Configurations of rotating magnetic Newtonian polytropics with small index

In this article we was shown and the realized symbol-numerical algorithm for the decision the equations of equilibrium rotating Newtonian polytropics with the small index $n$. The analytical kind of a new class is found nonellipsoidal configurations of Newtonian polytropics — the limiting wedge-shaped figures having the form of a circular wedge near to equator. Are calculated values of the principal curvatures of the surface of a configuration near to equator. We found of class of limiting points $e_{L}(n)$. For asymmetry parameter $X$ the cubic equation and on its basis is received the class of critical points (bifurcations points) is defined. Existence of the first limiting critical point is proved with value $n_{m}=0.1161$.