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Double Skew Tetrahedra (12 Tetrahedra) Animation

Double Skew Tetrahedra (12 Tetrahedra) Animation
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2020-07-17 00:25
SequenceSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
① This example demonstrates a double skew tetrahedra structure composed of 12 tetrahedra, shown as an animated paper-folding model to illustrate its spatial form and dynamic transformation. ② Core mathematical concepts include solid geometry of polyhedral combinations, spatial symmetry, and transformations (translation, rotation, reflection) in 3D space, along with sequence generation and geometric construction logic. ③ Construction highlights: Based on the construction summary, GeoGebra commands used include Intersect, Point, Circle, OrthogonalLine, Midpoint, Cube, Polygon, Plane, Translate, Mirror, Sequence, Line, and Rotate. Objects such as faces (faceBDEF, faceBFJG, etc.) and edges (edgeBF, edgeBD, etc.) are defined, with poly1 and poly2 as composite objects to build the overall model. ④ Suitable for high school and above, especially for teaching solid geometry, spatial reasoning, and dynamic geometry demonstrations, as well as for exploring mathematical origami.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. OrthogonalLine(A, xOyPlane) → f
  5. Circle(B, A) → d
  6. Intersect(c, d, 1) → C
  7. Midpoint(B, C) → D
  8. Point(Circle[D, Distance[B, D], Segment[B, D]]) → E
  9. Cube(B, D, E) → a, F, faceEFJI, faceGHIJ, edgeBF, edgeBD, edgeDE, edgeEF, edgeBG, edgeFJ, edgeGJ, edgeGH, G, edgeDH, edgeHI, edgeEI, edgeIJ, H, I, J, faceBDEF, faceBFJG, faceBDHG, faceDEIH
  10. Polygon(E, B, D) → poly1, d_1, e, b
  11. Polygon(E, G, B) → poly2, b_1, e_1, g
  12. Polygon(D, B, G) → poly3, g_1, d_2, b_2
  13. Polygon(D, E, G) → poly4, g_2, d_3, e_2
  14. Point(b) → K
  15. Plane(E, K, H) → h
  16. Translate({poly1, poly2, poly3, poly4}, Vector[A, A]) → SkewTet
  17. Mirror(SkewTet, h) → SkewTet'
  18. Sequence(Rotate[{SkewTet, SkewTet'}, (n * 60°), f], n, 0, 5, 1) → pos1
  19. Plane(E, B, G) → i
  20. Plane(D, E, G) → j
  21. Mirror(SkewTet, j) → SkewTet'_1
  22. Polygon(I, E, G) → poly5, g_3, i_1, e_3
  23. Intersect(e_3, b_1) → L
  24. Polygon(H, I, G) → poly6, g_4, h_1, i_2
  25. Line(H, D) → k
  26. Sequence(Rotate[{poly1, poly2, poly5, poly6}, (n * 90°), k], n, 0, 3, 1) → pos2
  27. Polygon(G, H, D) → poly7, d_4, g_5, h_2
  28. Polygon(J, G, B) → poly8, b_3, j_1, g_6
  29. Polygon(J, F, B) → poly9, b_4, j_2, f_1
  30. Polygon(J, H, G) → poly10, g_7, j_3, h_3
  31. Polygon(J, I, H) → poly11, h_4, j_4, i_3
  32. Polygon(I, F, J) → poly12, j_5, i_4, f_2
  33. Polygon(I, E, F) → poly13, f_3, i_5, e_4
  34. Polygon(I, E, D) → poly14, d_5, i_6, e_5
  35. Polygon(I, H, D) → poly15, d_6, i_7, h_5
  36. Translate({poly1, poly10, poly11, poly12, poly13, poly14, poly15, poly9, poly8, poly7, poly3}, Vector[A, A]) → cube3
  37. Rotate(cube3, (-α), k) → cube3'
  38. Translate({cube3, cube3'}, Vector[A, A]) → pos3

AI Drawing Prompt Reference

Create an animated paper-folding model of a double skew tetrahedra structure composed of 12 tetrahedra to illustrate its spatial form and dynamic transformation. Begin by constructing two intersecting circles and a perpendicular line, then build a cube and define its faces and edges. Combine the tetrahedra, perform mirror reflections and rotations along specific planes, and finally assemble all parts while animating their rotation around a designated axis to showcase spatial symmetry and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.