  Recent observations of XTE J1739-285 suggest that it contains a neutron star
rotating at 1122 Hz. Such rotation imposes bounds on the structure of neutron
star in XTE J1739-285. These bounds may be used to constrain poorly known
equation of state of dense matter. One-parameter families of stationary
configurations rotating rigidly at 1122 Hz are constructed, using a precise 2-D
code solving Einstein equations. Hydrostatic equilibrium solutions are tested
for stability with respect to axi-symmetric perturbations. A set of ten diverse
EOSs of neutron stars is considered. Hypothetical strange stars are also
studied. For each EOS, the family of possible neutron star models is limited by
the mass shedding limit, corresponding to maximum allowed equatorial radius,
R_max, and by the instability with respect to the axi-symmetric perturbations,
reached at the minimum allowed equatorial radius, R_min. We get R_min \simeq
10-13km, and R_max \simeq 16-18km, with allowed mass 1.4-2.3 M_\odot. Allowed
stars with hyperonic or exotic-phase core are supramassive and have a very
narrow mass range. Quark star with accreted crust might be allowed, provided
such a model is able to reproduce X-ray bursts from XTE J1739-285.
