On integer radii coin representations of the wheel graph

A {\em flower} is a coin graph representation of the wheel graph. A {\em petal} of the wheel graph is an edge to the center vertex. In this paper we investigate flowers whose coins have integer radii. For an \(n\)-petaled flower we show there is a unique irreducible polynomial \(P_n\) in \(n\) variables over the integers \(\ints\), the affine variety of which contains the cosines of the internal angles formed by the petals of the flower. We also establish a recursion that these irreducible polynomials satisfy. Using the polynomials \(P_n\), we develop a parameterization for all the integer radii of the coins of the 3-petal flower.