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n=32 Polyhedron Computer Constructions

n=32 Polyhedron Computer Constructions
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2015-03-10 20:21
SequenceCoordinate GeometrySolid GeometryGeometric ConstructionSlider Animation
This example demonstrates the computer construction of a polyhedron when n=32. Key mathematical concepts include the geometric construction of polyhedra and computer-aided geometry. Using GeoGebra commands such as Element, Sequence, and Sort, complex polyhedral structures can be constructed. Suitable for high school and above students or teachers for teaching geometric construction and solid geometry.

GeoGebra Commands & Parameters

  1. Element(A00_1, 1) → A00
  2. Sequence(((zoom * Element[Element[A00, i], 1]), (zoom * Element[Element[A00, i], 2]), (zoom * Element[Element[A00, i], 3])), i, 1, Length[A00]) → A0
  3. Element(A00_1, 2) → A00d
  4. Sort(Sequence[Segment[Element[A0, Element[Element[nom, i], 1]], Element[A0, Element[Element[nom, i], 2]]], i, 1, Length[nom]]) → Segments
  5. Sequence(Element[Segments, i], i, 1, i_s) → Segments_o
  6. Sort(Union[{}, ceil((Segments * 10^(k))) / 10^(k)]) → Segn
  7. Sequence(KeepIf[If[i ≟ 1, x ≤ Element[Segn, i], If[i ≟ Length[Segn], Element[Segn, i - 1] < x, Element[Segn, i - 1] < x ≤ Element[Segn, i]]], Segments], i, 1, Length[Segn]) → la0
  8. Sequence(Length[Element[la0, i]], i, 1, Length[Segn]) → lLength
  9. Element(la0, 1) → la1
  10. Element(la0, 2) → la2
  11. Element(la0, 3) → la3
  12. Element(la0, 4) → la4
  13. Sequence(((zoom * Element[Element[A00d, i], 1]), (zoom * Element[Element[A00d, i], 2]), (zoom * Element[Element[A00d, i], 3])), i, 1, Length[A00d]) → A0d
  14. Sort(Sequence[Segment[Element[A0d, Element[Element[nomd, i], 1]], Element[A0d, Element[Element[nomd, i], 2]]], i, 1, Length[nomd]]) → Segmentsd
  15. Sequence(Element[Segmentsd, i], i, 1, id_s) → Segmentsd_o
  16. Sort(Union[{}, ceil((Segmentsd * 10^(k_d))) / 10^(k_d)]) → Segnd
  17. Sequence(KeepIf[If[i ≟ 1, x ≤ Element[Segnd, i], If[i ≟ Length[Segnd], Element[Segnd, i - 1] < x, Element[Segnd, i - 1] < x ≤ Element[Segnd, i]]], Segmentsd], i, 1, Length[Segnd]) → la0d
  18. Sequence(Length[Element[la0d, i]], i, 1, Length[Segnd]) → lLengthd
  19. TableText({mm5ad, mm7ad}, "hr") → text2
  20. Element(la0d, 1) → la1d
  21. Element(la0d, 2) → la2d
  22. Element(la0d, 3) → la3d
  23. Element(la0d, 4) → la4d
  24. TableText({Segn, lLength}, "hr") → text8
  25. TableText({Segnd, lLengthd}, "hr") → text9
  26. Sequence(Polygon[Element[A0, Element[Element[mm1, f], 1]], Element[A0, Element[Element[mm1, f], 2]], Element[A0, Element[Element[mm1, f], 3]]], f, 1, Length[mm1]) → poly_3
  27. Sequence(Polygon[Element[A0d, Element[Element[mm1d, f], 1]], Element[A0d, Element[Element[mm1d, f], 2]], Element[A0d, Element[Element[mm1d, f], 3]]], f, 1, Length[mm1d]) → polyd_3
  28. TableText({Append["n=", mm5a], Append["N=", mm7a]}, "hr") → text1
  29. Sequence(Polygon[Element[A0d, Element[Element[Element[mm6d, 1], i], 1]], Element[A0d, Element[Element[Element[mm6d, 1], i], 2]], Element[A0d, Element[Element[Element[mm6d, 1], i], 3]], Element[A0d, Element[Element[Element[mm6d, 1], i], 4]], Element[A0d, Element[Element[Element[mm6d, 1], i], 5]]], i, 1, 12) → polyd_{5}
  30. Sequence(Polygon[Element[A0d, Element[Element[Element[mm6d, 2], i], 1]], Element[A0d, Element[Element[Element[mm6d, 2], i], 2]], Element[A0d, Element[Element[Element[mm6d, 2], i], 3]], Element[A0d, Element[Element[Element[mm6d, 2], i], 4]], Element[A0d, Element[Element[Element[mm6d, 2], i], 5]], Element[A0d, Element[Element[Element[mm6d, 2], i], 6]]], i, 1, 2) → polyd_{6}