Quandles of Cyclic Type with Several Fixed Points

A quandle of cyclic type of order $n$ with $f$ (greater than 1) fixed points is such that, by definition, each of its permutations splits into $f$ cycles of length 1 and one cycle of length $n-f$. In this article we prove that there is only one such connected quandle, up to isomorphism. This is a quandle of order 6 and 2 fixed points, known in the literature as octahedron quandle.