The Collaborative International Dictionary of English v.0.48:

Tetrastyle \Tet"ra*style\, a. [L. tetrastylon, Gr. ? with four
   pillars in front; te`tra- (see Tetra-) + ? a column.]
   (Arch.)
   Having four columns in front; -- said of a temple, portico,
   or colonnade. -- n. A tetrastyle building.
   [1913 Webster] Tetrasyllabic