Kurschaks Tile

Author

Eric W. Weisstein
August 4, 2010

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

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

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

Code

line[l_List]:=Line[Append[l,l[[1]]]]

KurschaksSquare:=Module[{i,s=Sqrt[3]/2,h=1/2,R=(Sqrt[6]-Sqrt[2])/4},Graphics[{line[{{0,0},{1,0},{1,-1},{0,-1}}],line[{{0,0},{1,0},{h,-s}}],line[{{1,0},{1-s,-h},{1,-1}}],line[{{1,-1},{0,-1},{h,s-1}}],line[{{0,0},{s,-h},{0,-1}}],line[{{h,-s},{1-s,-h},{h,s-1},{s,-h}}],Line[Table[h{1,-1}+R{Cos[2Pi (i+1/2)/12],Sin[2Pi(i+1/2)/12]},{i,0,12}]]}]]

KurschaksTile:=Module[{s=2 Sin[Pi/12],rho},
rho=1-s;
Graphics[{Table[{Line[{{0,0},{Cos[2Pi n/12],Sin[2Pi n/12]}}],Line[{{0,0},rho {Cos[2Pi (n+1/2)/12],Sin[2Pi (n+1/2)/12]}}],Line[{{Cos[2Pi n/12],Sin[2Pi n/12]},rho {Cos[2Pi (n+1/2)/12],Sin[2Pi (n+1/2)/12]},{Cos[2Pi (n+1)/12],Sin[2Pi (n+1)/12]},{Cos[2Pi n/12],Sin[2Pi n/12]}}]},{n,0,11}],Line[{{-1,-1},{-1,1},{1,1},{1,-1},{-1,-1}}],Table[Line[{{Cos[2Pi (3n+1)/12],Sin[2Pi (3n+1)/12]},Sqrt[2]{Cos[2Pi (n+1/2)/4],Sin[2Pi (n+1/2)/4]},{Cos[2Pi (3n+2)/12],Sin[2Pi (3n+2)/12]}}],{n,0,3}]}]]

Figures

KurschaksSquare

KurschaksTile