| Rhombus 8sym PDF 2.1MB | Rhombus 12sym PDF 2.4MB
| Rhombus 10sym PDF 2.2MB
| Rhomb 8 & 12 sub tiles PDF 5.0MB
| Rhomb 10 sub tiles PDF 4.3MB
| Rhomb 14 sub tiles PDF 0.7MB | Rhombus 6sym PDF 11.0MB | Rhomb 6 sub tiles PDF 5.7MB |
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image left click on the small image. To obtain a high definition image
left click on "PDF" below the small image.
Even
simpler than a hexagon "seed" shape (Eve, Penrose's rhombus,
Ammann-Beenker) is the rhombus seed shape. Here we have centres
with 8, 10 and 12-fold rotational symmetry in Rhombus 8sym, Rhombus 12sym and Rhombus 10sym. The substitution schemes follow in Rhomb 8 & 12 sub tiles and Rhomb 10 sub tiles. Rhomb 14 sub tiles shows the substitution scheme for 14-fold rotational symmetry,
which uses 10 prototiles. These tilings all adhere to unit sided
tiles as a restriction. In the 14-fold tiling at the 9th
inflation tile 10 will be inflated for the first time and the resulting
inflated rhombus will be over 794 units along its long diameter.
This is why you don't see the tiling completed to this stage - at
2cm per side it would be a little under 16 metres long! The others are
on A1 paper.
Rhombus 6sym and Rhomb 6 sub tiles.
This tiling was found to be describable with matching rules
entailing 18 prototiles and another with 12 prototiles but a rigorous
proof was never produced, 18 and 12 being very far from a single tile. |