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n=48 Polyhedron Computer Constructions

n=48 Polyhedron Computer Constructions
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2015-03-08 22:04
Solid GeometryProbability & StatisticsGeometric Construction
This example demonstrates the computer construction of a polyhedron with n=48, showcasing dynamic geometric methods for building complex shapes. Core math concepts include constructions, random variables, exponent, hypergeometric distribution, complex numbers, and exponential functions. Key GeoGebra commands and objects used, as per the construction summary, are Element, Sequence, Sort, TableText, A00, r0, Segments, etc. Suitable for high school and above learners to understand solid geometry constructions and probability statistics applications.

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[A0, Element[Element[Element[mm6, 1], i], 1]], Element[A0, Element[Element[Element[mm6, 1], i], 2]], Element[A0, Element[Element[Element[mm6, 1], i], 3]], Element[A0, Element[Element[Element[mm6, 1], i], 4]]], i, 1, 6) → poly_{4}
  30. 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, 72) → polyd_{4}

AI Drawing Prompt Reference

Draw a polyhedron with 48 vertices, consisting of two symmetric sets of points. Connect points within each set to form edges, then sort and group these edges by length. Count edges in each length interval. Use the edges to construct triangular and quadrilateral faces, forming the polyhedron's surface. Display two tables: one listing edge length groups with counts, and another showing the total number of vertices and edges. The final image shows a 3D solid with statistical data.
The prompt above was compiled from the original drawing commands and is for reference only.