  We consider a self-gravitating body composed of ideal Fermi gas of tachyons
at zero temperature. The Oppenheimer-Volkoff equation is solved for various
central densities and various tachyon mass parameter $m$. Although a pure
tachyon star has finite mass, it cannot occur in nature because the equilibrium
condition P=0 and the causality condition cannot be satisfied simultaneously. A
stable configuration with tachyon content must be covered with a non-tachyon
envelope. The boundary between the tachyon core and the envelope is determined
by the critical pressure $P_T$, which depends on the tachyon mass $m$. The
tachyon core is dominant and its mass can exceed many times the solar mass
$M_{\odot}$ when $m$ is much smaller than the nucleon mass $m_p$, while at
large $m$ compared with $m_p$, the main contribution to the total stellar mass
is due to the envelope whose material determines the parameters of the whole
star. However, the parameters of the tachyon core do not depend on the envelope
material. When the tachyon core appears, its mass $M_T$ and radius $r_T$ grow
up with increasing central density until maximum values are reached, after
which the mass and radius slowly decrease. The redshift at the surface of the
tachyon core does not depend on $m$ and never exceeds $z_{\max}\simeq 0.3$. The
maximum mass of tachyon core and its maximum radius are achieved at certain
central density and obey universal formulas $M_{T\max}/M_{\odot}=0.52m_p^2/m^2$
and $r_{T\max}=4.07m_p^2/m^2$ [km] that allow to estimate arbitrary
supermassive tachyonic bodies at the cosmological scale.
