  Archdeacon, in his seminal paper $[1]$, defined the concept of Heffter array
to provide explicit constructions of biembeddings of the complete graph $K_v$
into orientable surfaces, the so-called Archdeacon embeddings, and proved that
these embeddings are $\mathbb{Z}_{v}$-regular.
  In this paper, we show that an Archdeacon embedding may admit an automorphism
group that is strictly larger than $\mathbb{Z}_{v}$. Indeed, as an application
of the interesting class of arrays recently introduced by Buratti in $[2]$, we
exhibit, for infinitely many values of $v$, an embedding of this type having
full automorphism group of size ${v \choose 2}$ that is the largest possible
one.
