This article is an extension of work which suggests using formal concepts as optimal factors of Factor Analysis. They discussed a method for decomposing a p × q binary matrix W into the Boolean matrix product P ○ Q of a p × n binary matrix P and a n × q binary matrix Q with n as small as possible. We have generalised this factorization problem to the triadic case, looking for a decomposition of a p × q × r Boolean 3d-matrix B into the Boolean 3d-matrix product P ○ Q ○ R for p × n, q × n and r × n binary matrices P,Q and R with n as small as possible. The motivation is given by the increasing interest in Triadic Concept Analysis due to Web 2.0 applications.