It's a giant bugle.
Bugles were these conical cornchips that we used eat as kids. They just so happened to be the same shape of The Doomsday Machine. This one starred William Windom (My World and Welcome To It) as an Ahab-esque captain who goes up against a ginormous solar system destroyer. Obviously meant as a riff on the relations between the US and Russia and their nuclear buildup, this was a very effective commentary on the folly of war.