge156, edge162, edge158, edge163, G_4, H_4, I_4, face94, face96, face95, face97
  22. Cube(Point1322, Point2322, Point3322) → cube322, J_4, face104, face105, edge164, edgePoint1322Point2322, edgePoint2322Point3322, edge167, edge165, edge169, edge171, edge170, K_4, edge166, edge172, edge168, edge173, L_4, M_4, N_4, face100, face102, face101, face103
  23. Cube(Point1323, Point2323, Point3323) → cube323, O_4, face110, face111, edge174, edgePoint1323Point2323, edgePoint2323Point3323, edge177, edge175, edge179, edge181, edge180, P_4, edge176, edge182, edge178, edge183, Q_4, R_4, S_4, face106, face108, face107, face109
  24. Cube(Point1331, Point2331, Point3331) → cube331, T_4, face116, face117, edge184, edgePoint1331Point2331, edgePoint2331Point3331, edge187, edge185, edge189, edge191, edge190, U_4, edge186, edge192, edge188, edge193, V_4, W_4, Z_4, face112, face114, face113, face115
  25. Cube(Point1332, Point2332, Point3332) → cube332, A_5, face122, face123, edge194, edgePoint1332Point2332, edgePoint2332Point3332, edge197, edge195, edge199, edge201, edge200, B_5, edge196, edge202, edge198, edge203, C_5, D_5, E_5, face118, face120, face119, face121
  26. Cube(Point1333, Point2333, Point3333) → cube333, F_5, face128, face129, edge204, edgePoint1333Point2333, edgePoint2333Point3333, edge207, edge205, edge209, edge211, edge210, G_5, edge206, edge212, edge208, edge213, H_5, I_5, J_5, face124, face126, face125, face127
  27. If(anim ≟ 4, 1, 0) → afterStop

AI 绘图提示语参考

绘制一个魔方模型，包含六个面和十二条棱。首先绘制一个立方体，然后围绕它构建其他五个立方体，每个立方体代表魔方的一个面。确保每个立方体的棱与相邻立方体的棱对齐，形成完整的魔方结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。