Net of Cube

Loading the math board and drawing, please wait…

2016-07-04 19:20

In collections Nets of Solid Figures (Primary 6)

This example demonstrates the net of a cube and its folding process. It involves core mathematical concepts such as solid geometry, polygon construction, and spatial visualization. Key construction points include using GeoGebra commands/objects like Point, Cube, Intersect, Net, Polygon, Segment, and PointIn. Suitable for high school mathematics students or teachers for teaching demonstrations, helping to understand the transformation between three-dimensional shapes and two-dimensional plane figures.

GeoGebra Commands & Parameters

Point(yAxis) → F_2
Point(Circle[F_2, Distance[E_2, F_2], Segment[E_2, F_2]]) → G_2
Cube(E_2, F_2, G_2) → u, H_2, face11, face12, edge21, edge20, edge23, edge25, edge22, edge27, edge29, edge28, I_2, edge24, edge30, edge26, edge31, J_2, K_2, L_2, face7, face9, face8, face10
Point(xAxis) → B
Intersect(xAxis, zAxis) → A
Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
Cube(A, B, C) → b, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
Net(b, a, faceABCD, edgeBC, edgeCG, edgeGH, edgeEF, edgeAD, edgeBF) → n_{21}, I, R, S, T, U, V, faceIJKL, faceIMPO, faceIJNM, faceQRTS, faceKLVU, J, faceMPQR, edgeIL, edgeIJ, edgeJK, edgeKL, edgeIM, edgeIO, edgeOP, edgeMP, edgeMN, K, edgeJN, edgeQR, edgeQS, edgeST, edgeRT, edgeKU, edgeUV, edgeLV, edgePQ, edgeMR, L, M, N, O, P, Q
Intersect(xAxis, yAxis) → W
Polygon(W, Z, 4) → poly1, f, g, h, i, A_1, B_1
Polygon(Z, W, 4) → poly2, j, k, l, m, C_1, D_1
Polygon(C_1, W, 4) → poly3, n_2, p, q, r, E_1, F_1
Polygon(C_1, F_1, 4) → poly4, s, t, d, e, G_1, H_1
Polygon(H_1, G_1, 4) → poly5, f_1, g_1, h_1, i_1, I_1, J_1
Point(Circle[K_1, 1]) → L_1
Segment(K_1, L_1) → j_1
Polygon(K_1, L_1, 4) → poly6, k_1, l_1, m_1, n_1, M_1, N_1
Net(u, a, face7, edge25, edge21, edge27, edge22) → o, o_2, o_{11}, o_{12}, o_{13}, o_{14}, o_{15}, o_{16}, o_{17}, o_{18}, o_{19}, o_{20}, o_3, o_{21}, o_{22}, o_{23}, o_{24}, o_{25}, o_{26}, o_{27}, o_{28}, o_{29}, o_{30}, o_4, o_{31}, o_{32}, o_{33}, o_{34}, o_{35}, o_{36}, o_{37}, o_{38}, o_{39}, o_{40}, o_5, o_6, o_7, o_8, o_9, o_{10}
Net(u, a, face7, edge25, edge22, edge27, edge29) → v, O_1, Z_1, A_2, B_2, C_2, D_2, face1, face2, face3, face4, face5, P_1, face6, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, edge9, Q_1, edge10, edge11, edge12, edge13, edge14, edge15, edge16, edge17, edge18, edge19, R_1, S_1, T_1, U_1, V_1, W_1
Net(u, a, face7, edge25, edge21, edge27, edge29) → w, w_2, w_{11}, w_{12}, w_{13}, w_{14}, w_{15}, w_{16}, w_{17}, w_{18}, w_{19}, w_{20}, w_3, w_{21}, w_{22}, w_{23}, w_{24}, w_{25}, w_{26}, w_{27}, w_{28}, w_{29}, w_{30}, w_4, w_{31}, w_{32}, w_{33}, w_{34}, w_{35}, w_{36}, w_{37}, w_{38}, w_{39}, w_{40}, w_5, w_6, w_7, w_8, w_9, w_{10}
