  In this paper we consider the problem of constructing numerical algorithms
for approximating of convex compact bodies in d-dimensional Euclidean space by
polytopes with any given accuracy. It is well known that optimal with respect
to the order algorithms produces polytopes for which the accuracy in Hausdorff
metric is inversely proportional to the number of vertices (faces) in the
degree of 2/(d-1). Numerical approximation algorithms can be adaptive (active)
when the vertices or faces are constructed successively, depending on the
information obtained in the process of approximation, and non-adaptive
(passive) when parameters of algorithms are defined on the basis of a priory
information available. Approximation algorithms differ in the use of operations
applied to the approximated body. Most common are indicator, support and
distance (Minkowski) functions calculations. Some optimal active algorithms for
arbitrary bodies approximation are known using support or distance function
calculation operation. Optimal passive algorithms for smooth bodies
approximation are known using support function calculation operation and
extremal curvature information. It is known that there are no optimal
non-adaptive algorithms for arbitrary bodies approximation using support
function calculation operation. We consider optimal non-adaptive algorithms for
arbitrary bodies approximation using projection function calculation operation.
