  We give a detailed description of the arithmetic Fuchsian group of the Bolza
surface and the associated quaternion order. This description enables us to
show that the corresponding principal congruence covers satisfy the bound
sys(X) > 4/3 log g(X) on the systole, where g is the genus. We also exhibit the
Bolza group as a congruence subgroup, and calculate out a few examples of
"Bolza twins" (using magma). Like the Hurwitz triplets, these correspond to the
factoring of certain rational primes in the ring of integers of the invariant
trace field of the surface. We exploit random sampling combined with the
Reidemeister-Schreier algorithm as implemented in magma to generate these
surfaces.
