  Twisted bilayer graphene is known to host isolated and relatively flat bands
near charge neutrality, when tuned to specific magic angles. Nonetheless, these
rotational misalignments, lying below 1.1 degrees, result in long-period
moir\'e crystals, whose anomalous electronic properties are hardly accessible
to reliable atomistic simulations. Here, we present a map of differently
stacked graphene sheets, at arbitrary rotation angles corresponding to precise
interplanar distances, into an equivalence class represented by magic-angle
twisted bilayer graphene. We determine the equivalence relation in the class
within a continuum model, and extend its definition to a tight-binding
approach. Then, we use density functional theory to suggest that the
magic-angle physics may be characterized by costly computational strategies on
a twisted bilayer geometry, with conveniently large stacking angles. Our
results may pave the way for an ab initio characterization of the
unconventional topological phases and related excitations, associated with
currently observed low-energy quasi-flat bands.
