Gears - a 5.5.10 tiling

I have already presented a simple 5.5.10 tiling. The more complex one below includes a complete 5.5.10 rose - a circle of pentagons around a decagon.

I have called the tiling “Gears” because of the way the roses interlock. I’ve given names to each of the “forbidden” tilings in the next few pages to make them easier to refer to when I expand the site to examine other tilings.

As usual, I will present a tiling fragment, a translational unit and a skeleton tiling showing how the translational unit can be repeated to construct the full tiling. Because the “forbidden” tilings tend to be more complex than other tilings presented on this site before, I’ve provided larger images, often with several colouring variations including black and white.

I’ve also provided a colour-keyed legend for each tiling that lists the small angles for all the rhombs used in the tilings.

I’ve linked the first translational unit image for each tiling to an SVG file so that you can experiment with your own colouring schemes if you like. I recommend the Inkscape SVG editor.

Tiling

Translational Unit

Legend

Skeleton tiling

Tiling (black and white)

Translational Unit (black and white)