The poles of three great circles define always a not-degenerated triangle;

all great circles of the arrangement define a spherical mosaik of 2+n*(n-1) facets.

## Question: |
Is there a 3-coloring of the mosaic's vertices ? |

I.e.: How many colors do we need if we assign each vertex a color so that neighboured vertices have different colors ? Do we need just 3 colors ? | |

## Conjecture: |
Conjecture: yes, there is always a 3-coloring of the arrangement |

thus we need only two colors for coloring the vertices on one great circle.