Why do polygenic characteristics have many phenotypes?

The involvement of more than two genes.

Explanation:

The polygenic characteristics have many phenotypes because more than two genes governs the phenotype of individual organism. The single gene contains a pair of alleles that codes for two phenotype and two genes will code for 4 phenotype. Thus, more than two genes for example, three genes will have six phenotypes.

The skin color and height are polygenic characterstics in humans.