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Rhombicuboctahedron Construction

Rhombicuboctahedron Construction
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2017-11-21 14:39
PolygonSolid GeometryGeometric Construction
This example demonstrates the construction of a rhombicuboctahedron. Key mathematical concepts include solid geometry and polyhedron construction. Using GeoGebra commands such as Circle, Intersect, Rotate, and Polygon, the process of generating the polyhedron is visually illustrated. Suitable for high school students and teachers to understand the construction of polyhedra in solid geometry.

GeoGebra Commands & Parameters

  1. Circle(OO, 1, xOyPlane) → c
  2. Intersect(yAxis, c, 2) → A
  3. Rotate(A, 45°) → B
  4. Polygon(A, B, 8, xOyPlane) → veelhoek1, zijde, D, E, F, G, H, g, h, i, j, k, l, m, C
  5. Polygon(B, A, 4, xOyPlane) → veelhoek2, f, n, p, q, I, J
  6. Polygon(D, C, 4, xOyPlane) → veelhoek3, r, s, t, a, K, L
  7. Circle(r, K) → d
  8. Circle(f, J) → e
  9. Intersect(d, e) → M, N, ,
  10. Angle(J, B, N) → α
  11. Rotate(veelhoek2, (-(135°)), zijde) → schuin
  12. Line(OO, OOO) → as
  13. LineBisector(A, B, xOyPlane) → b
  14. Circle(OO, zijde / 2, xOyPlane) → c_1
  15. Intersect(b, c_1) → O, P
  16. OrthogonalLine(O, b, xOyPlane) → f_1
  17. Intersect(zijde, f) → Q
  18. Intersect(b, zijde) → R
  19. Vector(R, P) → u
  20. Translate(veelhoek2, u) → veelhoek2'
  21. Translate(veelhoek2', Vector[(0, 0, z(N))]) → boven
  22. Translate(veelhoek2', Vector[(0, 0, (-z(N)) - zijde)]) → veelhoek2''
  23. Rotate(veelhoek2, 90°, zijde) → recht
  24. Sequence(Rotate[schuin, (n * 90°), as], n, 0, 3) → lijst_1
  25. Sequence(Rotate[recht, (nn * 45°), as], nn, 0, 7) → lijst_2
  26. Mirror(lijst_1, o) → lijst_3
  27. Mirror(lijst_2, o) → lijst_4
  28. Mirror(N, Midden) → N'
  29. Polygon(B, C, N) → driehoek1, n_1, b_1, c_2
  30. Sequence(Rotate[driehoek1, (nn * 90°), as], nn, 0, 3) → lijst_5
  31. Mirror(lijst_5, o) → lijst_6