The Collaborative International Dictionary of English v.0.48:

Vertex \Ver"tex\, n.; pl. E. Vertexes, L. Vertices. [L.
   vertex, -icis, a whirl, top of the head, top, summit, from
   vertere to turn. See Verse, and cf. Vortex.]
   A turning point; the principal or highest point; top; summit;
   crown; apex. Specifically:
   [1913 Webster]
   (a) (Anat.) The top, or crown, of the head.
       [1913 Webster]
   (b) (Astron.) The zenith, or the point of the heavens
       directly overhead.
       [1913 Webster]
   (c) (Math.) The point in any figure opposite to, and farthest
       from, the base; the terminating point of some particular
       line or lines in a figure or a curve; the top, or the
       point opposite the base.
       [1913 Webster]

   Note: The principal vertex of a conic section is, in the
         parabola, the vertex of the axis of the curve: in the
         ellipse, either extremity of either axis, but usually
         the left-hand vertex of the transverse axis; in the
         hyperbola, either vertex, but usually the right-hand
         vertex of the transverse axis.
         [1913 Webster]

   Vertex of a curve (Math.), the point in which the axis of
      the curve intersects it.

   Vertex of an angle (Math.), the point in which the sides of
      the angle meet.

   Vertex of a solid, or Vertex of a surface of revolution
      (Math.), the point in which the axis pierces the surface.
      [1913 Webster]

WordNet (r) 3.0 (2006):

vertex
    n 1: the point of intersection of lines or the point opposite
         the base of a figure
    2: the highest point (of something); "at the peak of the
       pyramid" [syn: vertex, peak, apex, acme]

Moby Thesaurus II by Grady Ward, 1.0:

76 Moby Thesaurus words for "vertex":
   L, acme, angle, apex, apogee, bend, bifurcation, bight, brow, cant,
   cap, chevron, climax, cloud nine, coin, corner, crank, crest,
   crook, crotchet, crown, culmen, culmination, deflection, dogleg,
   edge, elbow, ell, extreme limit, extremity, fork, furcation,
   heaven, heavens, height, heights, high noon, highest pitch,
   highest point, hook, inflection, knee, limit, maximum, meridian,
   mountaintop, ne plus ultra, no place higher, nook, noon, peak,
   pinnacle, pitch, point, pole, quoin, ridge, roof, seventh heaven,
   sky, spire, summit, swerve, tip, tip-top, top, upmost,
   upper extremity, uppermost, utmost, veer, very top, zag, zenith,
   zig, zigzag