Coordinates of Penrose tiling

The following clusters of Penrose tiling were generated by iteratively applying the inflation-deflation rule. We regard each vertex of the rhombuses as a site. The coordinates of every sites are found in "coordinate", where the length of each edge of the rhombus is set to be 1. The order of the data in "coordinate" refers to the numbering^* denoted in the image of each cluster. This numbering is also used in "site connectivity", which shows pairs of sites connected by each edge of the rhombuses. Because of the symmetry, every site except for the central one has 5 or 10 symmetrically equivalent sites. These sets of equivalent sites are listed in "equivalent sites".

These data will be useful for constructing, for example, a tight-binding model for electrons or Ising model for spins on this two-dimensional Penrose structure.

^* The numbering follows the two rules:
(i) Smaller number for a site closer to the center
(ii) Among the sites equally distant from the center, smaller number for smaller angle in the range from -π to π.

Tips

Just in order to construct a tight-binding Hamiltonian, the information of "site connectivity (nnbond.txt)" is sufficient: Put the electron hopping between the two sites numbered at each line.
"coordinate (coordinate.txt)" will be needed when you plot a spatial variation of a calculated quantity.
The information of "equivalent sites (equivalentsites.txt)" will be useful when you facilitate your code by using the symmetry of the Penrose tiling.