Traditionally, B-rep geometric kernels possess oriented data structures, i.e. they possess oriented cells (e.g. half-edges, co-edges, face uses, etc.). The use of explicit oriented cells makes these data structures quite verbose and expensive in terms of memory space. Although orientation is important for visualization and engineering analysis purposes, it gives rise to difficult issues at the representation level; for example, keeping inclusion relationships between incident surfaces at a non-manifold vertex. Instead, we propose a non-manifold B-rep data structure whose cells are not oriented. This facilitates the design and implementation of its associated Euler operators, each one of which then reduces itself to a sequence of insertion and removal operations of cells into or from a list. Besides, these Euler operators call a single query operator to retrieve
incidence and adjacency information through a minimal number of accesses. As a result, we obtain a
non-oriented, non-manifold B-rep geometric kernel.