A straight, double-edged sword was the ubiquitous side-arm for Roman soldiers, just as much as any other in the West. The medieval Greek term is spathion (σπάθιον), from a Celtic language via Latin. As far as is presently known, there are no complete surviving examples of middle Byzantine spathia, but art shows a variety of hilt styles and several different blade cross-sections. The example depicted above is that of a senior officer, with its gilded, relief decorated fittings.
The standard method of carrying a spathion for all types of troops was from a shoulder strap, while more lightly armoured infantry could have a spathion zôstikion (~ ζωστίκιον), that is hung from a belt. See the infantryman reconstructed in the Roman armour category. zôstikia were also used as parade weapons just like the standard form.