cusp

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A point or pointed end.
• noun A pointed or rounded projection on the chewing surface of a tooth.
• noun A triangular fold or flap of a heart valve.
• noun Mathematics A point at which a curve crosses itself and at which the two tangents to the curve coincide.
• noun Architecture The point of intersection of two ornamental arcs or curves, such as the inner points of a trefoil.
• noun Astronomy Either point of a crescent moon.
• noun The boundary between two astrological signs or Zodiacal constellations.
• idiom (on the cusp) On the threshold or verge of a development or action.
• idiom (on the cusp) At the dividing line or border of two conditions or categories.

from The Century Dictionary.

• noun In astronomy, the point or horn of a crescent, specifically of the crescent moon.
• noun In astrology, the beginning or first entrance of any house in the calculation of nativities.
• noun In geometry, a stationary point on a curve, where a point describing the curve has its motion precisely reversed.
• noun In architecture, an intersecting point of the small arcs or foliations decorating the internal curves of the trefoils, cinquefoils, etc., of medieval tracery; also, the figure formed by the intersection of such arcs.
• noun In zoöl. and anatomy:
• noun Any special prominence or protuberance of the crown of a tooth.
• noun A sharp tooth-like process on a margin or part.
• noun In botany, a sharp and rigid point, as of a leaf.
• noun One of the segments, with pointed tip, of a valve of the heart.

from the GNU version of the Collaborative International Dictionary of English.

• transitive verb To furnish with a cusp or cusps.
• noun (Arch.) A triangular protection from the intrados of an arch, or from an inner curve of tracery.
• noun (Astrol.) The beginning or first entrance of any house in the calculations of nativities, etc.
• noun (Astron) The point or horn of the crescent moon or other crescent-shaped luminary.
• noun (Math.) A multiple point of a curve at which two or more branches of the curve have a common tangent.
• noun (Anat.) A prominence or point, especially on the crown of a tooth.
• noun (Bot.) A sharp and rigid point.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A sharp point or pointed end.
• noun figuratively An important moment when a decision is made that will determine future events.
• noun geometry A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.
• noun astrology A boundary between zodiacal signs and houses.
• noun dentistry Any of the pointed parts of a canine tooth or molar.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a thin triangular flap of a heart valve
• noun small elevation on the grinding surface of a tooth
• noun point formed by two intersecting arcs (as from the intrados of a Gothic arch)