  In this letter we present constant solutions to the tetrahedron equations
proposed by Zamolodchikov. In general, from a given solution of the Yang-Baxter
equation there are two ways to construct solutions to the tetrahedron equation.
There are also other kinds of solutions. We present some two-dimensional
solutions that were obtained by directly solving the equations using either an
upper triangular or Zamolodchikov's ansatz.
