The hand structure and Fermi surface of C8K are studied by the first-princi
ples calculation using two different types of basis sets to resolve the dis
agreements in the results of both experimental and theoretical studies. It
is concluded that C8K is a compensated metal with the same number of holes
and electrons. The Fermi surface of C8K is composed of the hole cylinders a
nd electron prisms. The hole cylinders originated from the state in which t
he graphite interlayer state, pi state, and potassium 4s state are hybridiz
ed have the simply connected topology. On the other hand, the topology of t
he electron prisms originated from the pi state is multiply connected with
the electron tube. Furthermore, we calculate the cross sections of these Fe
rmi surfaces and compare them with the dHvA frequencies. The observed two d
HvA frequencies can be assigned to the maximum and minimum cross sections o
f the electron prisms. We also predict that four dHvA frequencies originate
d from the hole cylinders should be observed.