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