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Rotational Symmetry of Cube by Anthony OR 柯志明

Rotational Symmetry of Cube by Anthony OR 柯志明
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2017-04-11 11:50
Solid GeometryTransformationGeometric ConstructionSlider Animation
This GeoGebra example dynamically demonstrates the rotational symmetry of a cube by rotating it about various axes. It visually explores how the cube maps onto itself under certain rotations, illustrating the concept of rotational symmetry in 3D. Core mathematical concepts include solid geometry, symmetry axes, rotation angles, and transformation groups. The construction uses the Cube command to create the cube, PointIn and Midpoint to define key points, Line to establish rotation axes, and Rotate to rotate the cube and its faces, generating copies like faceABCD' for comparison. Suitable for high school or early college students learning about symmetry in 3D shapes, and useful for teachers creating interactive geometry lessons.

GeoGebra Commands & Parameters

  1. Cube(H, E, xOyPlane) → a, F, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, G, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH, C, D, A, B, faceABCD, faceADHE, faceABFE
  2. PointIn(faceABCD) → J
  3. PointIn(faceEFGH) → I
  4. Line(I, J) → b
  5. Rotate(a, (-α), b) → a'
  6. Rotate(faceABCD, (-α), b) → faceABCD'
  7. Rotate(faceABFE, (-α), b) → faceABFE'
  8. Rotate(faceADHE, (-α), b) → faceADHE'
  9. Rotate(faceBCGF, (-α), b) → faceBCGF'
  10. Rotate(faceCDHG, (-α), b) → faceCDHG'
  11. Rotate(faceEFGH, (-α), b) → faceEFGH'
  12. Midpoint(D, B) → K
  13. Midpoint(H, F) → L
  14. Midpoint(edgeFG) → Q
  15. Midpoint(edgeGH) → R
  16. Midpoint(edgeEH) → S
  17. Midpoint(edgeEF) → T
  18. Midpoint(edgeBC) → W
  19. Midpoint(edgeAD) → B_1
  20. Midpoint(edgeAB) → C_1
  21. Midpoint(edgeCD) → D_1

AI Drawing Prompt Reference

Draw a cube and rotate it around an axis passing through the centers of two of its faces, generating the rotated cube and its faces. First, create a cube, then select two points within one of its faces to form the rotation axis. Next, rotate the cube and all its faces around this axis to generate the rotated faces for comparison, illustrating the cube's rotational symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.