The Collaborative International Dictionary of English v.0.48:

Sympodium \Sym*po"di*um\, n.; pl. Sympodia. [NL., fr. Gr. sy`n
   with + ?, dim. of ?, ?, foot.] (Bot.)
   An axis or stem produced by dichotomous branching in which
   one of the branches is regularly developed at the expense of
   the other, as in the grapevine.
   [1913 Webster]