  We give an elementary (not cut just paste) proof of results of Bott and
Shchepin: the space of non-empty subsets of a circle of cardinality at most 3,
which is called the third symmetric potency of the circle, is homeomorphic to a
3-sphere and the inclusion of the space of one element subsets is a trefoil
knot. Moreover, we give an explicit simplicial decomposition of the third
symmetric potency of the circle which is isomorphic to the Barnette sphere.