Net(u, a, face7, edge21, edge23, edge24, edge22) → n_{31}, PrP_3, D_3, E_3, F_3, G_3, H_3, face13, face17, face14, face16, face15, PrP_4, face18, edge33, edge32, edge35, edge37, edge40, edge48, edge50, edge41, edge34, PrP_2, edge42, edge36, edge38, edge39, edge49, edge47, edge46, edge43, edge45, edge44, PrP_1, PrP_5, PrP_6, PrP_7, PrP_8, C_3
Polygon(I_3, J_3, 4) → poly7, p_1, q_1, r_1, s_1, K_3, L_3
Polygon(I_3, L_3, 4) → poly8, t_1, a_1, b_1, c_1, M_3, N_3
Polygon(J_3, I_3, 4) → poly10, h_2, i_2, j_2, k_2, Q_3, R_3
Polygon(R_3, Q_3, 4) → poly11, l_2, m_2, p_2, q_2, S_3, T_3
Polygon(T_3, S_3, 4) → poly12, r_2, s_2, t_2, a_2, U_3, V_3
Net(u, a, face7, edge21, edge24, edge22) → n_{32}, O_2, C_4, D_4, E_4, F_4, G_4, face19, face23, face20, face21, face22, Q_2, face24, edge52, edge51, edge54, edge57, edge60, edge68, edge69, edge61, edge53, R_2, edge62, edge55, edge56, edge66, edge58, edge59, edge67, edge63, edge65, edge64, O_3, P_3, W_3, Z_3, A_4, B_4
Net(u, a, face7, edge21, edge23, edge22) → n_{33}, H_4, Q_4, R_4, S_4, T_4, U_4, face25, face29, face26, face27, face28, I_4, face30, edge71, edge70, edge73, edge76, edge78, edge87, edge88, edge79, edge72, J_4, edge80, edge74, edge83, edge85, edge75, edge77, edge86, edge81, edge84, edge82, K_4, L_4, M_4, N_4, O_4, P_4
Net(u, a, face7, edge21, edge23, edge22, edge24, edge26) → n_{34}, V_4, G_5, H_5, I_5, J_5, K_5, face31, face34, face32, face36, face33, W_4, face35, edge90, edge89, edge92, edge94, edge96, edge106, edge107, edge97, edge91, Z_4, edge98, edge93, edge100, edge103, edge104, edge101, edge95, edge105, edge99, edge102, A_5, B_5, C_5, D_5, E_5, F_5
Net(u, a, face7, edge21, edge25, edge28, edge30) → n_{41}, L_5, U_5, V_5, W_5, Z_5, A_6, face37, face39, face38, face40, face41, M_5, face42, edge109, edge108, edge112, edge115, edge110, edge111, edge121, edge119, edge118, N_5, edge113, edge114, edge124, edge116, edge125, edge126, edge117, edge122, edge123, edge120, O_5, P_5, Q_5, R_5, S_5, T_5
Polygon(B_6, C_6, 4) → poly9, c, d_1, e_1, f_2, D_6, E_6
Polygon(C_6, B_6, 4) → poly13, g_2, b_2, c_2, d_2, F_6, G_6
Polygon(F_6, B_6, 4) → poly14, e_2, f_3, g_3, h_3, H_6, I_6
Polygon(F_6, I_6, 4) → poly15, i_3, j_3, k_3, l_3, J_6, K_6
Polygon(J_6, I_6, 4) → poly16, m_3, n_3, p_3, q_3, L_6, M_6
Intersect(edge124, edge116) → O_6
PointIn(Plane[face41]) → P_6
Polygon(O_6, P_6, 4, face41) → poly17, r_3, s_3, t_3, a_3, Q_6, R_6
Polygon(P_6, O_6, 4, face41) → poly18, b_3, c_3, d_3, e_3, S_6, T_6
PointIn(Plane[face38]) → U_6
PointIn(Plane[face38]) → V_6
Polygon(U_6, V_6, 4, face38) → poly19, f_4, g_4, h_4, i_4, W_6, Z_6

AI Drawing Prompt Reference

Draw a net of a cube, including six square faces and their connecting lines. First, draw points F and G, then use these points and another point E to draw a cube u. Next, draw points B and C, and use them to draw another cube b. Then, draw the net n of cube b. After that, draw the nets o, v, and w of cube u. Finally, draw the other nets n31 to n34 and n41 of cube u.

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