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Icosidodecahedron with 30 vertices: sphere-based 3D construction

Icosidodecahedron with 30 vertices: sphere-based 3D construction
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2020-12-31 03:57
PolygonSolid GeometryTransformationGeometric Construction
This example demonstrates how an icosidodecahedron (a truncated icosahedral-type uniform solid) can be constructed as a 3D structure from a set of points located on a reference sphere, highlighting its spatial symmetry and the fact that it has 30 vertices. Key concepts include truncated/semiregular polyhedron structure, point sets in 3D space, sphere-based geometric visualization, and the use of vector/parameter-style auxiliary quantities to organize geometry and labels. Construction-wise, it uses Sphere to create the spherical reference surface, point objects (e.g., Points00 and related indexed points) to represent the vertex set, and Segments (plus grouped segment objects) to connect vertices into edges; Text/UnicodeToLetter together with TableText, Sum, Zip are used to assemble and display vertex-related information (such as counts and formatted annotations) in the interface. A vector-like set of objects (e.g., lVector1/2/3) and various computed symbols help parameterize or present auxiliary data. Suitable for secondary-to-early university learners studying solid geometry, symmetry of polyhedra, and GeoGebra-based geometric modeling.

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

AI Drawing Prompt Reference

Draw an icosidodecahedron constructed from 30 vertices on a reference sphere, highlighting its spatial symmetry. Create a sphere first, then connect the points with lines to form edges. Label each vertex with colored text showing information like angles and indices, using vector-like objects to organize geometry and annotations.
The prompt above was compiled from the original drawing commands and is for reference only.