  We determine the points of the epicyclic topos which plays a key role in the
geometric encoding of cyclic homology and the lambda operations. We show that
the category of points of the epicyclic topos is equivalent to projective
geometry in characteristic one over algebraic extensions of the infinite
semifield of max-plus integers. An object of this category is a pair of an
algebraic extension of the semifield and an archimedean semimodule over this
extension. The morphisms are projective classes of semilinear maps between
semimodules. The epicyclic topos sits over the arithmetic topos which we
recently introduced and the fibers of the associated geometric morphism
correspond to the cyclic site. In two appendices we review the role of the
cyclic and epicyclic toposes as the geometric structures supporting cyclic
homology and the lambda operations.
