cusp

US /kʌsp/
UK /kʌsp/
"cusp" picture
1.

a point of transition between two different states

:
She was on the cusp of a major career breakthrough.
The company is on the cusp of a new era of innovation.
2.

a pointed end where two curves meet, in particular on a tooth or a leaf

:
The dentist examined the cusp of her molar.
Each leaf has a distinct cusp at its tip.