  HD 12098 is an roAp star pulsating in the most distorted dipole mode yet
observed in this class of star. Using TESS Sector 58 observations we show that
there are photometric spots at both the magnetic poles of this star. It
pulsates obliquely primarily in a strongly distorted dipole mode with a period
of $P_{\rm puls} = 7.85$ min ($\nu_{\rm puls} = 183.34905$ d$^{-1}$; 2.12210
mHz) that gives rise to an unusual quadruplet in the amplitude spectrum. Our
magnetic pulsation model cannot account for the strong distortion of the
pulsation in one hemisphere, although it is successful in the other hemisphere.
There are high-overtone p~modes with frequencies separated by more than the
large separation, a challenging problem in mode selection. The mode frequencies
observed in the TESS data are in the same frequency range as those previously
observed in ground-based Johnson $B$ data, but are not for the same modes.
Hence the star has either changed modes, or observations at different
atmospheric depth detect different modes. There is also a low-overtone p mode
and possibly g modes that are not expected theoretically with the $> 1$ kG
magnetic field observed in this star.
