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1.
An eigenpun or eigen pun is a pun which is unintentional.
To someone short
"Sorry I didn't mean to overlook you... Oh wait, that was a pun! Wow, I just made an eigenpun!"
by Batman_Ravi November 26, 2008
 
2.
When you make a pun by accident, and you don't realise until after you say it.
My girlfriend was sick, so I said to her 'you're pretty hot' (referring to her temperature). It was only afterwards that I realised that what I said could be interpreted as referring to her physical beauty! What a great eigenpun...
by soniastar346 November 22, 2009
 
3.
When you make a pun by accident, and you don't realize until later, then it's an eigenpun.
(To a skinny guy):

Hey, you look pretty fine today... Oh snap! That was a total eigenpun!
by satirical.cynicist November 23, 2009