几何体的展开图
几何画板及绘图内容加载中,请稍等……
所属专题
Solid figures
①本范例演示了立方体、棱柱和金字塔的展开图及其折叠过程;②涉及的核心数学概念包括多边形、立体几何、空间想象能力;③作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象:Intersect(交点)、Point(点)、Polygon(多边形)、Prism(棱柱)、Cube(立方体)、Vector(向量)、Net(展开图)、Pyramid(金字塔);④适合的学段或用途:高中数学立体几何教学、几何建模、空间想象能力训练。
GeoGebra 命令及参数
Intersect(zAxis, xAxis) → APoint(xAxis) → BPolygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, DPrism(poly1, 2) → a, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGHPoint(Circle[B, Distance[A, B], Segment[A, B]]) → ICube(A, B, I) → b, J, faceIJNM, faceKLMN, edgeAJ, edgeAB_1, edgeBI_1, edgeIJ, edgeAK, edgeJN, edgeKN, edgeKL, K, edgeBL, edgeLM, edgeIM, edgeMN, L, M, N, faceABIJ, faceAJNK, faceABLK, faceBIMLVector(D_1, E_1) → uNet(a, c) → d, V_1, G_2, H_2, I_2, J_2, K_2, face1, face2, face4, face5, face3, W_1, face6, edge1, edge5, edge8, edge2, edge3, edge13, edge6, edge7, edge16, Z_1, edge9, edge10, edge17, edge11, edge12, edge18, edge4, edge15, edge19, edge14, A_2, B_2, C_2, D_2, E_2, F_2Vector(L_2, M_2) → vNet(b, k) → l, N_2, W_2, Z_2, A_3, B_3, C_3, face7, face9, face8, face10, face11, O_2, face12, edge21, edge20, edge24, edge27, edge30, edge32, edge22, edge23, edge36, P_2, edge25, edge26, edge37, edge28, edge29, edge38, edge31, edge34, edge35, edge33, Q_2, R_2, S_2, T_2, U_2, V_2Net(a, o) → p, H_3, Q_3, R_3, S_3, T_3, U_3, face13, face14, face16, face17, face15, I_3, face18, edge39, edge43, edge46, edge40, edge41, edge51, edge44, edge45, edge54, J_3, edge47, edge48, edge55, edge49, edge50, edge56, edge42, edge53, edge57, edge52, K_3, L_3, M_3, N_3, O_3, P_3Net(b, q) → r, V_3, G_4, H_4, I_4, J_4, K_4, face19, face21, face20, face22, face23, W_3, face24, edge59, edge58, edge62, edge65, edge68, edge70, edge60, edge61, edge74, Z_3, edge63, edge64, edge75, edge66, edge67, edge76, edge69, edge72, edge73, edge71, A_4, B_4, C_4, D_4, E_4, F_4Pyramid(poly1, 2) → b_1, T_4, face25, face27, face28, face26, edge77, edge78, edge79, edge80Net(b_1, c_1) → c_1, U_4, face29, face31, face32, face30, edge81, edge85, edge88, edge82, edge83, edge86, V_4, edge87, edge89, edge90, edge91, edge92, edge84, W_4, Z_4, A_5, B_5, C_5, D_5, face33Net(b_1, d_1) → e_1, E_5, face34, face36, face37, face35, edge93, edge97, edge100, edge94, edge95, edge98, F_5, edge99, edge101, edge102, edge103, edge104, edge96, G_5, H_5, I_5, J_5, K_5, L_5, face38Cube(A, B, I) → f_1, M_5, face43, face44, edge105, edgeAB, edgeBI, edge108, edge106, edge110, edge112, edge111, N_5, edge107, edge113, edge109, edge114, O_5, P_5, Q_5, face39, face41, face40, face42Net(f_1, g_1) → h_1, R_5, C_6, D_6, E_6, F_6, G_6, face45, face47, face46, face48, face49, S_5, face50, edge116, edge115, edge119, edge122, edge125, edge127, edge117, edge118, edge131, T_5, edge120, edge121, edge132, edge123, edge124, edge133, edge126, edge129, edge130, edge128, U_5, V_5, W_5, Z_5, A_6, B_6Net(f_1, i_1) → j_1, H_6, Q_6, R_6, S_6, T_6, U_6, face51, face53, face52, face54, face55, I_6, face56, edge135, edge134, edge138, edge141, edge144, edge146, edge136, edge137, edge150, J_6, edge139, edge140, edge151, edge142, edge143, edge152, edge145, edge148, edge149, edge147, K_6, L_6, M_6, N_6, O_6, P_6Pyramid(poly1, 3) → m_1, B_7, face57, face59, face60, face58, edge153, edge154, edge155, edge156Net(m_1, n_1) → o_1, C_7, face61, face63, face64, face62, edge157, edge161, edge164, edge158, edge159, edge162, D_7, edge163, edge165, edge166, edge167, edge168, edge160, E_7, F_7, G_7, H_7, I_7, J_7, face65Net(m_1, p_1) → q_1, K_7, face66, face68, face69, face67, edge169, edge173, edge176, edge170, edge171, edge174, L_7, edge175, edge177, edge178, edge179, edge180, edge172, M_7, N_7, O_7, P_7, Q_7, R_7, face70Prism(poly1, 2) → r_1, S_7, edge181, edge182, edge183, edge184, edge185, edge187, edge188, edge186, T_7, U_7, V_7, face71, face73, face74, face72, face75Net(r_1, s_1) → t_1, W_7, H_8, I_8, J_8, K_8, L_8, face76, face77, face79, face80, face78, Z_7, face81, edge189, edge193, edge196, edge190, edge191, edge201, edge194, edge195, edge204, A_8, edge197, edge198, edge205, edge199, edge200, edge206, edge192, edge203, edge207, edge202, B_8, C_8, D_8, E_8, F_8, G_8Net(r_1, u_1) → v_1, M_8, V_8, W_8, Z_8, A_9, B_9, face82, face83, face85, face86, face84, N_8, face87, edge208, edge212, edge215, edge209, edge210, edge220, edge213, edge214, edge223, O_8, edge216, edge217, edge224, edge218, edge219, edge225, edge211, edge222, edge226, edge221, P_8, Q_8, R_8, S_8, T_8, U_8