A Hinged Realization of a Plane Tessellation

The applet implements a hinged realization of one [Steinhaus, #81] of semi-regular plane tesselations that was suggested by D. Wells in his [Hidden Meanings, p. 139].

The tessellation is built around a rhombus, with regular hexagons and equilateral triangles attached to the two pairs of opposite sides. Steinhaus' tessellation #81 is obtained when the rhombus becomes a square.

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The applet allows to create various visual effects. For example, the following strongly reminds of the wobbling parallel lines in the Brick wall illusion.

wobbling parallel lines in a hinged plane tessellation

References

  • H. Steinhaus, Mathematical Snapshots, umpteen edition, Dover, 1999
  • D. Wells, Hidden connections, double meanings: A mathematical exploration, Cambridge University Press, 1988

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  • A Semi-regular Tessellation on Hinges A
  • A Semi-regular Tessellation on Hinges B
  • A Semi-regular Tessellation on Hinges C
  • Escher's Theorem
  • Napoleon Theorem by Plane Tessellation
  • Parallelogram Law: A Tessellation
  • Simple Quadrilaterals Tessellate the Plane
  • Pythagorean Theorem By Plane Tessellation
  • Pythagorean Theorem a la Friedrichs
  • Pythagorean Theorem By Hexagonal Tessellation
  • Hinged Greek Cross Tessellation

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