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正方体与四面体的切割

正方体与四面体的切割
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2014-12-04 19:28
立体几何变换几何作图
本范例演示如何将正方体切割成多个四面体。核心数学概念包括立体几何中的切割与组合。通过使用GeoGebra命令如Point, Cube, Intersect, Polygon, Tetrahedron等，可以直观地展示切割过程。适合初中及以上学生或教师用于教学和学习。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE_1, edgeDH, edgeEH, edgeEF_1, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Intersect(edgeCG, xOyPlane) → I
  4. Polygon(F, I, A) → poly1, a_1, f, i
  5. Point(Circle[Midpoint[A, F], (Distance[A, F] * sqrt(3) / 2), Segment[A, F]]) → J
  6. Tetrahedron(A, F, poly1) → b, K, edgeAL, edgeKL, edgeFL, L, faceAFK, faceAKL, faceAFL, faceFKL, edgeAK, edgeAF, edgeFK
  7. Ray(C, E) → c
  8. Point(c) → M
  9. Vector(E, M) → u
  10. Pyramid(faceAFL, E) → d, faceAEF, faceAEL, faceEFL, edgeEF, edgeAE, edgeEL
  11. Translate(d, u) → d'
  12. Plane(F, H, D) → e
  13. Mirror(d', e) → d''
  14. Plane(A, F, G) → g
  15. Mirror(d', g) → d''_1
  16. Plane(H, A, G) → h
  17. Mirror(d', h) → d''_2