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立方体生成菱形十二面体动画

立方体生成菱形十二面体动画
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2018-11-26 13:41
多边形向量立体几何几何作图
①本范例演示通过立方体动态生成菱形十二面体的过程；②涉及的核心数学概念包括多边形构造、立体几何、向量运算；③作图要点提炼自构造摘要，主要运用了Polygon（多边形）、Pyramid（棱锥）、If（条件判断）等GeoGebra命令及对象；④适合高中及以上学生及数学爱好者学习空间几何与动态几何作图。

GeoGebra 命令及参数

  1. Polygon(A3, A7, A1, A5) → poly1, a3, a7, a1, a5
  2. Polygon(A7, A6, A4, A1) → poly2, f, a6, a4, g
  3. Polygon(A6, A2, A8, A4) → poly3, h, a2, a8, i
  4. Polygon(A2, A3, A5, A8) → poly4, j, k, l, m
  5. Polygon(A8, A5, A1, A4) → poly5, n, p, q, r
  6. Pyramid(poly1, C) → P1, faceA3A7C_1, faceA1A7C_1, faceA1A5C_1, faceA3A5C_1, edgeA3C_1, edgeA7C_1, edgeA1C_1, edgeA5C_1
  7. Pyramid(poly2, C) → P2, faceA6A7C_1, faceA4A6C_1, faceA1A4C_1, faceA1A7C, edgeA7C_2, edgeA6C_1, edgeA4C_1, edgeA1C_2
  8. Pyramid(poly3, C) → P3, faceA2A6C_1, faceA2A8C_1, faceA4A8C_1, faceA4A6C, edgeA6C_2, edgeA2C_1, edgeA8C_1, edgeA4C_2
  9. Pyramid(poly4, C) → P4, faceA2A3C_1, faceA3A5C, faceA5A8C_1, faceA2A8C, edgeA2C_2, edgeA3C_2, edgeA5C_2, edgeA8C_2
  10. Pyramid(poly5, C) → P5, faceA5A8C, faceA1A5C, faceA1A4C, faceA4A8C, edgeA8C, edgeA5C, edgeA1C, edgeA4C
  11. If(0 ≤ t ≤ 1, Translate[P1, Vector[(0, 0, 0), (t, 0, 0)]], If[1 < t ≤ 2, Rotate[Translate[P1, Vector[(0, 0, 0), (1, 0, 0)]], (π * (t - 1)), Line[(2, 0, 0), (2, 0, 1)]], Translate[Rotate[Translate[P1, Vector[(0, 0, 0), (1, 0, 0)]], π, Line[(2, 0, 0), (2, 0, 1)]], Vector[(0, 0, 0), ((-t) + 2, 0, 0)]]]) → P1A
  12. Polygon(A2, A3, A7, A6) → poly6, s, a, b, c
  13. Pyramid(poly6, C) → P6, faceA2A3C, faceA3A7C, faceA6A7C, faceA2A6C, edgeA2C, edgeA3C, edgeA7C, edgeA6C
  14. If(0 ≤ t ≤ 1, Translate[P2, Vector[(0, 0, 0), (0, t, 0)]], If[1 < t ≤ 2, Rotate[Translate[P2, Vector[(0, 0, 0), (0, 1, 0)]], (π * (t - 1)), Line[(0, 2, 0), (0, 2, 1)]], Translate[Rotate[Translate[P2, Vector[(0, 0, 0), (0, 1, 0)]], π, Line[(0, 2, 0), (0, 2, 1)]], Vector[(0, 0, 0), (0, (-t) + 2, 0)]]]) → P2A
  15. If(0 ≤ t ≤ 1, Translate[P3, Vector[(0, 0, 0), ((-t), 0, 0)]], If[1 < t ≤ 2, Rotate[Translate[P3, Vector[(0, 0, 0), (-1, 0, 0)]], (π * (t - 1)), Line[(-2, 0, 0), (-2, 0, 1)]], Translate[Rotate[Translate[P3, Vector[(0, 0, 0), (-1, 0, 0)]], π, Line[(-2, 0, 0), (-2, 0, 1)]], Vector[(0, 0, 0), (t - 2, 0, 0)]]]) → P3A
  16. If(0 ≤ t ≤ 1, Translate[P4, Vector[(0, 0, 0), (0, (-t), 0)]], If[1 < t ≤ 2, Rotate[Translate[P4, Vector[(0, 0, 0), (0, -1, 0)]], (π * (t - 1)), Line[(0, -2, 0), (0, -2, 1)]], Translate[Rotate[Translate[P4, Vector[(0, 0, 0), (0, -1, 0)]], π, Line[(0, -2, 0), (0, -2, 1)]], Vector[(0, 0, 0), (0, t - 2, 0)]]]) → P4A
  17. If(0 ≤ t ≤ 1, Translate[P5, Vector[(0, 0, 0), (0, 0, t)]], If[1 < t ≤ 2, Rotate[Translate[P5, Vector[(0, 0, 0), (0, 0, 1)]], (π * (t - 1)), Line[(0, 0, 2), (0, -1, 2)]], Translate[Rotate[Translate[P5, Vector[(0, 0, 0), (0, 0, 1)]], π, Line[(0, 0, 2), (0, -1, 2)]], Vector[(0, 0, 0), (0, 0, (-t) + 2)]]]) → P5A
  18. If(0 ≤ t ≤ 1, Translate[P6, Vector[(0, 0, 0), (0, 0, (-t))]], If[1 < t ≤ 2, Rotate[Translate[P6, Vector[(0, 0, 0), (0, 0, -1)]], (π * (t - 1)), Line[(0, 0, -2), (0, -1, -2)]], Translate[Rotate[Translate[P6, Vector[(0, 0, 0), (0, 0, -1)]], π, Line[(0, 0, -2), (0, -1, -2)]], Vector[(0, 0, 0), (0, 0, t - 2)]]]) → P6A

AI 绘图提示语参考

请绘制一个动态生成的菱形十二面体，展示其从立方体演变的过程。首先构建多个菱形作为基础面，然后通过向量操作将这些菱形堆叠成金字塔形状，形成立方体的每个面。接着，通过按钮和滑块控制动画，使金字塔形状围绕不同轴旋转，最终动态展示出菱形十二面体的完整形态。
以上提示语为根据原始绘图命令整理而来，仅供参考。