  Geometric intuition is a crucial tool to obtain deeper insight into many
concepts of physics. A paradigmatic example of its power is the Bloch ball, the
geometrical representation for the state space of the simplest possible quantum
system, a two-level system (or qubit). However, already for a three-level
system (qutrit) the state space has eight dimensions, so that its complexity
exceeds the grasp of our three-dimensional space of experience. This is
unfortunate, given that the geometric object describing the state space of a
qutrit has a much richer structure and is in many ways more representative for
a general quantum system than a qubit. In this work we demonstrate that, based
on the Bloch representation of quantum states, it is possible to construct a
three dimensional model for the qutrit state space that captures most of the
essential geometric features of the latter. Besides being of indisputable
theoretical value, this opens the door to a new type of representation, thus
extending our geometric intuition beyond the simplest quantum systems.
