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Skeletal Octahedron Eversion

Skeletal Octahedron Eversion
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2017-05-03 02:30
Solid GeometryTransformationGeometric Construction
This example demonstrates the process of a skeletal octahedron eversion. Core mathematical concepts include geometric transformations and solid geometry. Using GeoGebra commands such as Point, Intersect, Line, Polygon, Dilate, etc., the skeletal structure of the octahedron is constructed, and the transformation to achieve the eversion is demonstrated. Suitable for high school or university students and teachers for teaching geometric construction and solid geometry.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → D
  5. Point(xAxis) → E
  6. Point(zAxis) → F
  7. Intersect(zAxis, xOyPlane) → O
  8. Line(O, Z) → a
  9. Polygon(B, C, D, E) → poly1, b, c, d, e
  10. Polygon(B, F, D, A) → poly2, b_1, f, d_1, a_1
  11. Polygon(E, F, C, A) → poly3, e_1, f_1, c_1, a_2
  12. Dilate(A, scalefactor, O) → A'
  13. Dilate(B, scalefactor, O) → B'
  14. Dilate(C, scalefactor, O) → C'
  15. Dilate(D, scalefactor, O) → D'
  16. Dilate(E, scalefactor, O) → E'
  17. Dilate(F, scalefactor, O) → F'
  18. Plane(F', C', D') → g
  19. Mirror(O, g) → O'
  20. Polygon(C', O', F') → poly4, f', c', o'
  21. Polygon(C', D', O') → poly5, o'_1, c'_1, d'
  22. Polygon(F', O', D') → poly6, d'_1, f'_1, o'_2
  23. Mirror(poly4, poly3) → poly4'
  24. Mirror(poly6, poly2) → poly6'
  25. Mirror(poly5, poly1) → poly5'
  26. Mirror(poly4', poly2) → poly4''
  27. Mirror(poly4, poly2) → poly4'_1
  28. Mirror(poly4', poly1) → poly4''_1
  29. Mirror(poly4, poly1) → poly4'_2
  30. Mirror(poly4'_1, poly1) → poly7
  31. Mirror(poly4'', poly1) → poly4'''
  32. Mirror(poly6', poly3) → poly6''
  33. Mirror(poly6, poly3) → poly6'_1
  34. Mirror(poly6'_1, poly1) → poly8
  35. Mirror(poly6'', poly1) → poly6'''
  36. Mirror(poly6', poly1) → poly6''_1
  37. Mirror(poly6, poly1) → poly6'_2
  38. Mirror(poly5, poly3) → poly5'_1
  39. Mirror(poly5', poly3) → poly5''
  40. Mirror(poly5'_1, poly2) → poly9
  41. Mirror(poly5'', poly2) → poly5'''
  42. Mirror(poly5, poly2) → poly5'_2
  43. Mirror(poly5', poly2) → poly5''_1

AI Drawing Prompt Reference

Draw a skeletal octahedron and demonstrate its eversion process, starting with constructing the basic vertices and edges of the octahedron, then applying a scaling transformation centered at the origin, followed by mirror operations to create the flipped structure, resulting in a dynamic eversion of the octahedron's skeletal model, highlighting key concepts in geometric transformations and solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.