In this paper, we study the Faber polynomials F n ( z ) {F_n}(z) generated by a regular m-star ( m = 3 , 4 , … ) (m = 3,4, \ldots ) \[ S m = { x ω k ; 0 ≤ x ≤ 4 1 / m , k = 0 , 1 , … , m − 1 , ω m = 1 } . {S_m} = \{ {x{\omega ^k};0 \leq x \leq {4^{1/m}},k = 0,1, \ldots ,m - 1,{\omega ^m} = 1} \}. \] An explicit and precise expression for F n ( z ) {F_n}(z) is obtained by computing the coefficients via a Cauchy integral formula. The location and limiting distribution of zeros of F n ( z ) {F_n}(z) are explored. We also find a class of second-order hypergeometric differential equations satisfied by F n ( z ) {F_n}(z) . Our results extend some classical results of Chebyshev polynomials for a segment [ − 2 , 2 ] [ - 2,2] in the case when m = 2 m = 2 .