We study formal regions of infinite Coxeter arrangements, which can be identified with biclosed subsets of the associated positive root system, and which are conjectured to be the topes of an oriented matroid on the reflections of the Coxeter group. They organize into a partial order which extends the weak Bruhat order on the group. Recently, we showed in joint work with David Speyer that this poset is a complete lattice when W is an affine Coxeter group, resolving a conjecture of Matthew Dyer for these groups. Focusing on the affine symmetric group (type A tilde), we show that the completely join-irreducible elements of this lattice correspond to shards of its Coxeter arrangement, as is known for finite Coxeter groups. We give a combinatorial description of the shards using cyclic non-crossing arc diagrams. We also show these objects biject with certain modules, called real bricks, over a type A tilde preprojective algebra, and discuss the relationship between the extended weak order and the lattice of torsion classes for this algebra.