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1.
A duncecap is a reference to the cap a dunce wears after a stupid mistake. In this form, it is used as a type of insult after an idiotic remark.
When she asked whether or not Julius Caesar was a famous person, i yelled, "Judy, you duncecap! Your stupidity angers me."
by Madstratt March 05, 2012
 
2.
a small, cone-shaped turd, most commonly encountered stuck to the "head" of one's penis during withdrawal from an unclean anus.
"As I pulled my cock from her chocolate starfish in anticipation of shooting my load onto her bare butt-cheeks, I noticed a smelly DUNCE CAP adorning my head. Too late to stop, my load propelled the DUNCE CAP like a stinky poo rocket ship square into the back of her head, knocking her unconscious."
by Old Carndog December 16, 2013