i.e. the poles of three great circles of the arrangement define always a not-degenerated triangle.
Thus all great circles of the arrangement define a spherical mosaik consisting of 2+n*(n-1) facets.
Conjeture:
The quotient of the facets' largest area and smallest area tends to infinity for n → ∞
Remarks:
the smallest and the largest angle sum up to π .
the smallest facet is always a triangle.
one facet has always n edges.
Literature:
Laszlo Fejes-Toth:
"On Spherical Tilings Generated by Great Circles",
Geometriae Dedicata 23 (1987), 67-71