立方体所有图案
几何画板及绘图内容加载中,请稍等……
①本范例演示立方体的各种图案与结构;②涉及核心数学概念包括立体几何、坐标几何、三角函数、向量运算;③作图要点使用了Vector(向量)、OrthogonalLine(垂线)、Mirror(镜像)、Polygon(多边形)等GeoGebra命令;④适合高中及以上学生及数学爱好者用于学习和探索三维图形的性质与变换。
GeoGebra 命令及参数
Vector(B_1, X) → uVector(B_1, Z) → wOrthogonalLine(View3D, yAxis) → aOrthogonalLine(View3D, xAxis) → b_2Vector(B_1, Y) → vMirror(J_1, V) → K_1Mirror(I_1, V) → L_1Polygon(K_1, L_1, J_1, I_1) → poly1, k_2, l_2, j_2, i_2Mirror(N_1, W) → S_1Mirror(M_1, W) → T_1Mirror(O_1, C) → U_1Mirror(C_1, C) → V_1Mirror(P_1, F_5) → W_1Mirror(F_1, F_5) → Z_1Mirror(R_1, Q) → A_2Mirror(Q_1, Q) → D_2Polygon(N_1, T_1, S_1, M_1) → poly2, n_2, t_1, s_1, m_2Polygon(F_1, P_1, Z_1, W_1) → poly3, f_2, p_2, z_1, w_1Polygon(C_1, O_1, V_1, U_1) → poly4, c_2, o_2, v_1, u_1Polygon(Q_1, R_1, D_2, A_2) → poly5, q_2, r_2, d_2, a_2Polygon(E_2, I_1, K_1, G_2) → poly6, e_2, i_3, k_3, g_2Polygon(H_2, I_2, I_1, E_2) → poly7, h_2, i_4, i_5, e_3Polygon(K_1, L_1, K_2, J_2) → poly8, k_4, l_3, k_5, j_3Polygon(J_1, L_2, M_2, L_1) → poly9, j_4, l_4, m_3, l_5Polygon(N_2, E_2, G_2, O_2) → poly10, n_3, e_4, g_3, o_3Polygon(R_2, S_1, M_1, P_2) → poly11, r_3, s_2, m_4, p_3Polygon(T_2, S_2, M_1, P_2) → poly12, t_2, s_3, m_5, p_4Polygon(R_2, S_1, U_2, V_2) → poly13, r_4, s_4, u_2, v_2Polygon(N_1, W_2, Z_2, T_1) → poly14, n_4, w_2, z_2, t_3Polygon(W_2, A_3, B_3, Z_2) → poly15, w_3, a_3, b_3, z_3Polygon(C_3, F_1, W_1, D_3) → poly16, c_4, f_3, w_4, d_4Polygon(C_3, E_3, F_3, F_1) → poly17, c_5, e_5, f_4, f_5Polygon(P_1, G_3, H_3, Z_1) → poly18, p_5, g_4, h_3, z_4Polygon(G_3, I_3, J_3, H_3) → poly19, g_5, i_6, j_5, h_4Polygon(Z_1, K_3, L_3, H_3) → poly20, z_5, k_6, l_6, h_5Polygon(M_3, Q_1, A_2, N_3) → poly21, m_6, q_1, a_4, n_5Polygon(M_3, P_3, O_3, Q_1) → poly22, m_7, p_6, o_1, q_3Polygon(R_1, Q_3, R_3, D_2) → poly23, r_5, q_4, r_6, d_5Polygon(A_2, D_2, S_3, T_3) → poly24, a_5, d_6, s_5, t_4Polygon(Q_3, U_3, V_3, R_3) → poly25, q_5, u_3, v_3, r_7Polygon(W_3, C_1, U_1, Z_3) → poly26, w_5, c_6, u_4, z_6Polygon(B_4, A_4, C_1, W_3) → poly27, b_4, a_6, c_7, w_6Polygon(O_1, C_4, D_4, V_1) → poly28, o_4, c_8, d_7, v_4Polygon(C_4, E_4, F_4, D_4) → poly29, c_9, e_7, f_7, d_8Polygon(D_4, F_4, G_4, H_4) → poly30, d_9, f_8, g_6, h_6Mirror(H, A) → FMirror(E, A) → GPolygon(E, H, G, F) → poly31, e_8, h_7, g_7, f_9Polygon(M_4, E, H, N_4) → poly32, m_8, e_9, h_8, n_6Polygon(H, J_4, L_4, G) → poly33, h_9, j_6, l_7, g_8Polygon(G, O_4, P_4, F) → poly34, g_9, o_5, p_7, f_{10}Polygon(F, S, R, E) → poly35, f_{11}, s_9, r_8, e_{10}Polygon(S, K_4, I_4, R) → poly36, s_6, k_7, i_7, r_9Mirror(D, B) → D'Mirror(I, B) → I'Polygon(I', D', N, O) → poly37, i', d', n, o_6Polygon(I', D', I, D) → poly38, i'_1, d'_1, i, d_1Polygon(D, I, P, T) → poly39, d_3, i_1, p, tPolygon(A_1, D, T, U) → poly40, a_1, d_{10}, t_5, u_5Polygon(D', J, K, I) → poly41, d'_2, j, k_1, i_8Polygon(J, L, M, K) → poly42, j_1, l, m, k_8Mirror(E_1, D_1) → H_1Mirror(G_1, D_1) → B_2Polygon(E_1, G_1, H_1, B_2) → poly43, e_1, g_1, h_1, b_1Polygon(H_1, C_2, F_2, G_1) → poly44, h_{10}, c_1, f_1, g_{10}Polygon(C_2, Q_2, Q_4, F_2) → poly45, c_{10}, q_6, q_7, f_6Polygon(G_1, R_4, S_4, E_1) → poly46, g_{11}, r_1, s_7, e_6Polygon(T_4, E_1, S_4, U_4) → poly47, t_6, e_{11}, s_8, u_6Polygon(W_4, T_4, U_4, V_4) → poly48, w_7, t_7, u_7, v_5Mirror(B_5, Z_4) → C_5Mirror(A_5, Z_4) → D_5Polygon(D_5, E_5, J_5, K_5) → poly49, d_{11}, e_{12}, j_7, k_9Polygon(C_5, D_5, B_5, A_5) → poly50, c_{11}, d_{12}, b_5, a_7Polygon(D_5, E_5, G_5, B_5) → poly51, d_{13}, e_{13}, g_{12}, b_6Polygon(E_5, H_5, I_5, G_5) → poly52, e_{14}, h_{11}, i_9, g_{13}Polygon(A_5, B_5, L_5, M_5) → poly53, a_8, b_7, l_1, m_1Polygon(M_5, N_5, O_5, A_5) → poly54, m_9, n_1, o_7, a_9Mirror(R_5, P_5) → S_5Mirror(Q_5, P_5) → T_5Polygon(Q_5, S_5, T_5, R_5) → poly55, q_8, s_{10}, t_8, r_{10}Polygon(T_5, U_5, V_5, S_5) → poly56, t_9, u_8, v_6, s_{11}Polygon(U_5, W_5, Z_5, V_5) → poly57, u_9, w_8, z_7, v_7Polygon(B_6, A_6, W_5, U_5) → poly58, b_8, a_{10}, w_9, u_{10}Polygon(Q_5, S_5, C_6, D_6) → poly59, q_9, s_{12}, c_{12}, d_{14}Polygon(F_6, Q_5, D_6, E_6) → poly60, f_{12}, q_{10}, d_{15}, e_{15}Mirror(H_6, G_6) → J_6Mirror(I_6, G_6) → K_6Polygon(U_6, T_6, Q_6, J_6) → poly61, u_{11}, t_{10}, q_{11}, j_8Polygon(H_6, K_6, J_6, I_6) → poly62, h_{12}, k_{10}, j_9, i_{10}Polygon(I_6, J_6, Q_6, P_6) → poly63, i_{11}, j_{10}, q_{12}, p_1Polygon(I_6, L_6, M_6, H_6) → poly64, i_{12}, l_8, m_{10}, h_{13}Polygon(M_6, N_6, O_6, H_6) → poly65, m_{11}, n_7, o_8, h_{14}Polygon(Q_6, R_6, S_6, T_6) → poly66, q_{13}, r_{11}, s_{13}, t_{11}
AI 绘图提示语参考
绘制一个三维立方体的各种图案和结构,展示核心数学概念,包括立体几何、坐标几何、三角学和向量运算。首先构建立方体的基本向量,然后利用正交线和镜像操作创建对称图案,最后将多个点连接成多边形,形成复杂的几何结构,体现立方体的对称性和空间关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。