  We consider simplest piecewise flat manifold consisting of two identical
4-tetrahedra (call it bisimplex). General relativity action for arbitrary
piecewise flat manifold can be expressed in terms of sum of the (half of)
bisimplex actions. We use representation of each bisimplex action in terms of
certain rotation matrices (connections). This gives representation of any
minisuperspace piecewise flat gravity system in terms of connections which do
not connect neighboring 4-tetrahedra (more appropriate would be call these
self-connections). If Regge calculus with independent 4-tetrahedra is
considered, i. e. when the length of an edge is not constrained to be the same
for all the 4-tetrahedra containing this edge, self-connection representation
leaves 4-tetrahedra independent also in connection matrices sector. Action
remains sum of independent 4-tetrahedra terms.
