Triples of circle-pencils forming a hexagonal three-web in E2

Abstract

The problem of determination of all triples of circle-pencils which form a hexagonal 3-web was considered as difficult by Blaschke. This problem is completely solved here by examining all the possibilities for the three circle-pencils: elliptic, hyperbolic, parabolic, given by base points or null-circles. The special cases when some base point are coincident are proved, too.