Thanks, Trevor - but no. The letters I've got now are c-e-i-h-n and I can't find a single (English) word to fit, never mind one that fits the clue. I'm sure about the c, e and h and 90% sure about the others.
I realised cheekbone was wrong because although it is a cetenary shape it is not inverted - unless you do a handstand.
Still cannot see the answer sorry.
if you Wikipedia "inverted catenary arch" you don't seem to find an alternative name for it. But you do find CTESIPHON described as the finest example of one. Could this be what you want.
You two are brilliant. I'd found the word, but not made the link to the arch. It's a bad clue (Ctesiphon is a city, not an arch). But I won't forget it in a hurry.