Harborth's Tiling

Author

Eric W. Weisstein
August 4, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Tilings/HarborthsTiling.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HarborthsTiling.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Code

rot[ang_][x_]:={{Cos[ang],-Sin[ang]},{Sin[ang],Cos[ang]}}.x

Harborth[{x_List,ang_}]:=Module[{b=2Pi/17.},
Table[x,{5}]+ rot[ang]/@{{0,0},{1,0},{1+Cos[b],Sin[b]},{Cos[b],Sin[b]},{0,0}}

Figure

size=4;
b=2Pi/17.;
Show[Graphics[{Line/@Harborth/@(Flatten[Table[{{rot[b k][{n,0}],b k},{rot[b k][{n,0}],b k-b}},{n,0,size},{k,0,16}],2]),
{Line/@Harborth/@(Flatten[Table[{rot[b k][{n,0}+{1+Cos[b],Sin[b]}+m{Cos[b],Sin[b]}],b k },{n,0,size},{k,0,16},{m,0,size}],2])}
}],
PlotRange->{{-size,size},{-size,size}},
Epilog->Line[size{{-1,-1},{-1,1},{1,1},{1,-1},{-1,-1}}]
]