  Using the method of sub-super-solution, we construct a solution of
$(-\Delta)^su-cu_z-f(u)=0$ on $\R^3$ of pyramidal shape. Here $(-\Delta)^s$ is
the fractional Laplacian of sub-critical order $1/2<s<1$ and $f$ is a bistable
nonlinearity. Hence, the existence of a traveling wave solution for the
parabolic fractional Allen-Cahn equation with pyramidal front is asserted.
  The maximum of planar traveling wave solutions in various directions gives a
sub-solution. A super-solution is roughly defined as the one-dimensional
profile composed with the signed distance to a rescaled mollified pyramid. In
the main estimate we use an expansion of the fractional Laplacian in the Fermi
coordinates.
