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A contrapasso is "punishment that fits the crime."
In Dante's Hell, sinners are punished in a way that somehow reflects what they did wrong on earth while they were living. Sometimes the contrapasso is
extremely similar in nature, but sometimes it is the opposite--a mirror image.
Paolo and Francesca:
Their sin on earth was their lust. They wanted to be with each other in
a sexual nature, even though it was forbidden. Here in Hell, their
punishment is the mirror image of their sin on earth--the same basic
concept, but the EXACT OPPOSITE. Here, they are stuck together sexually.
They are doomed to remain in the most intimate of positions for all
eternity, without rest or satisfaction. While in life all they wanted was
to be together, now that they are...They would love to be separated.
On the border of the 8th and 9th circles (Traitors), Count Ugolino sits straddling his former friend and co-conspirator, whose brain he now and then rips into with his teeth.
After all, it was his betraying friend's fault he was starved to death and ate his children to survive a short while longer. He even told Dante
"I am the perfect contrapasso."
is the story of Count Ugolino.
She was a whore who flattered her customers. Of course, it was lying. Typically, she told them they were the biggest, best, and her favorite. Now in Hell, she has intercourse with mud and slime, and continues to flatter it.
The king of Hell is himself a contrapasso. Prior to being kicked out of heaven and founding Hell, he was a majestic angel representing all of heaven's cardinal virtues: Love, Divine Omnipotence, and Wisdom.
Now that he screwed up Big Time and is down in the pit, he has been changed to reveal the mirror image of his former self. Now with a furry, frozen body with scales instead of wings, he has three heads:
one red (Hatred), one yellow (Impotence), and one black(Ignorance) to contrast the three highest virtues of heaven.