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Computer Construction of Polyhedra

Computer Construction of Polyhedra
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2015-11-04 01:20
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to construct polyhedra using computer software. It involves key concepts in solid geometry, such as the methods of constructing polyhedra. Using GeoGebra commands like Sum, If, Sequence, etc., the faces and edges of polyhedra can be created. Suitable for high school students and teachers for teaching or self-study.

GeoGebra Commands & Parameters

  1. Sum(Join[Sequence[Sequence[sqrt((Element[Element[A00, i], 1] - Element[Element[A00, j], 1])^(2) + (Element[Element[A00, i], 2] - Element[Element[A00, j], 2])^(2) + (Element[Element[A00, i], 3] - Element[Element[A00, j], 3])^(2)), j, i + 1, n], i, 1, n - 1]]) → pp
  2. If(bu, "Pause", "Play") → caption
  3. Textfield(h) → inputBox1
  4. Textfield(n) → inputBox2
  5. Textfield(ε) → inputBox3
  6. If(dd < ε, 0, 1) → bu2
  7. Sequence((2 * Element[pumfang0, i] / (((i + 3) * (i + 2)))), i, 1, Length[pumfang0]) → pumfang1
  8. TableText({Join[{{"n"}, Sequence[i, i, 4, Length[pumfang0] + 3]}], Join[{{"P_n"}, pumfang0}], Join[{{" p_n=P_n/[n*(n-1)/2]"}, pumfang1}], Join[{{"p_n/p_4"}, pumfang2}]}, "vl") → info1
  9. Sum(Zip[(T * F), T, SysTimeAkt1, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs1
  10. Sum(Zip[(T * F), T, SysTimeAkt2, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs2
  11. Div(TimeRelab, 3600) → H
  12. Div(TimeRelab - (H * 3600), 60) → M
  13. Element(ZwZeit, step) → text10
  14. Sequence(((r * Element[Element[A00, i], 1]), (r * Element[Element[A00, i], 2]), (r * Element[Element[A00, i], 3])), i, 1, n) → A01
  15. Join(Sequence[Sequence[Segment[Element[A01, i], Element[A01, j]], j, i + 1, a], i, 1, a - 1]) → l0
  16. Sort(l0) → la
  17. KeepIf(abs(Element[la, 1] - x) < 0.001, l0) → l1
  18. Length(l0) → lä0
  19. Length(A00) → lä00
  20. Length(l1) → lä1
  21. KeepIf(abs(Element[la, lä1 + 1] - x) < 0.01, l0) → l2
  22. Length(l2) → lä2
  23. KeepIf(abs(Element[la, lä1 + lä2 + 1] - x) < 0.01, l0) → l3
  24. Length(l3) → lä3
  25. KeepIf(abs(Element[la, lä1 + lä2 + lä3 + 1] - x) < 0.01, l0) → l4
  26. Length(l4) → lä4
  27. KeepIf(abs(Element[la, lä1 + lä2 + lä3 + lä4 + 1] - x) < 0.01, l0) → l5
  28. Length(l5) → lä5
  29. KeepIf(abs(Element[la, lä1 + lä2 + lä3 + lä4 + lä5 + 1] - x) < 0.01, l0) → l6
  30. Length(l6) → lä6
  31. TableText({Append["i duration", Last[ZwZeit, Min[10, Length[ZwZeit]]]]}, "v") → text2c
  32. Length(ZwZeit) → c

AI Drawing Prompt Reference

Create a polyhedron by first entering vertex coordinates, then calculating edge lengths based on these coordinates, and finally creating the edges and faces of the polyhedron. Adjust parameters to control the shape and size of the polyhedron, and observe how different parameters affect the polyhedron.
The prompt above was compiled from the original drawing commands and is for reference only.