  The main subject of the paper is the pentagon relation. This relation can be
expressed in different ways. We start with the natural geometric form of the
pentagon relation. Then we express it in algebraic form as a family of
equations with a set of linear maps as variables. Next, we derive several
equivalent forms of the algebraic pentagon relation. These forms can be
expressed using the classical notion of 6j-symbols. Finally, we show how to
extract a solution of the pentagon relation from any modular category.
