The wait-free read-write memory model has been characterized as an iterated
\emph{Immediate Snapshot} (IS) task. The IS task is \emph{affine}---it can be
defined as a (sub)set of simplices of the standard chromatic subdivision. It is
known that the task of \emph{Weak Symmetry Breaking} (WSB) cannot be
represented as an affine task. In this paper, we highlight the phenomenon of a
"natural" model that can be captured by an iterated affine task and, thus, by a
subset of runs of the iterated immediate snapshot model. We show that the
read-write memory model in which, additionally, k-set-consensus objects can
be used is, unlike WSB, "natural" by presenting the corresponding simple affine
task captured by a subset of 2-round IS runs. Our results imply the first
combinatorial characterization of models equipped with abstractions other than
read-write memory that applies to generic tasks
