# Explicit formula for the position of “bent wedge” tiles

Is there an explicit formula to compute the position and the angle of the $n$th tile of a bent wedge tiling ?

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"It is an isosceles $15^\circ$ triangle distorted into a curved enneagon. The apical angle is $15^\circ$, the three successive angles on each side are $165^\circ$, and the two end angles are $60^\circ$ and $105^\circ$." So, rotate by $15^\circ$ each time? Since $15\times24=360$ and there are $24$ innermost wedges... – J. M. Jul 29 '12 at 13:01

One general approach could be to let $a=n \bmod 48$ determine the orientation of the tile, and then use one of $48$ subsidiary functions to determine its location based on $\left\lfloor \frac{n}{48}\right\rfloor$. Typically many of these subsidiary functions will be the same except for global rotations about the origin, and each of these functions just place the tiles at selected positions in a rectangular grid. The only tricky thing is then to make sure that the right subset of the positions in the rectangular grid get filled.