  The Harborth graph is the smallest known example of a 4-regular planar
unit-distance graph. In this paper we give an analytical description of the
coordinates of its vertices for a particular embedding in the Euclidean plane.
More precisely, we show, how to calculate the minimal polynomials of the
coordinates of its vertices (with the help of a computer algebra system), and
list those. Furthermore some algebraic properties of these polynomials, and
consequences to the structure of the Harborth graph are determined.
