His rudeness is the height of unpleasantness.
この景色は美の極みと言える。
This scenery can be called the acme of beauty.
Used to indicate the furthest extent or limit of something, often in a more abstract or literary sense. Less common than sense 1.
苦しみの極みに達した。
He reached the limit of suffering.
Staying at such a luxury hotel is the height of extravagance.
His skill finally reached its pinnacle.
絶頂 emphasizes being at the very top of one's fortune or feeling (e.g. 絶頂期), whereas 極み is used in fixed phrases like ～の極み to express an extreme state.