Captain Boday is a Gallamite starship captain and occasional companion of Jadzia Dax, never seen on screen but often mentioned on account of his transparent skull and visible brain.
Boday is one of Deep Space Nine's running off-screen characters. He is first mentioned in The Maquis, Part I, when Kira is taken aback to learn that Dax is having dinner with him. Like all Gallamites he has a transparent skull, a feature Kira finds off-putting; Dax replies that she looks for more in a man than his appearance and notes the impressive size of his brain.
His name comes up again in later seasons as an example of Dax's adventurous taste in company, and he becomes a small irritant to Worf, who does not care to be reminded of her former admirers.
Because he never appears, everything known of Boday comes from these conversations: he commands a ship, he is charming, and one can see what he is thinking, or at least where.