  We introduce the concept of a {\it reflection quasilattice}, the
quasiperiodic generalization of a Bravais lattice with irreducible reflection
symmetry. Among their applications, reflection quasilattices are the reciprocal
(i.e. Bragg diffraction) lattices for quasicrystals and quasicrystal tilings,
such as Penrose tilings, with irreducible reflection symmetry and discrete
scale invariance. In a follow-up paper, we will show that reflection
quasilattices can be used to generate tilings in real space with properties
analogous to those in Penrose tilings, but with different symmetries and in
various dimensions. Here we explain that reflection quasilattices only exist in
dimensions two, three and four, and we prove that there is a unique reflection
quasilattice in dimension four: the "maximal reflection quasilattice" in terms
of dimensionality and symmetry. Unlike crystallographic Bravais lattices, all
reflection quasilattices are invariant under rescaling by certain discrete
scale factors. We tabulate the complete set of scale factors for all reflection
quasilattices in dimension $d>2$, and for all those with quadratic irrational
scale factors in $d=2$.
