Which net matches the displayed solid?

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2016-09-21 20:00

This example demonstrates how to identify which net corresponds to a given solid figure. Key math concepts include solid geometry, polygons, and spatial visualization. GeoGebra commands and objects used in construction are Intersect, Point, Polygon, Prism, Cube, Vector, Net, and Pyramid. Suitable for middle school students and above to learn the recognition and matching of solid figures and their nets, as well as for geometric modeling instruction.

GeoGebra Commands & Parameters

Intersect(zAxis, xAxis) → A
Point(xAxis) → B
Polygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, D
Prism(poly1, 2) → a, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
Point(Circle[B, Distance[A, B], Segment[A, B]]) → I
Cube(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, faceBIML
Vector(D_1, E_1) → u
Net(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_2
Vector(L_2, M_2) → v
Net(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_2
Net(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_3
Net(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_4
Pyramid(poly1, 2) → b_1, T_4, face25, face27, face28, face26, edge77, edge78, edge79, edge80
Net(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, face33
Net(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, face38
Cube(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, face42
Net(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_6
Net(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_6
Pyramid(poly1, 3) → m_1, B_7, face57, face59, face60, face58, edge153, edge154, edge155, edge156
Net(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, face65
Net(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, face70
Prism(poly1, 2) → r_1, S_7, edge181, edge182, edge183, edge184, edge185, edge187, edge188, edge186, T_7, U_7, V_7, face71, face73, face74, face72, face75
Net(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_8
Net(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