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72-Polyhedron Computer Constructions

72-Polyhedron Computer Constructions
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2015-12-24 22:00
VectorSequenceSolid GeometryGeometric Construction
This example demonstrates the computer-aided construction of a 72-sided polyhedron. It involves core mathematical concepts like constructions, similar triangles, kites, general quadrilaterals, and 3D vectors. Key GeoGebra commands and objects used in the construction include Sequence, Sort, Element, and TableText, as outlined in the construction summary. Suitable for high school and above, this resource helps learners understand complex geometric constructions.

GeoGebra Commands & Parameters

  1. Sequence(((zoom * Element[Element[A00, i], 1]), (zoom * Element[Element[A00, i], 2]), (zoom * Element[Element[A00, i], 3])), i, 1, Length[A00]) → A0
  2. Sort(Sequence[Segment[Element[A0, Element[Element[nom, i], 1]], Element[A0, Element[Element[nom, i], 2]]], i, 1, Length[nom]]) → Segments
  3. Sequence(Element[Segments, i], i, 1, i_s) → Segments_o
  4. Sort(Union[{}, ceil((Segments * 10^(k))) / 10^(k)]) → Segn
  5. 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
  6. Sequence(Length[Element[la0, i]], i, 1, Length[Segn]) → lLength
  7. Element(la0, 1) → la1
  8. Element(la0, 2) → la2
  9. Element(la0, 3) → la3
  10. Element(la0, 4) → la4
  11. Sequence(((zoom * Element[Element[A00d, i], 1]), (zoom * Element[Element[A00d, i], 2]), (zoom * Element[Element[A00d, i], 3])), i, 1, Length[A00d]) → A0d
  12. Sort(Sequence[Segment[Element[A0d, Element[Element[nomd, i], 1]], Element[A0d, Element[Element[nomd, i], 2]]], i, 1, Length[nomd]]) → Segmentsd
  13. Sequence(Element[Segmentsd, i], i, 1, id_s) → Segmentsd_o
  14. Sort(Union[{}, ceil((Segmentsd * 10^(k_d))) / 10^(k_d)]) → Segnd
  15. 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
  16. Sequence(Length[Element[la0d, i]], i, 1, Length[Segnd]) → lLengthd
  17. TableText({mm5ad, mm7ad}, "hr") → text2
  18. Element(la0d, 1) → la1d
  19. Element(la0d, 2) → la2d
  20. Element(la0d, 3) → la3d
  21. Element(la0d, 4) → la4d
  22. TableText({Segn, lLength}, "hr") → text8
  23. TableText({Segnd, lLengthd}, "hr") → text9
  24. TableText({Append["n=", mm5a], Append["N=", mm7a]}, "hr") → text1
  25. 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
  26. 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
  27. 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]]], i, 1, 65) → polyd_{4}
  28. 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]]], i, 1, 11) → polyd_{5}

AI Drawing Prompt Reference

Create a computer-aided construction of a 72-sided polyhedron, demonstrating core mathematical concepts like constructions, similar triangles, kites, general quadrilaterals, and 3D vectors. Start by generating a set of 3D points, then connect these points to form segments and sort them by length. Next, group and further sort these segments into multiple sequences. Finally, use these sequences to construct multiple polygons, including triangles and quadrilaterals, to form the complete structure of the 72-faced polyhedron, and label key data.
The prompt above was compiled from the original drawing commands and is for reference only.