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Euclidean Regular Tessellations (Geogebra Demo)

Euclidean Regular Tessellations (Geogebra Demo)
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2025-08-16 22:57
In collections Teselaciones regulares
This example demonstrates how to construct and visualize Euclidean regular tessellations on the plane, highlighting the way congruent regular polygons can tile the plane without overlaps or gaps through systematic repetition. The key mathematics includes regular polygon angle conditions (interior angles and matching rules), iterative geometric generation, and planar repeating patterns under explic

GeoGebra Commands & Parameters

  1. Polygon(pV) → actualp
  2. Flatten(Join[{{Vac(p)}, {Vac \ {Vac(p)}}}]) → Vacp
  3. Flatten(Join[{{Vac \ {Vac(1)}}, {Vac(1)}}]) → Vac2
  4. Sequence(Rotate[(1, 0), ((k * 2) * pi / p) + pi / p], k, 0, p - 1) → celda0
  5. Polygon(celda0) → pol
  6. Sequence({Vac(k), q - 1, ncActual}, k, 3, p - 1) → Vplus
  7. If(floor(p / 2) ≠ p / 2 ∧ q ≟ 3, 4, floor(q / 2) ≟ q / 2, 2, 3) → nc
  8. Flatten(Join[{{Vac \ {Vac(1), Vac(2)}}, {Vac(1), Vac(2)}}]) → Vac2'
  9. Flatten(Join[{{Vac(p - 1), Vac(p)}, {Vac \ {Vac(p - 1), Vac(p)}}}]) → Vacp'
  10. Sequence(Rotate[(1, 0), ((k * 2) * pi / p) + pi / p], k, 0, p - 1) → V
  11. Sequence({V(k), q - 1, 0}, k, 1, p) → vert0
  12. Line(celda0(p), celda0(1)) → hc1
  13. Sequence(PolyLine[{celda0(5) + (k * u), celda0(6) + (k * u), celda0(1) + (k * u), celda0(2) + (k * u), celda0(2) + ((k + 1) * u)}], k, -12, 12, 3) → r63