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Wallpaper Symmetry Group pgg

Wallpaper Symmetry Group pgg
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2017-11-01 22:53
MatrixTransformationGeometric Construction
In collections Wallpaper Symmetry Groups
This example demonstrates the wallpaper symmetry group pgg. It involves transformations such as translation, reflection, and rotation. Using GeoGebra commands like Intersect, Vector, Mirror, and Translate, a pattern with pgg symmetry can be constructed. Suitable for high school geometry education and learning symmetry concepts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. OrthogonalLine(A, u) → f
  4. Point(f) → C
  5. Vector(A, C) → v
  6. Line(C, D) → g
  7. Line(D, B) → h
  8. Midpoint(C, D) → E
  9. Midpoint(D, B) → F
  10. Mirror(pic1, E) → pic1'
  11. Sequence(Sequence[Translate[pic1, Vector[((4 * a) * v) + ((2 * b) * u)]], a, -10, 10], b, -10, 10) → L_1
  12. Sequence(Sequence[Translate[pic1', Vector[((4 * a) * v) + ((2 * b) * u)]], a, -10, 10], b, -10, 10) → L_2
  13. OrthogonalLine(F, h) → i
  14. Mirror(F, g) → F'
  15. OrthogonalLine(F', h) → j
  16. Translate(Mirror[pic1, i], u) → pic2
  17. Translate(Mirror[pic1', j], u) → pic3
  18. Sequence(Sequence[Translate[pic1, Vector[((2 * a) * v) + ((2 * b) * u)]], a, -10, 10], b, -10, 10) → L_3
  19. Sequence(Sequence[Translate[pic1', Vector[((2 * a) * v) + ((2 * b) * u)]], a, -10, 10], b, -10, 10) → L_4
  20. Sequence(Sequence[Translate[pic2, Vector[((2 * a) * v) + ((2 * b) * u)]], a, -10, 10], b, -10, 10) → L_5
  21. Sequence(Sequence[Translate[pic3, Vector[((2 * a) * v) + ((2 * b) * u)]], a, -10, 10], b, -10, 10) → L_6

AI Drawing Prompt Reference

Draw a wallpaper pattern with pgg symmetry, including horizontal and vertical reflection axes and translations. Start by plotting the intersection of the coordinate axes, then create a vector and draw a line perpendicular to it. Use these lines and vectors to perform mirror and translation operations, generating repeating pattern units, and adjust the translation parameters to display the symmetry of the entire pattern.
The prompt above was compiled from the original drawing commands and is for reference only.