Biscribed Pentakis Snub Dodecahedron and Its Dual with Edge and Face Coloring

Biscribed Pentakis Snub Dodecahedron and Its Dual with Edge and Face Coloring
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2020-09-26 03:03
This example demonstrates the edge and face coloring of a biscribed pentakis snub dodecahedron and its dual. Key mathematical concepts include polyhedra, duals, edge and face coloring. GeoGebra commands such as Sequence, Sphere, Textfield are used in construction. Suitable for high school students or math enthusiasts.

GeoGebra Commands & Parameters

  1. Sequence(((zoom * Element[Element[A00d, i], 1]), (zoom * Element[Element[A00d, i], 2]), (zoom * Element[Element[A00d, i], 3])), i, 1, Length[A00d]) → A0d
  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. Sphere(O, r_o) → sp02d
  4. Textfield(R1sphere) → InputBox5
  5. Sphere(O, R1sphere) → sp01
  6. Textfield(r_o) → InputBox6
  7. Textfield(jarc) → InputBox8
  8. Textfield(jarc_d) → InputBox9
  9. Textfield(f_{Poly}) → InputBox11
  10. Textfield(k) → InputBox15
  11. Textfield(k_d) → InputBox14
  12. TableText({Append["i", 1…Length[mm5a]], Append["\fgcolor{orange}{n}", mm5a], Append["\fgcolor{orange}{N}", mm7a], Append["\fgcolor{#007FFF}{n/dual}", mm5ad], Append["\fgcolor{#007FFF}{N}", mm7ad]}, "hr") → text24
  13. Textfield(iseg) → InputBox17
  14. Textfield(f_{Poly}d) → InputBox18
  15. Textfield(isegd) → InputBox19
  16. UnicodeToLetter(34) → u34
  17. TableText({Append["i", 1…Max[Length[Segn], Length[Segnd]]], Append["\fgcolor{orange}{s_i}", Segn / Segments_o1], Append["\fgcolor{orange}{N}", lLength], Append["\fgcolor{#007FFF}{s_id}", Segnd / Segments_o1d], Append["\fgcolor{#007FFF}{N}", lLengthd]}, "hr") → text23
  18. Textfield(n_3) → InputBox20
  19. If(n_3 ≟ 0, "", Text["" + n_3]) → txt_3
  20. Textfield(nd_3) → InputBox21
  21. If(nd_3 ≟ 0, "", Text["" + nd_3]) → txtd_3
  22. Circle(A_{farbe}, rfabe) → farbekreis
  23. PointIn(farbekreis) → A
  24. Angle(A) → α
  25. Segment(C, D) → h
  26. Sort(Sequence[Segment[Element[A0, Element[Element[nom, i], 1]], Element[A0, Element[Element[nom, i], 2]]], i, 1, Length[nom]]) → Segments
  27. First(Segments, i_s) → Segments_o
  28. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 1], Segments) → la1
  29. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 2], Segments) → la2
  30. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 3], Segments) → la3
  31. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 4], Segments) → la4
  32. 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}
  33. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}S, 1], poly_{3}) → poly_{3}1
  34. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}S, 2], poly_{3}) → poly_{3}2
  35. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}S, 3], poly_{3}) → poly_{3}3
  36. Sort(Sequence[Segment[Element[A0d, Element[Element[nomd, i], 1]], Element[A0d, Element[Element[nomd, i], 2]]], i, 1, Length[nomd]]) → Segmentsd
  37. First(Segmentsd, id_s) → Segmentsd_o
  38. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 1], Segmentsd) → lad1
  39. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 2], Segmentsd) → lad2
  40. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 3], Segmentsd) → lad3
  41. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 4], Segmentsd) → lad4
  42. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 5], Segmentsd) → lad5
  43. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 6], Segmentsd) → lad6
  44. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 7], Segmentsd) → lad7
  45. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 8], Segmentsd) → lad8
  46. 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}
  47. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 1], polyd_{3}) → polyd_{3}1
  48. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 2], polyd_{3}) → polyd_{3}2
  49. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 3], polyd_{3}) → polyd_{3}3
  50. KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 4], polyd_{3}) → polyd_{3}4
  51. Sequence(Polygon[Sequence[A0d(mm6d(1, f, k)), k, 1, Length[mm6d(1, 1)]]], f, 1, Length[mm6d(1)]) → polyd_{5}

AI Drawing Prompt Reference

Draw a biscribed pentakis snub dodecahedron and its dual, and color its edges and faces. The drawing includes color labels and text annotations. The construction order is to first draw the polyhedron, then color and annotate.
The prompt above was compiled from the original drawing commands and is for reference only.