  New class of special functions of three real variables, based on the
alternating subgroup of the permutation group $S_3$, is studied. These
functions are used for Fourier-like expansion of digital data given on lattice
of any density and general position. Such functions have only trivial analogs
in one and two variables; a connection to the $E-$functions of $C_3$ is shown.
Continuous interpolation of the three dimensional data is studied and
exemplified.
