  We study self-similar attractors in the space $\mathbb{R}^d$, i.e.,
self-similar compact sets defined by several affine operators with the same
linear part. The special case of attractors when the matrix $M$ of the linear
part of affine operators and the shifts are integer, is well known in the
literature due to many applications in the construction of wavelet and in
approximation theory. In this case, if an attractor has measure one, it is
called a tile. We classify self-similar attractors and tiles in case when they
are either polyhedra or union of finitely many polyhedra. We obtain a complete
description of the integer contraction matrices and of the digit sets for
tiles-parallelepipeds and for convex tiles in arbitrary dimension. It is proved
that on a two-dimensional plane, every polygonal tile (not necessarily convex)
must be a parallelogram. Non-trivial examples of multidimensional tiles which
are a finite union of polyhedra are given, and in the case $d = 1$ their
complete classification is provided. Applications to orthonormal Haar systems
in $\mathbb{R}^d$ and to integer univariate tiles are considered.
