MathPlotAI Logo MathPlotAI

Icosidodecahedron Construction in GeoGebra: 30 Vertices

Icosidodecahedron Construction in GeoGebra: 30 Vertices
Loading the math board and drawing, please wait…
2019-08-13 00:07
PolygonVectorSolid GeometryTransformationGeometric Construction
① This example demonstrates how to construct an icosidodecahedron, an Archimedean solid with 30 vertices, composed of regular pentagons and equilateral triangles, using GeoGebra's 3D capabilities. ② Core mathematical concepts include solid geometry, polyhedra, Euler's formula, vertex-edge-face relationships, truncation of regular polyhedra, and spatial coordinates. ③ Construction highlights: from the summary, the construction uses GeoGebra commands such as Sphere, Zip, Sum, Text, and TableText, along with numerous objects like Points00 (vertex list), Segments (edges), multiple buttons (button2/3/4) for interactive control, vectors (lVector1/lVector2), and text labels (txt_p, txtUm1), reflecting a parametric and dynamic approach. ④ This is suitable for high school or university-level geometry courses, helping students visualize Archimedean solids, understand vertex coordinates, and explore 3D modeling techniques; it also serves as an example for mathematical modeling or computer-assisted geometry instruction.

GeoGebra Commands & Parameters

  1. UnicodeToLetter(34) → u34
  2. Text("" + Um1) → txt_p
  3. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m01(k), m02(k)], " "], k, 1, 5]]) → txtUm1
  4. Zip(Vector[a, a + UnitVector[a]], a, Points00) → lVector1
  5. Zip(Vector[a, a + (1.5 * UnitVector[b])], a, Points00, b, Wi_Pc) → lVector2
  6. Zip(Vector[a, a + (1.5 * UnitVector[b])], a, Points00, b, Wi_P) → lVector3
  7. Sphere((0, 0, 0), 5) → sph
  8. TableText(Append["i", 1…n], Append[" \fgcolor{orange}{GM :Δφ_i}, rad", l1w], Append["\fgcolor{magenta}{GC :Δφ_i} , rad", l1cw], "v") → text23r
  9. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(1)) → ll1
  10. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(2)) → ll2
  11. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(3)) → ll3
  12. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(4)) → ll4
  13. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(5)) → ll5
  14. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(6)) → ll6
  15. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(7)) → ll7
  16. Zip(Segment[Element[Points00, y(a)], Element[Points00, z(a)]], a, ll1bb(8)) → ll8