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Icosahedron Faces and Edges

Icosahedron Faces and Edges
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2017-11-17 16:43
Solid GeometryMatrixGeometric Construction
In collections Solids, graphs and paths
This example demonstrates the construction of the faces and edges of an icosahedron. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Circle, Intersect, Rotate, and Point, the various faces and edges of the icosahedron can be constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Circle(OO, 1, xOyPlane) → c
  2. Intersect(xAxis, c, 1) → A
  3. Rotate(A, 72°) → B
  4. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  5. Icosahedron(A, B, C) → a, D, zijvlakABC, zijvlakACF, zijvlakAFG, zijvlakADG, zijvlakABD, zijvlakBDH, zijvlakBEH, zijvlakBCE, zijvlakCEI, zijvlakCFI, E, zijvlakEHK, zijvlakEIK, zijvlakIKL, zijvlakFIL, zijvlakHJK, zijvlakJKL, zijvlakGJL, zijvlakFGL, zijvlakDHJ, zijvlakDGJ, F, RibbeAC, RibbeAB, RibbeBC, RibbeAF, RibbeCF, RibbeAG, RibbeFG, RibbeAD, RibbeDG, RibbeBD, G, RibbeBH, RibbeDH, RibbeBE, RibbeEH, RibbeCE, RibbeCI, RibbeEI, RibbeFI, RibbeEK, RibbeHK, H, RibbeIK, RibbeIL, RibbeKL, RibbeFL, RibbeJK, RibbeHJ, RibbeJL, RibbeGL, RibbeGJ, RibbeDJ, I, J, K, L
  6. TableText({{"A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L"}}) → tekst1
  7. TableText({{"A"}, {"B"}, {"C"}, {"D"}, {"E"}, {"F"}, {"G"}, {"H"}, {"I"}, {"J"}, {"K"}, {"L"}}) → tekst2
  8. Point(ribben) → PP