The Collaborative International Dictionary of English v.0.48:

Geodesic \Ge`o*des"ic\ (j[=e]`[-o]*d[e^]s"[i^]k), Geodesical
\Ge`o*des"ic*al\ (-[i^]*kal), a. [Cf. F. g['e]od['e]sique.]
   1. (Math.) Of or pertaining to geodesy; geodetic.
      [1913 Webster]

   2. (Architecture) Made of lightweight structural supporting
      elements connected in a manner to provide great rigidity;
      -- of structures; as, The geodesic dome was invented by R.
      Buckminster Fuller.
      [PJC]

The Collaborative International Dictionary of English v.0.48:

Geodesic \Ge`o*des"ic\, n.
   A geodetic line or curve.
   [1913 Webster]

WordNet (r) 3.0 (2006):

geodesic
    adj 1: of or relating to or determined by geodesy [syn:
           geodetic, geodesic, geodesical]
    n 1: (mathematics) the shortest line between two points on a
         mathematically defined surface (as a straight line on a
         plane or an arc of a great circle on a sphere) [syn:
         geodesic, geodesic line]