On the Supersingular K3 Surface in Characteristic 5 with Artin Invariant 1

We present three interesting projective models of the supersingular K3 surface X in characteristic 5 with Artin invariant 1.For each projective model, we determine smooth rational curves on X with the minimal degree and the projective automorphism group.Moreover, by using the superspecial Abelian surface we construct six sets of 16 disjoint smooth rational curves on X and show that they form a beautiful configuration.