About degree of nondegeneracy of a tetrahedron (Preprint)

Abstract

In work characteristic is offered nondegeneracies of a simplex, defined through ρ?-distance between classes orthogonally equivalent families of points (numbered sets of tops of a simplex). This characteristic it can be used, in particular, for drawing up criteria of quality of a grid. In work the problem of calculation is investigated ρ?-distances from the set tetrahedron (a 4-vertex simplex) to a set degenerate tetrahedrons. It is shown that this the task comes down to calculation of ρ?-distance from this tetrahedron to families of points (on the plane) some three classes. For the correct 4-vertex tetrahedron the ρ?-distance is calculated obviously.