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Truncated Octahedron by chris cambré

Truncated Octahedron by chris cambré
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2017-11-20 21:13
Solid GeometryTransformationGeometric Construction
This example demonstrates the construction of a truncated octahedron. It involves transformations in solid geometry. Using commands such as Circle, Intersect, Rotate, Polygon, Line, OrthogonalLine, Angle, Plane, Mirror, Sequence, and Midpoint, a geometric model of the truncated octahedron can be constructed. Suitable for teaching and learning in high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Circle(OO, 1, xOyPlane) → c
  2. Intersect(yAxis, c, 2) → A
  3. Rotate(A, 90°) → B
  4. Polygon(A, B, 4, xOyPlane) → veelhoek1, f, g, h, i, C, D
  5. Polygon(B, A, 6, xOyPlane) → veelhoek2, j, H, k, l, m, n, p, E, F, G
  6. Polygon(A, D, 6, xOyPlane) → veelhoek3, q, L, r, s, t, a, b, I, J, K
  7. Polygon(D, C, 6, xOyPlane) → veelhoek4, d, P, e, f_1, g_1, h_1, i_1, M, N, O
  8. Polygon(C, B, 6, xOyPlane) → veelhoek5, j_1, T, k_1, l_1, m_1, n_1, p_1, Q, R, S
  9. Circle(j_1, Q) → c_1
  10. Circle(j, H) → d_1
  11. Intersect(c_1, d_1) → U, V, ,
  12. Line(C, B) → q_1
  13. OrthogonalLine(Q, q_1, xOyPlane) → r_1
  14. Intersect(q_1, r_1) → W
  15. Angle(Q, W, V) → α
  16. Rotate(veelhoek5, (-α), g) → schuin1
  17. Line(OO, OOO) → as
  18. Rotate(veelhoek2, (-α), f) → veelhoek2'
  19. Rotate(veelhoek3, (-α), i) → veelhoek3'
  20. Rotate(veelhoek4, α, d) → veelhoek4'
  21. Rotate(F, (-α), f) → FF
  22. Rotate(FF, (-(90°)), as) → FFF
  23. Rotate(FF, (-(180°)), as) → FFFF
  24. Plane(FFF, FFFF, FF) → o
  25. Mirror(schuin1, o) → schuin1'
  26. Sequence(Rotate[schuin1', (n * 90°), as], n, 1, 3) → lijst_1
  27. Midpoint(FF, FFFF) → Mid
  28. Mirror(veelhoek1, Mid) → veelhoek1'
  29. Rotate(G, α, j) → G'
  30. Rotate(R, (-α), g) → R'
  31. Mirror(V, o) → V'
  32. Polygon(G', V, R', V') → vierhoek1, g', v, r', v'
  33. Sequence(Rotate[vierhoek1, (n * 90°), as], n, 1, 3) → lijst_2
  34. Mirror(A, Mid) → AA

AI Drawing Prompt Reference

Construct a truncated octahedron by first drawing a circle on the xOy plane, then using rotations and polygons to create each face, and finally adjusting the positions of the faces with reflections and translations to form a complete truncated octahedron.
The prompt above was compiled from the original drawing commands and is for reference only.