From Gineipaedia, the Legend of Galactic Heroes wiki
Axes are the weapon of choice for melee combat in the LOGH universe. One speculative reason for this is that weight of an axe-head combined with the leverage afforded by the long handle makes them more effective at piercing the heavy combat armour used in the series than other melee weapons.
The Free Planets Alliance forces favour a single-edged axe, which Schönkopf refers to at one point as a 'tomahawk', while the Galactic Empire use double-edged battle-axes, possibly inspired by an ancient Prussian design.
An extension of the axe-centric melee combat in the series is the 'axe-bayonet', which can be seen briefly being used by Imperial landing troops prior to an attack on Alliance-occupied Iserlohn, as well as by troops of the Imperial Forces stationed on the Brünhild, the Imperial Flagship, when it is boarded by the Rosen Ritter during the Battle of Shiva. It appears to consist of an axe-head which is attached to the stock of a soldier's rifle, allowing them to swing it by the barrel in order to use it in close combat. Such weapons are only used by ordinary soldiers, and not the "Panzer-Grenadiers", which wear combat armor similar to the Rosen Ritter design.