D-branes and orientifolds on quasicrystalline orbifold backgrounds

We construct and analyse orientifold descendants of a six-dimensional type IIB ${\mathbb{Z}}_{12}$ quasicrystalline orbifold. The parent background is defined by a Narain-lattice automorphism that is not crystallographic on the geometric torus. We determine the closed-string spectrum and twisted-sector orbit structure, construct a compatible unoriented projection, and compute the Klein bottle, annulus and Möbius strip amplitudes. Tadpole cancellation selects boundary orbits that admit a partially T-dual description as D7-branes at angles and fixes the Chan-Paton gauge group and massless spectrum. The resulting supersymmetric six-dimensional vacuum satisfies the irreducible anomaly constraints, its reducible anomaly polynomial factorizes through the Green-Schwarz mechanism, and its anomaly lattice obeys the Kim-Shiu-Vafa string-probe bound. We also construct a Brane Supersymmetry Breaking descendant with a perturbatively tachyon-free rigid branch, and a freely acting five-dimensional orientifold whose two decompactification limits reproduce a geometric type IIA ${\mathbb{Z}}_3$ orientifold and an antisymmetric type IIB ${\mathbb{Z}}_4$ orientifold. These examples show that quasicrystalline closed-string backgrounds can admit controlled perturbative open-string completions with non-trivial boundary and crosscap sectors.