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

Star of David and other patterns in the Hosoya-like polynomials triangles