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Equilateral 2N-gon Tiling

Equilateral 2N-gon Tiling
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2015-10-17 02:24
PolygonTransformationGeometric Construction
This example demonstrates an equilateral 2N-gon tiling inspired by Regolo54's hexagon tiling. It showcases the symmetry and geometric transformations of polygon tilings. Using GeoGebra commands such as Rotate, If, Sequence, Point, Join, and Polygon, specific symmetric polygons can be constructed. Suitable for high school and above students to learn about geometric transformations and polygon tilings.

GeoGebra Commands & Parameters

  1. Rotate(A, (-360 * ° / N)) → A'
  2. If(N ≟ 4, (0, 0) + Vector[A] + OrthogonalVector[Vector[A]], Intersect[Line[A, (0, 0)], Rotate[OrthogonalLine[A, Line[A, (0, 0)]], (-360 * ° / N)]]) → C
  3. If(N ≟ 4, 45*°, ((Min[Angle[A, C, A'], Angle[A', C, A]] * 180) * ° / π)) → α
  4. Sequence(Rotate[A, ((i * 360) * ° / N), (0, 0)], i, 1, N) → list1
  5. Rotate(Ray[(0, 0), A], (180 * ° / N)) → a
  6. Point(a) → B
  7. Sequence(Rotate[B, ((i * 360) * ° / N), (0, 0)], i, 1, N) → list2
  8. Join(Sequence[{Element[list1, i], Element[list2, i]}, i, 1, N]) → list3
  9. Polygon(list3) → poly1
  10. If(Mod[N, 2] ≟ 0, 1, Distance[B, (0, 0)] / Distance[A, (0, 0)]) → ulong
  11. Rotate(OrthogonalLine[A, Line[A, (0, 0)]], (-360 * ° / N)) → b
  12. Sequence(Rotate[poly1, ((2 * i) * α), C], i, 0, c - 1) → list5
  13. Circle(C, A) → d
  14. Intersect(OrthogonalLine[A, Vector[A]], a) → D
  15. Sequence(Rotate[list5, ((((2 - f) * i) * 360) * ° / N), (0, 0)], i, 0, M - 1) → list6