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Sonobe 12 Piece Octahedral Construction

Sonobe 12 Piece Octahedral Construction
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2017-05-03 04:10
PolygonTransformationGeometric Construction
This example demonstrates the construction of a Sonobe 12 piece octahedral. Key mathematical concepts include polygons, transformations, and geometric construction. Using GeoGebra commands such as Intersect, Point, Circle, and LineBisector, the construction process of the octahedron is dynamically shown. Suitable for middle or high school geometry education to help students understand the construction and transformations of polyhedra.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(B, A) → p
  4. LineBisector(A, B) → e
  5. Polygon(A, B, 3) → poly1, a, b, d, C
  6. LineBisector(A, C) → f
  7. Intersect(f, d) → K
  8. Intersect(e, f) → D
  9. Dilate(K, fac, D) → K'
  10. OrthogonalLine(D, xOyPlane) → g
  11. Point(g) → E
  12. Circle(A, B) → c
  13. Intersect(c, p, 1) → J
  14. Polygon(B, J, E) → poly3, e_2, b_2, j_1
  15. Intersect(b_2, e) → L
  16. Octahedron(A, B, C) → h, F, faceCGH, faceFGH, edgeAC, edgeAB, edgeBC, edgeAH, edgeCH, edgeAF, edgeFH, edgeBF, G, edgeBG, edgeFG, edgeCG, edgeGH, H, faceABC, faceACH, faceAFH, faceABF, faceBFG, faceBCG
  17. Plane(F, H, C) → i
  18. Mirror(E, i) → E'
  19. Intersect(edgeCG, edgeBG) → I
  20. Line(I, A) → j
  21. Polygon(A, B, E) → poly2, e_1, a_1, b_1
  22. Polygon(J, A, E) → poly4, e_3, j_2, a_2
  23. Mirror(ListPoly, i) → ListPoly'
  24. Sequence(Rotate[ListPoly', (-((n * α))), j], n, 1, 4) → ListPyramid'
  25. Mirror(ListPyramid', i) → ListPyramid''
  26. Polygon(K', E, L) → poly5, k, l, m
  27. Angle(B, E, J) → β
  28. Rotate(F, (-γ), g) → F'
  29. Rotate(A, (-γ), g) → A'
  30. Segment(F', A') → edgeAF'
  31. Rotate(poly5, (-γ), g) → poly5'
  32. Rotate(poly5', (-γ), g) → poly5''
  33. Sequence(Rotate[poly5, ((-n) * γ), g], n, 1, 3) → ListDecoration
  34. Intersect(edgeAF', edgeAH) → M
  35. Line(B, H) → n
  36. Rotate(ListDecoration, (-α), n) → ListDecoration'
  37. Sequence(Rotate[ListDecoration, ((-n) * α), j], n, 1, 4) → ListDecorationRing
  38. Sequence(Rotate[ListDecoration', ((-n) * α), j], n, 1, 4) → ListDecorationRing'