BOATSWAIN. Aye, Little Buttercup – and well called – for you're the rosiest, the roundest, and the reddest beauty in all Spithead.
BUTTERCUP. Red, am I? and round – and rosy! Maybe, for I have dissembled well! But hark ye, my merry friend – hast ever thought that beneath a gay and frivolous exterior there may lurk a canker-worm which is slowly but surely eating its way into one's very heart?
BOAT. No, my lass, I can't say I've ever thought that.
Enter Dick Deadeye. He pushes through sailors, and comes down.
DICK. I have thought it often. (All recoil from him.)
BUT. Yes, you look like it! What's the matter with the man? Isn't he well?
BOAT. Don't take no heed of him; that's only poor Dick Deadeye.
DICK. I say – it's a beast of a name, ain't it – Dick Deadeye?
BUT. It's not a nice name.
DICK. I'm ugly too, ain't I?
BUT. You are certainly plain.
DICK. And I'm three-cornered too, ain't I?
BUT. You are rather triangular.
DICK. Ha! ha! That's it. I'm ugly, and they hate me for it; for you all hate me, don't you?
ALL. We do!
BOAT. Well, Dick, we wouldn't go for to hurt any fellow-creature's feelings, but you can't expect a chap with such a name as Dick Deadeye to be a popular character – now can you?
BOAT. It's asking too much, ain't it?
DICK. It is. From such a face and form as mine the noblest sentiments sound like the black utterances of a depraved imagination. It is human nature – I am resigned.
This exchange, which introduces the character of Dick Deadeye, foreshadows his role as "villain" -- the one who, even though he has nothing to gain by it, deliberately sets out to thwart the hero and heroine's attempts to form a romantic union. Throughout the operetta, Dick repeatedly reminds his fellow shipmates that lofty sentiments such as equality among men, or the power of love to overcome all obstacles is no more than a) empty rhetoric, and b) wishful, delusional, thinking. Since this is a romantic comedy, Dick Deadeye's machinations come to naught -- although, to be fair, his insights into the true power of rank and privilege are still borne out. H. M. S. Pinafore was written as a comedy and a political satire, and as such, this portrayal of ugliness giving rise to cynicism and bitterness might be seen as a spoof of the melodramatic villain -- if only this weren't something that comes up in serious fiction as well.
Dick's shipmates are absolved of all responsibility for their feelings and actions toward him -- it just can't be helped. And at the same time, Dick's cynical feelings toward his fellow man, and the actions he's driven to by those feelings, are painted as entirely his own responsibility -- a weakness of his own spirit. Variations on this trope persist even into the twenty-first century, when so often, in police procedural television, the only motivation for a disabled character to commit murder is to get revenge -- either on the individual he blames for causing his disability (it's almost always a man), or bitter rage against the world at large.
Meanwhile, Dick Deadeye might just be skeptical toward those egalitarian ideals and talk of "love conquering all," because he's experienced the bigotry and hypocrisy of society.
There's no physical description of Dick Deadeye in the libretto, by the way, and no further explanation of what "Triangular" or "Three-cornered" means. It could be that he is missing an arm or a leg... although I've never seen the character portrayed that way in any production I've seen (either in a live or a televised production). That, however, may say more about the difficulty of disabled actors have in getting hired, than it does about the original intent of the operetta's authors.
Wikipedia article on H.M.S. Pinafore
The Full Libretto for H.M.S. Pinafore