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Dodecahedron: 3D Solid Geometry with 20 Vertices

Dodecahedron: 3D Solid Geometry with 20 Vertices
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2019-08-13 00:00
PolygonVectorSolid GeometryGeometric Construction
This GeoGebra example demonstrates a regular dodecahedron, a Platonic solid composed of 12 regular pentagonal faces, with 20 vertices and 30 edges. It illustrates key concepts in solid geometry, including properties of regular polyhedra, vertex coordinates in 3D space, and the relationship between the polyhedron and its circumscribed sphere. The construction uses GeoGebra commands such as Sphere to create the circumsphere, UnicodeToLetter, Text, Sum, and Zip for labeling and text generation, and TableText for data tables. Interactive buttons (button7, button2, etc.) control the display, while numerous points (Points00, lll00, etc.) and segments (Segments) define the edges and faces. This resource is suitable for high school or early university students studying solid geometry, polyhedra, or 3D visualization in mathematics.

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