Decagonal quasicrystal tilings

A description is given of three new distinct quasiperiodic tilings that exhibit tenfold symmetry. Related to each other by decomposition, these tilings are most easily generated from their respective Fibonacci pentagrid dual tilings. The latter, one of which is singular, are based on the property that there are three principle Fibonacci quasiperiodic sequences that possess mirror symmetry. The resulting tilings, while somewhat analogous to the Penrose tilings, are more complex in that they contain inequivalent tiles of the same shape. Associated with each of these decagonal tilings, which belong to different local isomorphism classes, are one twofold and two different fivefold tilings. Twelve inflations or deflations are necessary before each of the latter reoccurs with the same orientation.