  This paper introduces a data structure, called simplex tree, to represent
abstract simplicial complexes of any dimension. All faces of the simplicial
complex are explicitly stored in a trie whose nodes are in bijection with the
faces of the complex. This data structure allows to efficiently implement a
large range of basic operations on simplicial complexes. We provide theoretical
complexity analysis as well as detailed experimental results. We more
specifically study Rips and witness complexes.
