正方体展开图动态演示 by 季阳天
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所属专题
Cuboids & their Nets
①本范例动态演示正方体的展开图及其变化过程;②涉及的核心数学概念包括立体几何、多边形、面与棱的关系;③作图要点:使用了Point、Cube、Net等GeoGebra命令,构建了正方体的顶点、面、棱等对象;④适合初中及以上学生学习立体几何,或用于教学演示。
GeoGebra 命令及参数
Point(Circle[B, Distance[A, B], Segment[A, B]]) → CCube(A, B, C) → a, D, 面CDHG, 面EFGH, 棱AD, 棱AB, 棱BC, 棱CD, 棱AE, 棱DH, 棱EH, 棱EF, E, 棱BF, 棱FG, 棱CG, 棱GH, F, G, H, 面ABCD, 面ADHE, 面ABFE, 面BCGFNet(a, c, 棱AE, 面ABCD, 棱AD, 棱AE, 棱DH, 棱CG, 棱GH, 棱EF, 棱BF) → b, I, R, S, T, U, V, 面1, 面2, 面3, 面4, 面5, J, 面6, 棱1, 棱2, 棱3, 棱4, 棱5, 棱6, 棱7, 棱8, 棱9, K, 棱10, 棱11, 棱12, 棱13, 棱14, 棱15, 棱16, 棱17, 棱18, 棱19, L, M, N, O, P, QNet(a, c, 棱AE, 面ABCD, 棱BF, 棱CD, 棱AE, 棱CG, 棱GH, 棱EF, 棱EH) → d, W, H_1, I_1, J_1, K_1, L_1, 面7, 面8, 面9, 面10, 面11, Z, 面12, 棱20, 棱21, 棱22, 棱23, 棱24, 棱25, 棱26, 棱27, 棱28, A_1, 棱29, 棱30, 棱31, 棱32, 棱33, 棱34, 棱35, 棱36, 棱37, 棱38, B_1, C_1, D_1, E_1, F_1, G_1Net(a, c, 棱AE, 面ABCD, 棱AB, 棱CD, 棱AE, 棱CG, 棱GH, 棱EF, 棱EH) → e, M_1, V_1, W_1, Z_1, A_2, B_2, 面13, 面14, 面16, 面15, 面17, N_1, 面18, 棱40, 棱39, 棱42, 棱45, 棱47, 棱49, 棱41, 棱43, 棱44, O_1, 棱56, 棱53, 棱52, 棱46, 棱48, 棱51, 棱50, 棱54, 棱57, 棱55, P_1, Q_1, R_1, S_1, T_1, U_1Net(a, c, 棱AE, 面ABCD, 棱AB, 棱CD, 棱AE, 棱CG, 棱GH, 棱BF, 棱EH) → f, C_2, L_2, M_2, N_2, O_2, P_2, 面19, 面20, 面24, 面21, 面22, D_2, 面23, 棱59, 棱58, 棱61, 棱63, 棱65, 棱67, 棱60, 棱71, 棱72, E_2, 棱76, 棱75, 棱62, 棱70, 棱64, 棱66, 棱69, 棱68, 棱74, 棱73, F_2, G_2, H_2, I_2, J_2, K_2Net(a, c, 棱AE, 面ABCD, 棱BF, 棱DH, 棱AE, 棱CG, 棱GH, 棱EF, 棱EH) → g, Q_2, B_3, C_3, D_3, E_3, F_3, 面25, 面27, 面26, 面28, 面29, R_2, 面30, 棱78, 棱77, 棱81, 棱84, 棱87, 棱89, 棱79, 棱80, 棱90, S_2, 棱82, 棱83, 棱91, 棱85, 棱86, 棱95, 棱88, 棱92, 棱94, 棱93, T_2, U_2, V_2, W_2, Z_2, A_3Net(a, c, 棱AE, 面ABCD, 棱AB, 棱DH, 棱AE, 棱CG, 棱GH, 棱EF, 棱EH) → h, G_3, P_3, Q_3, R_3, S_3, T_3, 