Dürer–Kepler–Penrose, the development of pentagon tilings

As Kepler’s Aa tiling is sometimes regarded as the pentagon tiling described by Penrose, the two tilings are compared considering their acceptance domains. The acceptance domain of the Penrose tiling is a decagon, whereas the acceptance domain of Kepler’s Aa tiling looks like a 10-fold toothed wheel; it exhibits a hole in the centre and it has therefore unusual inflation properties. A related tiling proposed by Dürer a century earlier than Kepler’s starts with an inflated pentagon and Dürer described the possibility of glueing tiles with random distribution.