  We report magnetic quantum oscillations measured using torque magnetisation
in the Kondo insulator YbB$_{12}$ and discuss the potential origin of the
underlying Fermi surface. Observed quantum oscillations as well as
complementary quantities such as a finite linear specific heat capacity in
YbB$_{12}$ exhibit similarities with the Kondo insulator SmB$_6$, yet also
crucial differences. Small heavy Fermi sections are observed in YbB$_{12}$ with
similarities to the neighbouring heavy fermion semimetallic Fermi surface, in
contrast to large light Fermi surface sections in SmB$_6$ which are more
similar to the conduction electron Fermi surface. A rich spectrum of
theoretical models is suggested to explain the origin across different Kondo
insulating families of a bulk Fermi surface potentially from novel itinerant
quasiparticles that couple to magnetic fields, yet do not couple to weak DC
electric fields.
