부산대학교 도서관

The paper is a continuation of two previous papers [the author, same Toimetised Vih. 305 (1972), 116--126; ibid. Vih. 342 (1974), 110--121; MR0370362 (51 \#6589)]. Here the author solves the problem of obtaining an affinely invariant classification of convex polytopes in $R_n$ determined by the system of $m$ linear inequalities $\sum_{\alpha=1}^na_{i\alpha}x^\alpha\leq b_i$. Let $\rho$ be the rank of the matrix $\|a_{i\alpha}\|$. The complete classification (by means of analytic methods) is done for the cases: $m$ arbitrary and $\rho=1$ or $m=4$ and $\rho=2$ or $m=3$ (Paper II [see also the second reference above]).