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Cube to Truncated Cube and Cubo Transformation

Cube to Truncated Cube and Cubo Transformation
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2016-01-31 12:52
PolygonVectorSolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates a transformation from a cube to a truncated cube and a related cubo polyhedron. It involves solid geometry, polyhedra, vertices, edges, faces, truncation, vector translation, and coordinate-based construction. The construction uses Point to define vertices such as A, B, D, E, F, G, and H, Vector and Translate to generate transformed objects like A′, B′, D′, and F′, and Polygon, PolyLine, and Segment to draw edges and faces. Lists such as list1 and list2 help organize vertex sequences, while poly1 and poly2 represent constructed polygonal structures. It is suitable for secondary or undergraduate geometry teaching, spatial visualization, and GeoGebra 3D modeling examples.

GeoGebra Commands & Parameters

  1. Vector(H, G) → u
  2. Translate(A, u) → A'
  3. Translate(D, Vector[(-u)]) → D'
  4. Translate(F, Vector[(-u)]) → F'
  5. Translate(B, u) → B'
  6. Vector(H, M) → v
  7. Translate(A, v) → A'_1
  8. Translate(B, Vector[(-v)]) → B'_1
  9. Translate(D, v) → D'_1
  10. Translate(F, Vector[(-v)]) → F'_1
  11. Polygon(D'_1, F'_1, F', B', B'_1, A'_1, A', D') → poly1, d'_1, f'_1, f', b', b'_1, a'_1, a', d'
  12. Translate(D, w) → D'_2
  13. Translate(E, Vector[(-w)]) → E'
  14. Polygon(D'_2, D'_1, D') → poly2, d'_2, d'_3, d'_4
  15. Translate({E, K}, v) → list1
  16. Translate({I, J}, Vector[(-v)]) → list2
  17. Translate({A, B, F}, w) → list3
  18. Translate({K, J, I}, Vector[(-w)]) → list4
  19. Point(list1) → L
  20. Point(list2) → N
  21. Point(list4) → O
  22. Point(list3) → P
  23. Polygon(D'_2, E', L, N, O, P, F'_1, D'_1) → poly3, d'_5, e', l, n, o, p, f'_2, d'_6
  24. Point(list3) → Q
  25. Point(list4) → R
  26. Polygon(F'_1, P, F') → poly4, f'_3, f'_4, p_1
  27. Translate({K, B, J}, u) → list5
  28. Translate({E, I, F}, Vector[(-u)]) → list6
  29. Point(list5) → S
  30. Point(list6) → T
  31. Polygon(B', Q, R, S, T, O, P, F') → poly5, b'_2, q_1, r, s, t, o_1, p_2, f'_5
  32. Polygon(B'_1, B', Q) → poly6, q_2, b'_3, b'_4
  33. Polygon(N, O, T) → poly9, t_1, n_1, o_2
  34. PolyLine(D, F, B, A, K, E) → a
  35. PolyLine(A, D, E, I, J, B) → b
  36. Segment(J, K) → c
  37. Segment(F, I) → d
  38. Point(list6) → C
  39. Polygon(E', L, C) → poly7, c_1, e'_1, l_1
  40. Point(list5) → U
  41. Point(list4) → V
  42. Point(list1) → W
  43. Polygon(U, V, W) → poly8, w_1, u_1, v_1
  44. Point(list2) → Z
  45. Polygon(Z, R, S) → poly10, s_1, z_1, r_1
  46. Point(list3) → A_1
  47. Polygon(A', A_1, A'_1) → poly11, a'_2, a'_3, a_1
  48. Polygon(D'_2, E', C, U, V, A_1, A', D') → poly12, d'_7, e'_2, c_2, u_2, v_2, a_2, a'_4, d'_8
  49. Polygon(C, L, N, T, S, Z, W, U) → poly13, c_3, l_2, n_2, t_2, s_2, z_2, w_2, u_3
  50. Polygon(V, W, Z, R, Q, B'_1, A'_1, A_1) → poly14, v_3, w_3, z_3, r_2, q_3, b'_5, a'_5, a_3

AI Drawing Prompt Reference

Draw a cube and transform it into a truncated cube and related polyhedra by translating specific vertices using vectors. Show the changes in vertices, edges, and faces, using polygon tools to create shapes. Demonstrate geometric construction through vector translation and coordinate-based transformations, resulting in a complex structure of a truncated cube and cubo transformation.
The prompt above was compiled from the original drawing commands and is for reference only.