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Origami Skeletal Octahedron Eversion

Origami Skeletal Octahedron Eversion
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2020-06-24 16:03
PolygonVectorSolid GeometryTransformationGeometric Construction
This example demonstrates the dynamic process of eversion (inversion) of an octahedron's skeletal structure through origami techniques. It involves core mathematical concepts such as polygon construction, geometric transformations, solid geometry, and spatial visualization. Key GeoGebra commands and objects used in the construction include Point, Intersect, Line, Polygon, Dilate, Plane, and Mirror, as outlined in the construction summary. It is suitable for high school students and math enthusiasts studying spatial geometric transformations and dynamic geometry demonstrations.

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 the skeletal structure of an octahedron and demonstrate its inversion through origami techniques. Start by creating points A, B, C, D, E, and F on the coordinate axes, then construct point O on the xOy plane and line a through point O and the coordinate axes. Construct quadrilaterals BCEF, BCDE, and ECFA, then perform a scaling transformation around point O to generate new points A', B', C', D', E', and F'. Next, construct plane g and use a series of mirror transformations to generate new quadrilaterals, and finally, use more mirror transformations to complete the final shape.
The prompt above was compiled from the original drawing commands and is for reference only.