  The concept of typical and weighted typical spherical faces for tessellations
of the $d$-dimensional unit sphere, generated by $n$ independent random great
hyperspheres distributed according to a non-degenerate directional
distribution, is introduced and studied. Probabilistic interpretations for such
spherical faces are given and their directional distributions are determined.
Explicit formulas for the expected $f$-vector, the expected spherical Querma\ss
integrals and the expected spherical intrinsic volumes are found in the
isotropic case. Their limiting behaviour as $n\to\infty$ is discussed and
compared to the corresponding notions and results in the Euclidean case. The
expected statistical dimension and a problem related to intersection
probabilities of spherical random polytopes is investigated.
