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 ) .