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Truncated Dodecahedron, n=60

Truncated Dodecahedron, n=60
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2020-11-10 02:33
SequenceSolid GeometryGeometric Construction
In collections ₈Polyhedra with extreme distribution of equivalent vertices
This example demonstrates a truncated dodecahedron with an extreme distribution of equivalent vertices. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Sum, If, Length, and Sequence, a specific polyhedron with a particular vertex distribution can be constructed. Suitable for high school students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Text("" + p) → txt_p
  2. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m01(k), m02(k)], " "], k, 1, 5]]) → txtUm1
  3. If(bu0, A00, A00d) → A00_0
  4. Length(A00_0) → n
  5. Length(l2) → läl2
  6. Sequence(sgn(Determinant[{Element[A00_0, i1] - Element[A00_0, j], Element[A00_0, i2] - Element[A00_0, j], Element[A00_0, i3] - Element[A00_0, j]}]), j, 1, n) → l01
  7. Length(A00d) → zzz
  8. Sum(Zip[(T * F), T, SysTimeAkt1, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs1
  9. Sum(Zip[(T * F), T, SysTimeAkt2, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs2
  10. Div(TimeRelab, 3600) → H
  11. Div(TimeRelab - (H * 3600), 60) → M
  12. Element(ZwZeit, step) → text10
  13. TableText({Append["a duration", Last[ZwZeit, Min[10, Length[ZwZeit]]]]}, "v") → text2c
  14. Length(A00) → lm1
  15. If(Length[Unique[l01 \ {0}]] ≟ 1, 7, -7) → a7
  16. Sum(Zip[(T * F), T, SysTimeAkt0, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs0
  17. Div(TimeRelab0, 3600) → H0
  18. Div(TimeRelab0 - (H0 * 3600), 60) → M0
  19. Text("" + (TimeRelab0 - (H0 * 3600) - (M0 * 60))) → S0a
  20. Text("" + (TimeRelab - (H * 3600) - (M * 60))) → S
  21. IndexOf(".", S) → index
  22. IndexOf(".", S0a) → indexa
  23. First(S, index + 1) → txtS
  24. First(S0a, indexa + 1) → txtS0a
  25. If(bu0, " ", "d") → txtbuo
  26. Max(Length[A00], Length[A00d]) → maxlä
  27. Element(A00, 24) → m11
  28. TableText({{"\underline{Polyhedron}"}, Append["Vertices: n=", {Length[A00]}], Append["r=", {r}], Append["\bar{r}=", {r_m}], Append["k-gon : k=", mm5a], Append["their\; numbers: n_k=", mm7a], Append["Volume: V=", {Vol_r}], Append["Average\; distance: p=", {txtUm1}]}, "hr ") → text7
  29. TableText({{"\underline{dual\;Polyhedron}"}, Append["Vertices: n=", {Length[A00d]}], Append["r=", {r_d}], Append[" \bar{r_d}= ", {r_md}], Append["k-gon : k=", mm5ad], Append["their\; numbers: n_k=", mm7ad], Append["Volume: V=", {Vold_r}]}, "hr ") → text20

AI Drawing Prompt Reference

Draw a truncated dodecahedron with 60 equivalent vertices, showing its extreme vertex distribution. Include the polyhedron and its dual, with labels for vertex count, circumradius, mean distance, face edge counts and numbers, and volume. Construct by first defining the vertex set, then using determinant signs to check coplanarity for face generation. Also display time-dependent text and statistical tables to highlight geometric construction and mathematical analysis.
The prompt above was compiled from the original drawing commands and is for reference only.