  Bazhanov--Stroganov (4-simplex) maps are set-theoretical solutions to the
4-simplex equation, namely the fourth member of the family of $n$-simplex
equations, which are fundamental equations of mathematical physics. In this
paper, we develop a method for constructing Bazhanov--Stroganov maps as
extensions of tetrahedron maps which are set-theoretical solutions to the
Zamolodchikov tetrahedron (3-simplex) equation. We employ this method to
construct birarional Bazhanov--Stroganov maps which boil down to the famous
electric network and Hirota tetrahedron maps at a certain limit.
