@techreport{TR-IC-06-16,
  number = {IC-06-16},
  author = {Arnaldo J. Montagner and Jorge Stolfi},
  title = {Gems: A general data structure for
           $d$-dimensional triangulations},
  month = {September},
  year = {2006}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 11 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       We describe in detail a novel data structure for
       $d$-dimensional triangulations.  In an arbitrary $d$-dimension
       triangulation, there are $d!$ ways in which a specific facet of
       an simplex can be glued to a specific facet of another simplex.
       Therefore, in data structures for general $d$-dimensional
       triangulations, this information must be encoded using $\lceil
       \log_2(d!) \rceil$ bits for each adjacent pair of simplices. We
       study a special class of triangulations, called the
       \emph{colored triangulations}, in which there is a only one way
       two simplices can share a specific facet. The \emph{gem data
       structure}, described here, makes use of this fact to greatly
       simplify the repertoire of elementary topological operators.
  }
}