cusp
noun
\ ˈkəsp
\
\
Definition of cusp
a
: a point of transition (as from one historical period to the next) : turning point
also
: edge, verge
on the cusp of stardom … you're on the cusp between heat exhaustion and life-threatening heatstroke. — Mark Jannot
b
: either horn of a crescent moon
c
: a fixed point on a mathematical curve at which a point tracing the curve would exactly reverse its direction of motion
d
: an ornamental pointed projection formed by or arising from the intersection of two arcs or foils (see foil entry 2 sense 4)
e(1)
: a point on the grinding surface of a tooth
(2)
: a fold or flap of a cardiac valve