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3-in-1: Constructing, Surface Triangulation, Visualizing Polyhedron (New Version

3-in-1: Constructing, Surface Triangulation, Visualizing Polyhedron (New Version
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2020-10-20 20:15
PolygonVectorSolid GeometryGeometric ConstructionSlider Animation
① This example demonstrates a comprehensive GeoGebra workspace that simultaneously handles the construction of a polyhedron, its surface triangulation, and 3D visualization, serving as an integrated tool for solid geometry. ② Core mathematical concepts include polyhedron vertices, edges, faces, surface triangulation (decomposing polygonal faces into triangles), and 3D geometric quantities such as vectors, centroid, and volume. ③ Construction highlights: from the summary, commands like Sphere, Text/Textfield, TableText, Append, Zip, If, and Sum are used, along with objects such as points (p1), vectors (Wii_P), centroid (Cm), radius (r), input boxes (InputBox1/2), and a slider (n) to control triangulation resolution, enabling dynamic interaction. ④ Suitable for high school to undergraduate courses in solid geometry, computer graphics, or mathematical experimentation, useful for understanding polyhedral structure, triangulation principles, and 3D visualization techniques.

GeoGebra Commands & Parameters

  1. LaTeX(Um1) → lll1_1
  2. LaTeX(Um0) → lll0
  3. Sphere(O, R) → p1
  4. Textfield(n) → InputBox1
  5. Textfield(i0) → InputBox2
  6. Text(r) → Txtr
  7. Textfield(k_1) → InputBox4
  8. UnicodeToLetter(34) → u34
  9. Textfield(k_2) → InputBox5
  10. TableText(ltxt0, ltxt1, "v") → textltxt01
  11. Append(A, Sequence[((random(), random(), random()) * R), i, 2, n]) → l2s
  12. Text(("(up\; to\; 10^{-15})\;\\ accuracy= " * ScientificText[cc, 3]), C, true, true) → text5r
  13. Zip(Vector[a, a + UnitVector[a]], a, lP') → lVector1
  14. Textfield(scale) → InputBox6
  15. TableText(Append["i", 1…n], Append[" \fgcolor{orange}{GM :Δφ_i}, rad", l1], Append["\fgcolor{magenta}{GC :Δφ_i} , rad", l1c], "v") → text23
  16. Text("\;\;\;\;\;\;\;\;\;\;\;\;\;\fgcolor{" + (If[c', "orange", "brown"]) + "} \boxed{ " + c' + "}\;\;\;\; \;\;\;\;\; \\\;\; ( accuracy- up\; to\;\; 2.*10^{" + k_2 + ("\;})\;\\\;\; ➤➤➤\;\;\;\scalebox{1.3}{ " + (ScientificText[cc, 3])) + "}\;█ ", C, true, true) → text9
  17. If(bu, "Animation", "Stop") → bue0
  18. Zip(Vector[a, a + (1.5 * UnitVector[b])], a, lP', b, Wi_P) → lVector3
  19. Zip(Vector[a, a + (1.5 * UnitVector[b])], a, lP', b, Wi_Pc) → lVector2
  20. TableText({Join[{{"n"}, Sequence[i, i, 4, 69 + 3]}], Join[{{" p_n=P_n/[R*n*(n-1)/2]"}, lp}]}, "vl") → txt_lp
  21. Text("" + Um1) → txt_p
  22. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m1(k), m2(k)], " "], k, 1, 5]]) → txtUm1

AI Drawing Prompt Reference

Visualize a polyhedron with surface triangulation and 3D rendering. Start by constructing a sphere, then dynamically generate vertices and faces of the polyhedron using a slider to control triangulation precision. Label the vertices, edges, faces, and centroid of the polyhedron, highlighting them in different colors. Finally, display the surface of the polyhedron as a mesh of triangles, showing related 3D quantities like vectors, centroid, and volume.
The prompt above was compiled from the original drawing commands and is for reference only.