制作立方体展开图
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①本范例演示如何通过拖动正方形面片在灰色网格上构建立方体的展开图;②涉及的核心数学概念包括多边形、立体几何、几何作图;③作图要点——使用了Polygon(多边形)、Intersect(相交)、Point(点)、Cube(立方体)、Net(网格)等GeoGebra命令;④适合高中阶段学习立体几何的学生或用于教学演示。
GeoGebra 命令及参数
Polygon(M, N, C_1, N_2) → poly3, m_2, n, c_1, n_2Polygon(K_4, T_4, 4) → poly11, q, r, s, t, D_5, E_5Polygon(C_4, D_4, 4) → poly9, b, e, f_1, g_1, F_5, G_5Polygon(V_3, W_3, 4) → poly8, r_1, s_1, t_1, a_1, Z_3, A_4Polygon(Z_2, A_3, 4) → poly7, m_1, n_1, p_1, q_1, B_3, C_3Polygon(I_4, F_4, 4) → poly10, h_1, i_1, j_1, k_1, H_5, I_5Polygon(A_5, V_4, 4) → poly12, b_1, d_1, e_1, f_2, J_5, K_5Intersect(zAxis, xAxis) → APoint(xAxis) → BPolygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, DCube(A, B, Point[Circle[B, Distance[A, B], Segment[A, B]]]) → a, E, face11, face12, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, F, edge28, edge29, edge30, edge31, G, H, B_4, face7, face8, face9, face10Point(Circle[B, Distance[A, B], Segment[A, B]]) → INet(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_2Net(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_3Polygon(J, K, L, M) → poly2, j, k, l, mPolygon(L, O_2, P_2, Q_2) → poly4, l_1, o_2, p_2, q_2Polygon(N, O_2, R_2, S_2) → poly5, n_3, o_1, r_2, s_2Polygon(L, O_2, N, M) → poly6, l_2, o_3, n_4, m_3Polygon(T_2, U_2, P_2, Q_2) → poly13, t_2, u_2, p_3, q_3Vector(B_5, C_5) → u
AI 绘图提示语参考
绘制一个立方体的展开图,包含六个正方形面。首先画一个底面,然后依次添加四个侧面和一个顶面,确保每个正方形面都与相邻的面共享边。
以上提示语为根据原始绘图命令整理而来,仅供参考。