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problem icon  LOGO Challenge 5 - Patch   Tessellating Hexagons
This problem follows on from some of the ideas in Tessellating
Triangles and Tessellating Quadrilaterals. It was inspired by a
problem in "Tiles and Tiling", an activity book published by the
Association of Teachers of Mathematics.  Here is a tessellation
of regular hexagons:   Can you explain why regular hexagons
tessellate?  What about a hexagon where each pair of opposite
sides is parallel, and opposite sides are the same length, but
different pairs of sides are not the same length?  You can print
off some square dotty paper, or some isometric dotty paper, and
try drawing hexagons of this form on it. You could also draw
some hexagons using this interactive. Can you tessellate them?
Do all hexagons of this form tessellate? How do you know?  Now
let's consider hexagons with three adjacent angles which add up
to $360^{\circ}$, sandwiched by two sides of equal length, as in
the diag