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Rotational Symmetry of Cube

Rotational Symmetry of Cube
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2018-01-17 16:27
Solid GeometryTransformationGeometric Construction
This example demonstrates the rotational symmetry of a cube. Key mathematical concepts include rotational symmetry and solid geometry. Using GeoGebra commands such as Cube, PointIn, Line, Rotate, and Midpoint, the construction of the cube and its rotational symmetry figures is illustrated. Suitable for middle school and above students to learn about solid geometry and symmetry.

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