On a smooth quartic surface containing 56 lines which is isomorphic as a   K3 surface to the Fermat quartic
  We give a defining equation of a complex smooth quartic surface containing 56 lines, and investigate its reductions to positive characteristics. This surface is isomorphic to the complex Fermat quartic surface, which contains only 48 lines. We give the isomorphism explicitly. 
Ichiro Shimada, Tetsuji Shioda
math.AG