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This paper examines number theoretic and topological properties of fullyaugmented pretzel link complements. In particular, we determine exactly whenthese link complements are arithmetic and exactly which are commensurable withone another. We show these link complements realize infinitely many CM-fieldsas invariant trace fields, which we explicitly compute. Further, we constructtwo infinite families of non-arithmetic fully augmented link complements: onethat has no hidden symmetries and the other where the number of hiddensymmetries grows linearly with volume. This second family realizes the maximalgrowth rate for the number of hidden symmetries relative to volume fornon-arithmetic hyperbolic 3-manifolds. Our work requires a careful analysis ofthe geometry of these link complements, including their cusp shapes and totallygeodesic surfaces inside of these manifolds.

Arithmeticity and Hidden Symmetries of Fully Augmented Pretzel Link Complements