Consider the following 2 tiles:- 1.Tile ABCD has angles A=80, B=80, C=40 and D=160 degrees.Segment BC has length 1-2sin(pi/18). The other sides have length 2sin(pi/18). 2.Tile PQRS has angles P=20, Q=200, R=60 and S=80 degrees.Segment SP has length 1-2sin(pi/18). The other sides have length 2sin(pi/18).
Can above 2 tiles be made aperiodic by giving some matching conditions?
I had given this problem on this site in 2003 also.That time John Conway had also shown little interest in this problem.Nothing much of interest came out after lot of discussions.I hope Mary Krimmel remember all that.I am giving it again with the hope that new readers may find it interesting and this time something special comes out. Reason behind my belief on this tiles is my already expressed view that 2sin(pi/18) seems as interesting as Golden Ratio. In 2006, I knew about Heesch tiling which is again very interesting topic.Using these I formed a single tile which were of Heesh no.1 and 2.