  A discrete Fourier analysis on the dodecahedron is studied, from which
results on a tetrahedron is deduced by invariance. The results include Fourier
analysis in trigonometric functions, interpolation and cubature formulas on
these domains. In particular, a trigonometric Lagrange interpolation on the
tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue
constant of the interpolation is shown to be in the order of $(\log n)^3$.
