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构建立方体展开图

构建立方体展开图
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2018-03-19 20:11
多边形立体几何变换
本范例演示如何通过拖拽蓝色和绿色面将棱柱的展开图拼合成立方体。涉及的核心数学概念包括多边形、立体几何和几何变换。作图要点：使用了Intersect（交集）、Point（点）、Polygon（多边形）、Prism（棱柱）、Net（展开图）、AreEqual（相等判断）和Vector（向量）等GeoGebra命令与对象。适合初中及以上学生用于学习立体几何和空间想象能力。

GeoGebra 命令及参数

  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