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Build the net of a cube

Build the net of a cube
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2018-03-19 20:11
PolygonSolid GeometryTransformation
This example demonstrates how to construct a cube by dragging the blue and green faces onto the grey net of a prism. Key math concepts include polygons, solid geometry, and geometric transformations. Construction highlights the use of GeoGebra commands like Intersect, Point, Polygon, Prism, Net, AreEqual, and Vector. Suitable for middle school students and above to enhance spatial reasoning skills in geometry.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, D
  4. Prism(poly1, 2) → a, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  5. Point(Circle[B, Distance[A, B], Segment[A, B]]) → I
  6. 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
  7. 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
  8. Polygon(Z_2, A_3, 4) → poly7, m_1, n_1, p_1, q_1, B_3, C_3
  9. Polygon(V_3, W_3, 4) → poly8, r_1, s_1, t_1, a_1, Z_3, A_4
  10. Point(Circle[B_4, 2]) → C_4
  11. Polygon(B_4, C_4, D_4, E_4) → poly9, b_4, c_4, d_4, e_4
  12. Point(Circle[F_4, 2]) → G_4
  13. Polygon(F_4, G_4, H_4, I_4) → poly10, f_4, g_4, h_4, i_4
  14. Point(Circle[J_4, 2]) → K_4
  15. Polygon(J_4, K_4, T_4, U_4) → poly11, j_4, k_4, t_4, u_4
  16. Point(Circle[V_4, 2]) → W_4
  17. Polygon(V_4, W_4, Z_4, A_5) → poly12, v_4, w_4, z_4, a_5
  18. Polygon(J, K, L, M) → poly2, j, k, l, m
  19. Polygon(M, N, C_1, N_2) → poly3, m_2, n, c_1, n_2
  20. Polygon(L, O_2, P_2, Q_2) → poly4, l_1, o_2, p_2, q_2
  21. Polygon(N, O_2, R_2, S_2) → poly5, n_3, o_1, r_2, s_2
  22. Polygon(L, O_2, N, M) → poly6, l_2, o_3, n_4, m_3
  23. Polygon(T_2, U_2, P_2, Q_2) → poly13, t_2, u_2, p_3, q_3
  24. AreEqual(poly7, poly8) → CheckSquares
  25. Vector(B_5, C_5) → u