  We examine the geometric structure of qutrit state space by identifying the
outcome probabilities of symmetric informationally complete (SIC) measurements
with quantum states. We categorize the infinitely many qutrit SICs into eight
SIC families corresponding to independent orbits of the extended Clifford
group. Every SIC can be uniquely identified from a set of geometric invariants
that we use to establish several properties of the convex body of qutrits,
which include a simple formula describing its extreme points, an expression for
the rotation between the probability vectors for distinct qutrit SICs, and a
polar equation for its boundary states.
