Shield - a 3.7.42 tiling

The shield jewel.

This tiling, sent to me by Robert Fathauer, is made up of two nutshells of alternating heptagons and 42-gons, shown below. The larger nutshell contains a shield-shaped irregular polygon. Two copies of this shield appear in the translational unit. The shield has a remarkable similarity to the "jewel" found in the 3.8.24 Dancer tiling.

The tiling requires only six prototiles: the 42-gon, the triangle, the heptagon, the 21-rhomb and two fractional rhombs shown in the legend below. This is three less than the 3.7.42 Mirror tiling shown above.


Translational Unit


Skeleton tiling

Tiling (Black and white)

Translational Unit (Black and white)