On pentagon, ten-term, and tetrahedron relations
  The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. $O$-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra, provide a particular algebraic solution to the problem. 
R.M. Kashaev, S.M. Sergeev