  Let E be a Frobenius category, let_E_ denote its stable category. The shift
functor on_E_ induces a first shift functor on the category of acyclic
complexes with entries in_E_ by pointwise application. Shifting a complex by 3
positions yields a second shift functor on this category. Passing to the
quotient modulo split acyclic complexes, Heller remarked that these two shift
functors become isomorphic, via an isomorphism satisfying still a further
compatibility. Moreover, Heller remarked that a choice of such an isomorphism
determines a triangulation on_E_, except for the octahedral axiom. We
generalize the notion of acyclic complexes such that the accordingly enlarged
version of Heller's construction includes octahedra.
