Net of Solids

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2018-06-26 02:19

In collections Solid figures

This example demonstrates the nets of cubes, prisms, and pyramids, including their folding and unfolding processes. It involves core mathematical concepts such as polygons, solid geometry, and spatial visualization. Key GeoGebra commands and objects used include Intersect, Point, Polygon, Prism, Cube, Vector, Net, and Pyramid. Suitable for high school mathematics teaching on solid geometry, geometric modeling, and spatial reasoning training.

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