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立方体的平面展开图

立方体的平面展开图
几何画板及绘图内容加载中，请稍等……
2016-02-04 04:48
解析几何立体几何几何作图
这个范例展示了立方体的一个平面展开图及其在平面上的投影。核心数学概念包括立体几何和投影。通过使用GeoGebra命令如Circle, OrthogonalLine, Intersect等，可以构造出立方体及其展开图。适合初中及以上学生学习立体几何和投影概念。

GeoGebra 命令及参数

  1. Circle(A, r, zAxis) → c
  2. OrthogonalLine(B, xOyPlane) → a
  3. OrthogonalLine(C, xOyPlane) → b
  4. Intersect(a, c) → D,
  5. Intersect(b, c) → E,
  6. Segment(D, E) → d
  7. Circle(D, r, a) → e
  8. Circle(E, r, b) → f
  9. Line(D, xAxis) → g
  10. Line(E, xAxis) → h
  11. Intersect(g, e) → V03, V10
  12. Intersect(h, f) → V04, V07
  13. Point(Circle[V04, Distance[V03, V04], Segment[V03, V04]]) → J
  14. Cube(V03, V04, J) → i, K, faceJKON, faceLMNO, edgeFK, edgeFH, edgeHJ, edgeJK, edgeFL, edgeKO, edgeLO, edgeLM, L, edgeHM, edgeMN, edgeJN, edgeNO, M, N, O, faceFHJK, faceFKOL, faceFHML, faceHJNM
  15. Net(i, Net) → k, P, V01, V05, V06, V08, V09, facePQRS, facePSUT, face1, face2, face3, Q, faceTUVW, edgePS, edgePQ, edgeQR, edgeRS, edgeSU, edgeTU, edgePT, edgePZ, edge6, R, edge1, edge2, edge7, edge3, edge4, edge8, edge5, edgeUV, edgeVW, edgeTW, S, V14, V11, V12, V13, V02
  16. Ray(Foco, V01) → j
  17. Ray(Foco, V02) → l
  18. Ray(Foco, V03) → m
  19. Ray(Foco, V04) → n
  20. Intersect(j, xOyPlane) → VP02
  21. Intersect(l, xOyPlane) → VP03
  22. Intersect(m, xOyPlane) → VP01
  23. Intersect(n, xOyPlane) → VP04
  24. Ray(Foco, V05) → p
  25. Ray(Foco, V06) → q
  26. Ray(Foco, V07) → s
  27. Intersect(s, xOyPlane) → VP07
  28. Intersect(q, xOyPlane) → VP06
  29. Intersect(p, xOyPlane) → VP05
  30. Ray(Foco, V08) → t
  31. Ray(Foco, V09) → a_1
  32. Ray(Foco, V10) → b_1
  33. Intersect(t, xOyPlane) → VP08
  34. Intersect(a_1, xOyPlane) → VP09
  35. Intersect(b_1, xOyPlane) → VP10
  36. Ray(Foco, V11) → c_1
  37. Ray(Foco, V12) → d_1
  38. Ray(Foco, V13) → e_1
  39. Ray(Foco, V14) → f_1
  40. Intersect(c_1, xOyPlane) → VP11
  41. Intersect(d_1, xOyPlane) → VP12
  42. Intersect(e_1, xOyPlane) → VP13
  43. Intersect(f_1, xOyPlane) → VP14
  44. Polygon(VP06, VP05, VP04, VP07) → poly1, vp06, vp05, vp04, vp07
  45. Polygon(VP04, VP02, VP03, VP01) → poly2, vp04_1, vp02, vp03, vp01
  46. Polygon(VP07, VP04, VP01, VP10) → poly3, vp07_1, vp04_2, vp01_1, vp10
  47. Polygon(VP10, VP01, VP14, VP11) → poly4, vp10_1, vp01_2, vp14, vp11
  48. Polygon(VP11, VP14, VP13, VP12) → poly5, vp11_1, vp14_1, vp13, vp12
  49. Polygon(VP08, VP07, VP10, VP09) → poly6, vp08, vp07_2, vp10_2, vp09

AI 绘图提示语参考

绘制一个立方体的展开图和其在平面上的投影。首先画出立方体，然后画出展开图，接着画出立方体在平面上的投影，包括四个顶点和四个多边形。
以上提示语为根据原始绘图命令整理而来，仅供参考。