A Semi-regular Tessellation on Hinges B

The applet implements a hinged realization of one [Steinhaus, #82] semi-regular plane tessellations. The tessellation itself is identified as (4, 3, 3, 4, 3) because 5 regular polygons meet at every vertex: a square, followed by two equilateral triangles, followed by a square and then again by an equilateral triangle. In particular this is what makes it semi-regular: a semi-regular tessellation combines more than one kind of regular polygons, but the same arrangement at every vertex.

There are two ways to set this tessellation on hinges. Something has to give. We may only preserve either the squares or the equilateral triangles, but not both. Accordingly, there are two implementations. The one below lets loose the equilateral triangles. As a result, it is easily morphs into a derivative of a 4, 4, 4, 4 tessellation.

It is possible to further relax the original constraints. For example, a less regular tessellation is obtained when the rhombi are free to become parallelograms.

What if applet does not run?

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 Hinged Realization of a Plane Tessellation
	A Semi-regular Tessellation on Hinges A
	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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