The Collaborative International Dictionary of English v.0.48:

Uni- \U"ni-\ [L. unus one. See One.]
   A prefix signifying one, once; as in uniaxial, unicellular.
   [1913 Webster] Uniat

V.E.R.A. -- Virtual Entity of Relevant Acronyms (February 2016):

UNI
       Universal Network Interface (Cogent)


V.E.R.A. -- Virtual Entity of Relevant Acronyms (February 2016):

UNI
       User Network Interface