  In 2015, Archdeacon introduced the notion of Heffter arrays and showed the
connection between Heffter arrays and biembedding m-cycle and an n-cycle
systems on a surface. In this paper we exploit this connection and prove that
for every n >= 3 there exists an orientable embedding of the complete graph on
6n+1 vertices with each edge on both a 3-cycle and an $n$-cycle. We also give
an analogous (but partial) result for biembedding a 5-cycle system and an
n-cycle system.
