  A parameterization of Grassmann-algebraic relations corresponding to the
Pachner move 3--3 is proposed. In these relations, each 4-simplex is assigned a
Grassmann weight depending on five anticommuting variables associated with its
3-faces. The weights are chosen to have the "simplest" form - a
Grassmann--Gaussian exponent or its analogue (satisfying a similar system of
differential equations). Our parameterization works for a Zariski open set of
such relations, looks relevant from the algebraic-topological viewpoint, and
reveals intriguing nonlinear relations between objects associated with
simplices of different dimensions.
