What are the advantages/disadvantages of octagonal barrels?

Because of flats and peaks. It would would be a stiffer barrel. Back in the day the barrel needed to be longer hense needed to be stiffer so to vibrate less. No most gun maker could make round barrels in the mid 1800s look at all the civil war rifles. And it was cheaper then to make a round barrel.

A octagonal barrel has several advantages,

• They look really cool and historic. The historical reason they were made that way is,

  Practically all are barrels are now turned to a round circumference or shape, concentric with the bore. Our old gunsmith makers of muzzle loading rifles almost invariably make their barrels octagonal, or eight sided in shape, most likely because none of them had a modern lathe with which they could turn them truly round, and they found it easier to make the barrel uniform by forging or grinding it into an octagon.

  Small Arms Design and Ballistics; Volume I by Colonel Townsend Whelen

  Quote sent by the Buffalo Bill Cody Center of the West after I emailed and asked if they knew why.

  There really is no clear cut answer but the general consensus is that before the popularity of lathes it was easier to file flats than make a round barrel for cost and time saving.

  Email from Henry Repeating Arms in response to my question.

• The flat surface will help one keep the barrel straight and not slanted when aiming

  An octagon barrel has but one advantage-- it calls attention to any canting or sideways tilting of the barrel when in the act of aiming,

  Small Arms Design and Ballistics

• They can be slightly heavier/thicker than a round barrel.

  Don't know that there is an actual "advantage" of an octagon over a round barrel other than usually they are slightly heavier/thicker than a round barrel. Octagons are usually installed on firearms to obtain a classic look.

  Email from McGowen Precision Barrels

The disadvantages include,

• Unequal expansion when in use.

  and it may have a disadvantage in that it may not expand equally when it heats up from firing.

  Small Arms Design and Ballistics

• Cost more (at least in 1945).

  Many think that an octagon barrel present a great deal of beauty, and it is doubtful if the disadvantages would be at all apparent in a heavy barrel, but the cost of making such a barrel today is rather excessive.

  Small Arms Design and Ballistics