积极 AI Logo 积极 AI

六面体星形构造

六面体星形构造
几何画板及绘图内容加载中，请稍等……
2018-10-25 00:52
多边形立体几何几何作图
所属专题 surface 3D /3D-Oberflächen 1
①本范例演示了如何通过构造六面体并生成其星形多面体；②涉及的核心数学概念包括立体几何、多边形构造、线性优化、椭圆、幂函数、直方图和几何平均值；③作图要点使用了GeoGebra命令：立方体构造、交点计算、中点确定、多边形绘制；④适合高中及以上学生学习和理解复杂几何形状的构造方法，可用于立体几何和几何作图的教学。

GeoGebra 命令及参数

  1. Cube((1, 0, 0), (0, 1, 0), zAxis) → a_1, A, Fläche4, FlächeABFE, FlächeCDEF, Kante2, Kante1, Kante4, KanteAB, Kante3, KanteBF, KanteCF, B, KanteCD, Kante5, KanteDE, KanteAE, KanteEF, C, D, E, F, Fläche1, Fläche3, Fläche2
  2. Intersect(Kante2, xAxis) → G
  3. Intersect(Kante1, yAxis) → H
  4. Midpoint(B, C) → S3
  5. Midpoint(E, C) → S6
  6. Midpoint(A, D) → S5
  7. Midpoint(D, G) → S4
  8. Midpoint(A, G) → S1
  9. Midpoint(E, B) → S2
  10. Polygon(A, P1, B) → d1, b, a_2, p1
  11. Polygon(P1, G, B) → d2, b_1, f, g
  12. Polygon(P1, H, G) → d3, g_1, h, h_1
  13. Polygon(P1, A, H) → d4, h_2, i, a_3
  14. Polygon(E, P2, F) → d5, f_1, e, p2
  15. Polygon(P2, B, F) → d6, f_2, j, b_2
  16. Polygon(P2, A, B) → d7, b_3, k, a_4
  17. Polygon(P2, E, A) → d8, a_5, l, e_1
  18. Polygon(F, P3, C) → d9, c, f_3, p3
  19. Polygon(F, B, P3) → d10, m, f_4, b_4
  20. Polygon(B, G, P3) → d11, n, b_5, g_2
  21. Polygon(G, C, P3) → d12, p, g_3, c_1
  22. Polygon(C, P4, D) → d13, d, c_2, p4
  23. Polygon(C, G, P4) → d14, q, c_3, g_4
  24. Polygon(P4, G, H) → d15, h_3, r, g_5
  25. Polygon(P4, H, D) → d16, d_1, s, h_4
  26. Polygon(D, P5, E) → d17, e_2, d_2, p5
  27. Polygon(D, H, P5) → d18, t, d_3, h_5
  28. Polygon(P5, H, A) → d19, a_6, i_1, h_6
  29. Polygon(P5, A, E) → d20, e_3, j_1, a_7
  30. Polygon(C, P6, D) → d21, d_4, c_4, p6
  31. Polygon(D, P6, E) → d22, e_4, d_5, k_1
  32. Polygon(F, P6, E) → d23, e_5, f_5, l_1
  33. Polygon(F, C, P6) → d24, m_1, f_6, c_5