AbstractIn algebraic topology, compact two‐dimensional manifolds are usually dealt through a well‐defined class of words denoting polygonal presentations. In this article, we show how to eliminate the useless bureaucracy intrinsic to word‐based presentations by considering very simple combinatorial structures called pq‐permutations. Thanks to their specific effectiveness, pq‐permutations induce a rewriting system P able to compute, in a very easy and intuitive way, the quotient surface associated with any given polygonal presentation. The system P is shown to enjoy both the fundamental computational properties of strong normalization and strict strong confluence. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 132–139, 2009.