  The geometry of the Quantum State Space, described by Bloch vectors, is a
very intricate one. A deeper understanding of this geometry could lead to the
solution of some difficult problems in Quantum Foundations and Quantum
Information such as the existence of SIC-POVMs and the cardinality of the
maximal set of MUBs. In this paper we show that the geometry of quantum states
can be described by the probability distributions that quantum states induce
over the outcomes of symmetric POVMs not necessarily of arbitrary rank or
informationally complete. We also describe the properties of these symmetric
POVMs.
