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Cube Mirror with Rotation Transform

Cube Mirror with Rotation Transform
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2023-03-14 00:43
AngleVectorSolid GeometryTransformationGeometric Construction
In collections geometriadinamica.es
This GeoGebra example demonstrates how to create a cube with mirror effects and apply rotation transformations in 3D space. Core mathematical concepts include 3D vectors, rotation angles, coordinate axis transformations, and ellipse projections. Construction uses: Punto3D for creating 3D points, Vector for spatial vectors, Angle for defining rotation, Line and Segment for drawing lines, Ellipse for projection elements, Polygon for creating surfaces, and Intersect for finding intersections. Suitable for high school and college students studying solid geometry and spatial transformations, helping understand 3D coordinate systems, rotation matrices, and mirror symmetry concepts.

GeoGebra Commands & Parameters

  1. Ellipse((-3.62, 5 + nada), (-2.38, 5 + nada), 0.65) → zElipse1
  2. Point(zElipse1) → XY
  3. Angle((-2, 5), (-3, 5), XY) → zAngRot
  4. Ellipse((-3, 4.38), (-3, 5.62), 0.65) → zElipse2
  5. Point(zElipse2) → Z
  6. Angle((-3, 6), (-3, 5), Z) → zAngInc
  7. Line(O, zX) → zEjeX
  8. Line(O, zY) → zEjeY
  9. Line(O, zZ) → zEjeZ
  10. Vector(O, zX) → zVectorX
  11. Vector(O, zY) → zVectorY
  12. Vector(O, zZ) → zVectorZ
  13. Intersect(zElipse2, zElipse1, 1) → zPunto1
  14. Intersect(zElipse2, zElipse1, 4) → zPunto2
  15. Segment((-3, 4.35) + O, (-3, 5.65) + O) → zSeg1
  16. Segment(zPunto1, zPunto2) → zSeg2
  17. Segment((-3.65, 5) + O, (-2.35, 5) + O) → zSeg3
  18. Punto3D(XY, Z, E1) → E1'
  19. Punto3D(XY, Z, E2) → E2'
  20. Punto3D(XY, Z, E3) → E3'
  21. Punto3D(XY, Z, E4) → E4'
  22. Punto3D(XY, Z, F1) → F1'
  23. Punto3D(XY, Z, F2) → F2'
  24. Punto3D(XY, Z, F3) → F3'
  25. Punto3D(XY, Z, F4) → F4'
  26. Punto3D(XY, Z, V1) → V1'
  27. Punto3D(XY, Z, V2) → V2'
  28. Punto3D(XY, Z, V3) → V3'
  29. Punto3D(XY, Z, V4) → V4'
  30. Punto3D(XY, Z, V5) → V5'
  31. Punto3D(XY, Z, V6) → V6'
  32. Punto3D(XY, Z, V7) → V7'
  33. Punto3D(XY, Z, V8) → V8'
  34. Angle(E1', E2', E4') → ang
  35. Polygon(V7', V1', V15', V73') → poly13, v7', v1'_3, v15'_1, v73'
  36. Polygon(V7', V5', V51', V73') → poly14, v7'_1, v5'_3, v51'_1, v73'_1
  37. Polygon(V1', V18', V72', V7') → poly15, v1'_4, v18', v72', v7'_2
  38. Polygon(V1', V18', V27', V2') → poly16, v1'_5, v18'_1, v27', v2'_3
  39. Polygon(V2', V27', V81', V8') → poly17, v2'_4, v27'_1, v81', v8'
  40. Polygon(V8', V81', V72', V7') → poly18, v8'_1, v81'_1, v72'_1, v7'_3
  41. Polygon(V2', V26', V84', V8') → poly19, v2'_5, v26'_1, v84', v8'_2
  42. Polygon(V8', V84', V62', V6') → poly20, v8'_3, v84'_1, v62'_1, v6'_3
  43. Polygon(V7', V76', V85', V8') → poly21, v7'_4, v76', v85', v8'_4
  44. Polygon(V7', V76', V58', V5') → poly22, v7'_5, v76'_1, v58', v5'_4
  45. Polygon(V5', V58', V67', V6') → poly23, v5'_5, v58'_1, v67', v6'_4
  46. Polygon(V8', V85', V67', V6') → poly24, v8'_5, v85'_1, v67'_1, v6'_5
  47. Polygon(E1', F1', F4', E4') → tapa_i, e1'_1, f1', f4', e4'_1
  48. Polygon(E2', F2', F3', E3') → tapa_d, e2'_1, f2', f3', e3'_1
  49. Polygon(V1', V15', V37', V3') → poly1, v1', v15', v37', v3'
  50. Polygon(V3', V37', V51', V5') → poly2, v3'_1, v37'_1, v51', v5'
  51. Polygon(V1', V14', V32', V3') → poly3, v1'_1, v14', v32', v3'_2
  52. Polygon(V3', V4', V41', V32') → poly4, v3'_3, v4', v41', v32'_1
  53. Polygon(V3', V36', V54', V5') → poly5, v3'_4, v36', v54', v5'_1
  54. Polygon(V3', V36', V45', V4') → poly6, v3'_5, v36'_1, v45', v4'_1
  55. Polygon(V5', V54', V63', V6') → poly7, v5'_2, v54'_1, v63', v6'
  56. Polygon(V6', V4', V45', V63') → poly8, v6'_1, v4'_2, v45'_1, v63'_1
  57. Polygon(V1', V2', V23', V14') → poly9, v1'_2, v2', v23', v14'_1
  58. Polygon(V2', V4', V41', V23') → poly10, v2'_1, v4'_3, v41'_1, v23'_1
  59. Polygon(V2', V26', V48', V4') → poly11, v2'_2, v26', v48', v4'_4
  60. Polygon(V4', V6', V62', V48') → poly12, v4'_5, v6'_2, v62', v48'_1
  61. Polygon(E1', E2', E3', E4') → espejo, e1', e2', e3', e4'
  62. Punto3D(XY, Z, R1) → R1'
  63. Punto3D(XY, Z, R2) → R2'
  64. Punto3D(XY, Z, R4) → R4'

AI Drawing Prompt Reference

Draw a cube with mirror effects and rotation transformations. Start by drawing two ellipses, then use their intersection points to create line segments. Next, construct the cube's faces using these segments and points. Finally, apply rotation and mirroring to show the cube's transformation in 3D space.
The prompt above was compiled from the original drawing commands and is for reference only.