MathPlotAI Logo MathPlotAI

Dodecahedron with Extreme Distribution of Equivalent Vertices

Dodecahedron with Extreme Distribution of Equivalent Vertices
Loading the math board and drawing, please wait…
2020-10-28 00:51
Solid GeometryOptimization
In collections ₈Polyhedra with extreme distribution of equivalent vertices
This example demonstrates a dodecahedron with an extreme distribution of equivalent vertices. Key mathematical concepts include geometric mean, solid geometry, and optimization. It is constructed using GeoGebra commands such as If, Length, Sequence, and Sum. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. If(bu0, A00, A00d) → A00_0
  2. Length(A00_0) → n
  3. Length(l2) → läl2
  4. 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
  5. Length(A00d) → zzz
  6. Sum(Zip[(T * F), T, SysTimeAkt1, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs1
  7. Sum(Zip[(T * F), T, SysTimeAkt2, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs2
  8. Div(TimeRelab, 3600) → H
  9. Div(TimeRelab - (H * 3600), 60) → M
  10. Element(ZwZeit, step) → text10
  11. TableText({Append["a duration", Last[ZwZeit, Min[10, Length[ZwZeit]]]]}, "v") → text2c
  12. Length(A00) → lm1
  13. If(Length[Unique[l01 \ {0}]] ≟ 1, 7, -7) → a7
  14. Sum(Zip[(T * F), T, SysTimeAkt0, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs0
  15. Div(TimeRelab0, 3600) → H0
  16. Div(TimeRelab0 - (H0 * 3600), 60) → M0
  17. Text("" + (TimeRelab0 - (H0 * 3600) - (M0 * 60))) → S0a
  18. Text("" + (TimeRelab - (H * 3600) - (M * 60))) → S
  19. IndexOf(".", S) → index
  20. IndexOf(".", S0a) → indexa
  21. First(S, index + 1) → txtS
  22. First(S0a, indexa + 1) → txtS0a
  23. If(bu0, " ", "d") → txtbuo
  24. Max(Length[A00], Length[A00d]) → maxlä
  25. Element(A00, 24) → m11
  26. 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}]}, "hr ") → text7
  27. 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 dodecahedron with an extreme distribution of equivalent vertices, showing both the primary polyhedron and its dual. The primary has 12 pentagonal faces, with vertices labeled n, each vertex's distance r from center and average r̄ displayed. The dual polyhedron also shows its vertex count, distances, and volume. Include data tables listing for both polyhedra: number of vertices, radius r, mean radius r̄, face type (k-gon) and count, and volume. Construct the primary dodecahedron first, then derive its dual, and finally add annotations and tables.
The prompt above was compiled from the original drawing commands and is for reference only.