  We present spatial analysis of the deep (57ks) ROSAT HRI X-ray image of the
E4 galaxy NGC 720. The orientation of the HRI surface brightness is consistent
with the optical position angle $(PA)$ interior to semi-major axis $a\sim
60\arcsec$ (optical $R_e\sim 50\arcsec$). For larger $a$ the isophotes twist
and eventually $(a\gtrsim 100\arcsec)$ orient along a direction consistent with
the $PA$ measured with the PSPC data (Buote & Canizares 1994) -- the $\sim
30\arcdeg$ twist is significant at an estimated 99% confidence level. We argue
that this twist is not the result of projected foreground and background
sources, ram pressure effects, or tidal distortions. If spheroidal symmetry and
a nearly isothermal hot gas are assumed, then the azimuthally averaged radial
profile displays features which, when combined with the observed $PA$ twist,
are inconsistent with the simple assumptions that the X-ray emission is due
either entirely to hot gas or to the combined emission from hot gas and
discrete sources. We discuss possible origins of the $PA$ twist and radial
profile features (e.g., triaxiality).
