Net of a Solid

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2017-02-23 16:17

This example demonstrates how to identify the net that matches a given solid. Key mathematical concepts include the geometry of polyhedra. Using GeoGebra commands such as Polygon, Prism, Cube, etc., the net of a polyhedron can be constructed. Suitable for students in middle school and above.

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

AI Drawing Prompt Reference

In 3D space, start with a square base lying on the horizontal plane. Build a right prism of height 2 on this base. Then construct a cube sharing one edge with the base, with another edge pointing to a point in space. Also build a pyramid of height 2 on the same base. Finally, display multiple nets (unfolded surfaces) for each solid—at least two different nets for the prism, cube, and pyramid—with vectors indicating the unfolding directions.

The prompt above was compiled from the original drawing commands and is for reference only.