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.


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

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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  • Dancing Rectangles Model Auxetic Behavior
  • 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
  • Pythagorean Theorem: A Variant of Proof by Tessellation
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