Fractal rep tiles of ℝ2 and ℝ3 using integer matrices

This paper is devoted to the study of self-similar fractal rep tiles of the Euclidean planes [Formula: see text] and [Formula: see text] using integer matrices. We construct many examples appearing in the literature, as well as new examples by integer matrices. Several exotic and radially symmetric self-similar rep tiles and their variations are obtained with change of bases extending the work by Bandt and others. We also present a few examples of polyhedral self-similar rep tiles including variations.