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Truncated Icosidodecahedron: Relationship Between Average Distance and Truncatio

Truncated Icosidodecahedron: Relationship Between Average Distance and Truncatio
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2020-01-13 03:01
Solid GeometryOptimizationGeometric Construction
This example demonstrates a truncated icosidodecahedron and explores the relationship between the average distance between vertices and the truncation parameter. By adjusting the truncation parameter, extreme distributions of vertices can be observed. Commands used include Join, Unique, Length, Text, Sum, Sphere, Ray, Zip, UnicodeToLetter, and TableText. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Join(Zip[lP0(x(a)) + ((lP0(y(a)) - lP0(x(a))) * {t, 1 - t}), a, segN]) → lVV
  2. Unique(lVV) → lP'
  3. Length(lP') → n
  4. Length(lVV(1)) → R2
  5. Text("" + p3) → txt_p
  6. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m1(k), m2(k)], " "], k, 1, 5]]) → txtUm1
  7. Sphere(O, R1) → sp1
  8. Sphere(O, R2) → sp2
  9. Ray(B, AA) → h
  10. Text(text12, C, false, true) → text8
  11. Zip(Segment[lP0(x(a)), lP0(y(a))], a, segN1) → seg1
  12. Zip(Segment[lP0(x(a)), lP0(y(a))], a, segN2) → seg2
  13. Zip(Polygon[a], a, v_poly06) → poly06
  14. Zip(Polygon[a], a, v_poly04) → poly04
  15. Zip(Polygon[a], a, v_poly10) → poly10
  16. UnicodeToLetter(34) → u34
  17. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ4) → segΔ4
  18. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ6) → segΔ6
  19. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ10) → segΔ10
  20. TableText(Append["\;\;\; \fgcolor{#0087BD}{4-gons}", segΔ4], Append["\;\;\; \fgcolor{red}{6-gons}", segΔ6], Append["\;\;\; \fgcolor{#79443B}{10-gons}", segΔ10], "v") → text3a

AI Drawing Prompt Reference

Draw a truncated icosidodecahedron and explore the change in average vertex distance by adjusting the truncation parameter. First, create the edges of the truncated icosidodecahedron, then calculate all vertices, followed by the number of vertices and radii under the truncation parameter, and finally show the distribution of polygons for different truncation parameters.
The prompt above was compiled from the original drawing commands and is for reference only.