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We consider simplest piecewise flat manifold consisting of two identical4-tetrahedra (call it bisimplex). General relativity action for arbitrarypiecewise flat manifold can be expressed in terms of sum of the (half of)bisimplex actions. We use representation of each bisimplex action in terms ofcertain rotation matrices (connections). This gives representation of anyminisuperspace piecewise flat gravity system in terms of connections which donot connect neighboring 4-tetrahedra (more appropriate would be call theseself-connections). If Regge calculus with independent 4-tetrahedra isconsidered, i. e. when the length of an edge is not constrained to be the samefor all the 4-tetrahedra containing this edge, self-connection representationleaves 4-tetrahedra independent also in connection matrices sector. Actionremains sum of independent 4-tetrahedra terms.

Independent 4-tetrahedra connection representation of Regge calculus