About the degree of nondegeneracy of a tetrahedron

The work offers of characteristic nondegeneracy of a simplex defined through the $\rho$-distance between classes of orthogonally equivalent families of points (numbered sets of simplex tops). This characteristic can be used, in particular, for drawing up criteria of grid quality. The work investigates the problem of calculating $\rho$-distances from the given tetrahedron (a 4-vertexsimplex) to a set of degenerate tetrahedrons. It is shown that the task comes down to calculating the $\rho$-distance from this tetrahedron to families of points (on the plane) of some three classes. For a regular 4-vertex tetrahedron the $\rho$-distance is calculated explicity.