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Planar 'jitterbugs' can be derived from a square tiling
and a triangle tiling of the plane. The tiles are oriented alternately,
and connected by vertices to their neighbours, with the choice of
vertex depending on orientation.
At maximum expansion the triangle transformation requires four times
the area of the base tiling, and the square transformation requires
double the area of the base tiling.
These tiles may also represent faces or sections of a polyhedron,
and the transformation can then control a transformation of vertex
bonded polyhedra in space. The ratio of the space required
at the maximum and minimum expansion is the same as for the
corresponding plane tiling
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