MATCHING RULES FOR THE ICOSAHEDRAL PENROSE TILING DERIVED BY INFLATION-DEFLATION PROCEDURES

Matching rules for the Penrose tiling can be derived in different ways. One way is the decoration by Ammann bars. In the three-dimensional case, these bars have to be replaced by Ammann planes. The vertices of the P1 (Penrose pentagon) tiling coincide with the vertices of the projections of the icosahedral Penrose lattice along the five-fold axes. The procedures of inflation and deflation of the P1 tiling are well understood. Therefore the deflation tiles of the next generation can be derived in the projection along the five-fold axes. If these tiles are decorated by Ammann planes according to the decoration of the projection and if the obstructions are obeyed, matching rules can be derieved. The different possibilities of decorations in the procedure of deflation of large bricks are enumerated. © 1990.