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Rotating Cuboid

Rotating Cuboid
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2018-06-24 22:05
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the dynamic process and 3D shape transformation of a cuboid rotating around an axis. Core math concepts include solid geometry, vector operations, 3D coordinate transformations, and geometric transformations. Construction highlights involve GeoGebra commands like Segment and Polygon, and objects such as v_x, B1, A1, v_z, B3, γ, β, α, T_z, v_y, v, P, T_y, T_x, w, A, A2, A3, C1, C2, B2, b, u, B, C3, c, t, C, D1, D2, D3, d, s, D, f, E1, E2, E3, e, r. Suitable for high school and above learning solid geometry, spatial visualization, and 3D modeling applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, D) → h
  4. Segment(D, E) → i
  5. Segment(E, F) → j
  6. Segment(G, D) → k
  7. Segment(G, B) → a
  8. Segment(A, F) → f_1
  9. Segment(A, H) → g_1
  10. Segment(H, E) → h_1
  11. Segment(F, G) → i_1
  12. Segment(C, H) → j_1
  13. Polygon(A, H, E, F) → q1, a_1, h_2, e_1, f_2
  14. Polygon(B, C, D, G) → q2, b_1, c_1, d_1, g_2
  15. Polygon(H, C, D, E) → q3, h_3, c_2, d_2, e_2
  16. Polygon(A, H, C, B) → q4, a_2, h_4, c_3, b_2
  17. Polygon(A, B, G, F) → q5, a_3, b_3, g_3, f_3
  18. Polygon(E, F, G, D) → q6, e_3, f_4, g_4, d_3

AI Drawing Prompt Reference

Draw a cuboid and then rotate it around one of its edges. First, draw the six faces of the cuboid: ABHE, BCDG, HCEF, ABGF, EFGD, and ACDH. Then, choose one edge as the rotation axis, for example, edge AB, and rotate the entire cuboid around this axis to observe the dynamic rotation process.
The prompt above was compiled from the original drawing commands and is for reference only.