The Collaborative International Dictionary of English v.0.48:

Illicium \Il*li"ci*um\, n. [So called, in allusion to its aroma,
   from L. illicium an allurement.] (Bot.)
   A genus of Asiatic and American magnoliaceous trees, having
   star-shaped fruit; star anise. The fruit of Illicium
   anisatum is used as a spice in India, and its oil is largely
   used in Europe for flavoring cordials, being almost identical
   with true oil of anise.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Badian \Ba"di*an\, n. [F. badiane, fr. Per. b[=a]di[=a]n anise.]
   (Bot.)
   An evergreen Chinese shrub of the Magnolia family (Illicium
   anisatum), and its aromatic seeds; Chinese anise; star
   anise.
   [1913 Webster]

WordNet (r) 3.0 (2006):

Illicium anisatum
    n 1: small shrubby tree of Japan and Taiwan; flowers are not
         fragrant [syn: star anise, Illicium anisatum]