  In this paper we first generalize the numerical recurrence relation given by
Hosoya to polynomials. Using this generalization we construct a Hosoya-like
triangle for polynomials, where its entries are products of generalized
Fibonacci polynomials (GFP). Examples of GFP are: Fibonacci polynomials,
Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell
polynomials, Fermat polynomials, Jacobsthal polynomials, Vieta polynomials and
other familiar sequences of polynomials. For every choice of a GFP we obtain a
triangular array of polynomials. In this paper we extend the star of David
property, also called the Hoggatt-Hansell identity, to this type of triangles.
We also establish the star of David property in the gibonomial triangle. In
addition, we study other geometric patterns in these triangles and as a
consequence we give geometric interpretations for the Cassini's identity,
Catalan's identity, and other identities for Fibonacci polynomials.
