  A throughout study of statistical characteristics of fidelity in different
protocols of quantum tomography is given. We consider protocols based on
geometry of platonic solids and other polyhedrons with high degree of symmetry
such as fullerene and its dual polyhedron. Characteristics of fidelity in
different protocols are compared to the theoretical level of the minimum
possible level of fidelity loss. Tomography of pure and mixed states in Hilbert
spaces of different dimension is analyzed. Results of this work could be used
for a better control of quantum gates and quantum states in quantum information
technologies.