面31, 面32, 面34, 面33, 面35, H_3, 面36, 棱97, 棱96, 棱99, 棱102, 棱105, 棱107, 棱98, 棱100, 棱101, I_3, 棱112, 棱109, 棱108, 棱103, 棱104, 棱114, 棱106, 棱110, 棱113, 棱111, J_3, K_3, L_3, M_3, N_3, O_3Net(a, c, 棱BF, 面ABCD, 棱AD, 棱CD, 棱AB, 棱EH, 棱GH, 棱DH, 棱EH) → i, U_3, F_4, G_4, H_4, I_4, J_4, 面37, 面42, 面41, 面38, 面39, V_3, 面40, 棱116, 棱115, 棱117, 棱119, 棱128, 棱131, 棱132, 棱129, 棱123, W_3, 棱124, 棱130, 棱118, 棱122, 棱120, 棱126, 棱133, 棱121, 棱127, 棱125, Z_3, A_4, B_4, C_4, D_4, E_4Net(a, c, 棱BF, 面ABCD, 棱AD, 棱CD, 棱AB, 棱EH, 棱CG, 棱DH, 棱EH) → j, K_4, T_4, U_4, V_4, W_4, Z_4, 面43, 面48, 面46, 面44, 面47, L_4, 面45, 棱135, 棱134, 棱136, 棱138, 棱146, 棱151, 棱152, 棱147, 棱141, M_4, 棱142, 棱150, 棱137, 棱140, 棱139, 棱143, 棱148, 棱149, 棱144, 棱145, N_4, O_4, P_4, Q_4, R_4, S_4Net(a, c, 棱BF, 面ABCD, 棱AD, 棱CG, 棱AB, 棱EH, 棱GH, 棱DH, 棱EH) → k, A_5, J_5, K_5, L_5, M_5, N_5, 面49, 面54, 面53, 面50, 面51, B_5, 面52, 棱154, 棱153, 棱155, 棱157, 棱166, 棱169, 棱170, 棱167, 棱162, C_5, 棱163, 棱168, 棱156, 棱161, 棱158, 棱159, 棱171, 棱160, 棱165, 棱164, D_5, E_5, F_5, G_5, H_5, I_5Net(a, c, 面ABCD, 棱AB, 棱BC, 棱AE, 棱DH, 棱GH, 棱FG, 棱EF) → l, O_5, Z_5, A_6, B_6, C_6, D_6, 面55, 面56, 面60, 面58, 面57, P_5, 面59, 棱173, 棱172, 棱175, 棱176, 棱179, 棱181, 棱174, 棱187, 棱188, Q_5, 棱190, 棱189, 棱177, 棱178, 棱186, 棱185, 棱180, 棱183, 棱184, 棱182, R_5, S_5, T_5, U_5, V_5, W_5Net(a, c, 面ABCD, 棱AD, 棱CD, 棱BF, 棱DH, 棱EF, 棱EH, 棱FG) → m, E_6, N_6, O_6, P_6, Q_6, R_6, 面61, 面63, 面62, 面64, 面65, F_6, 面66, 棱192, 棱191, 棱195, 棱198, 棱193, 棱194, 棱203, 棱202, 棱201, G_6, 棱196, 棱197, 棱204, 棱199, 棱205, 棱207, 棱200, 棱206, 棱209, 棱208, H_6, I_6, J_6, K_6, L_6, M_6
AI 绘图提示语参考
绘制一个立方体的展开图,包含六个正方形面和它们之间的连接线。首先画一个正方形ABCD,然后依次添加棱AE、BF、CG、DH,接着画出六个面ABCD、ADHE、ABFE、BCGF、CDHG、EFGH,最后通过Net命令将这些面和棱展开成平面图形,展示立方体的所有面和棱。
以上提示语为根据原始绘图命令整理而来,仅供参考。