A Semi-regular Tessellation on Hinges A
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 frees the squares by letting them become rhombi. As a consequence, the tessellation easily morphs into a derivative of the tessellation designated (3, 3, 3, 3, 3, 3) in which naturally 6 equilateral triangles meet at every vertex.
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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