正多边形棱柱及其展开图

几何画板及绘图内容加载中，请稍等……

2016-05-10 19:56

多边形立体几何几何作图

①本范例演示了正多边形棱柱的几何构造及其展开图；②涉及的核心数学概念包括多边形、棱柱、展开图、内切圆、几何变换等；③作图要点提炼自构造摘要，使用了点、线段、多边形、棱柱、展开图等 GeoGebra 命令与对象；④适合高中立体几何教学或几何作图练习，有助于理解空间图形与平面图形的转换关系。

GeoGebra 命令及参数

Point(Circle[A, s]) → B
Segment(A, B) → f
Polygon(A, B, n) → poly1, g, r, C, D, E, F, G, H, Q, S, p, i, j, k, l, m, p_1, q
Prism(poly1, h) → a, I, T, faceABJI, faceBCKJ, faceCDLK, faceADLI, face1, face2, face3, face4, face5, J, face6, faceIJKL, edgeAI, edgeBJ, edgeCK, edgeDL, edge1, edge3, edge5, edge7, K, edge9, edge11, edgeIJ, edgeJK, edgeKL, edgeIL, edge2, edge4, edge6, edge8, L, edge10, edge12, M, N, O, P, R
Net(a, net) → c, U, S_1, Z, A_1, B_1, C_1, D_1, E_1, K_1, L_1, M_1, V, N_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, W, J_2, F_1, I_1, J_1, T_1, U_1, V_1, W_1, Z_1, faceUVW, G_1, face8, face10, face9, face11, face12, face13, face14, face15, face16, face17, H_1, face7, edgeUV, edgeVW, edgeUW, edge25, edge26, edge38, edge39, edge40, edge41, O_1, edge42, edgeUZ, edge18, edge14, edge15, edge21, edge16, edge17, edge22, edge13, P_1, edge27, edge28, edge29, edge30, edge31, edge32, edge43, edge44, edge45, edge46, Q_1, edge47, edge48, edge49, edge50, edge51, edge52, edge53, edge54, edge55, edge56, R_1, edge57, edge20, edge19, edge23, edge24, edge33, edge34, edge35, edge36, edge37

AI 绘图提示语参考

绘制一个正多边形棱柱及其展开图。首先在平面上取一点作为圆心，画一个圆，在圆上取一点，连接圆心与该点形成一条边，然后以该边为基础构造一个正多边形底面。接着以该底面为基准，向上拉伸指定高度，形成一个正棱柱，棱柱的侧面由矩形构成。最后，将棱柱的各个面展开到平面上，形成其展开图，展开图包含底面、顶面以及所有侧面，各面之间通过棱边相连，整体展示从立体到平面的几何变换关系。

以上提示语为根据原始绘图命令整理而来，仅供参考。