Great Circles in General Position I

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