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We investigate a type of Hermite orthogonal polynomials on $r$ lines in theplane which have a common point at the origin and endpoints at the $r$ roots ofunity and we show that their related Hermite functions are eigenfunctions of adifferential-difference operator. A supersymmetric harmonic oscillator on $r$radial lines is presented and analyzed. Its eigenfunctions are given in termsof these polynomials.

Supersymmetric Quantum mechanics on the radial lines