六棱柱的展开图 by powere

六棱柱的展开图 by powere
几何画板及绘图内容加载中,请稍等……
2018-08-14 02:10
①本范例演示了六棱柱的展开图,直观展示其表面由六个矩形和两个正六边形组成;②涉及的核心数学概念包括立体几何、多边形性质、相似变换;③作图要点提炼自GeoGebra命令:使用Polygon绘制多边形,Prism生成棱柱,Segment和Point创建顶点,Rotate和Mirror实现旋转与镜像变换;④适合高中阶段学习立体几何、几何作图的学生使用,也可用于教学演示。

GeoGebra 命令及参数

  1. Polygon(A, B, 6, xOyPlane) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Prism(poly1, A + (0, 0, 4)) → g, G, faceEFKJ, face2, face3, edge1, edgeBG, edgeCH, edgeDI, edgeEJ, edgeFK, edge2, H, edgeGH, edgeHI, edgeIJ, edgeJK, edge3, I, J, K, face1, faceBCHG, faceCDIH, faceDEJI
  3. Segment(M, M + (0, 0, 2)) → h
  4. Point(h) → N
  5. Rotate(Polygon[E, D, I, J], (90° * t), Segment[D, E]) → poly2
  6. Rotate(Polygon[G, H, I, J, K, L], (90° * t), Segment[I, J]) → poly3
  7. Rotate(poly3, (90° * t), Segment[D, E]) → poly3'
  8. Rotate(Polygon[C, D, I, H], (60° * t), Segment[D, I]) → poly4
  9. Rotate(poly4, (90° * t), Segment[D, E]) → poly4'
  10. Mirror(poly4, OrthogonalPlane[Midpoint[D, E], Segment[D, E]]) → poly4'_1
  11. Rotate(poly4'_1, (90° * t), Segment[D, E]) → poly5
  12. Rotate(C, (60° * t), Segment[D, I]) → C'
  13. Mirror(Polygon[D, E, J, I], OrthogonalPlane[Midpoint[D, C'], Segment[D, C']]) → poly6
  14. Mirror(poly6, OrthogonalPlane[Midpoint[D, E], Segment[D, E]]) → poly6'
  15. Rotate(poly6, (90° * t), Segment[D, E]) → poly6'_1
  16. Rotate(poly6', (90° * t), Segment[D, E]) → poly6''
  17. Mirror(E, OrthogonalPlane[Midpoint[D, C'], Segment[D, C']]) → E'
  18. Mirror(poly4, OrthogonalPlane[Midpoint[E', C'], Segment[E', C']]) → poly4'_2
  19. Rotate(poly4'_2, (90° * t), Segment[D, E]) → poly7
  20. Rotate(poly3, (90° * t), Segment[D, E]) → poly3'_1
  21. Polygon(A, B, 6, xOyPlane) → poly8, i, R, j, k, l, m, n, O, P, Q
  22. Rotate(poly6', (90° * t), Segment[D, E]) → poly6''_1
  23. Rotate(poly4'_1, (90° * t), Segment[D, E]) → poly9
  24. Rotate(Polygon[E, D, I, J], (90° * t), Segment[D, E]) → poly10
  25. Rotate(poly4, (90° * t), Segment[D, E]) → poly4'_3
  26. Rotate(poly6, (90° * t), Segment[D, E]) → poly6'_2
  27. Rotate(poly4'_2, (90° * t), Segment[D, E]) → poly11

AI 绘图提示语参考

画一个六棱柱的展开图,包含六个矩形和两个六边形,展示其表面结构。首先绘制一个六边形,然后向上延伸形成柱体,接着将六边形和矩形展开,通过旋转和镜像操作得到完整的展开图,最后将所有部分组合在一起,呈现六棱柱的展开形态。
以上提示语为根据原始绘图命令整理而来,仅供参考。