If $H_1, ..., H_n$ are hyperplanes in $\mathbb{R}^m$ such that the complement of the union $\cup_i H_i$ is the interior of a complete polyhedral fan, then how does one determine ray generators for each face of the fan?
This question came about by trying to figure this out when the hyperplanes come from the Weyl chamber decomposition associated to a semisimple group. In dimension 1 or 2 one can just draw it and see what the answer is. But even in dimension three this seems difficult and seems to offer little help in higher dimensions.
Its relatively simple to describe the 1-dimensional cones (Mariano's answer) but it seems like more work needs to be done to be able to describe the higher dimensional cones.