Combinatorial maps define a general framework which allows to encode any subdivision of an nD orientable quasi-manifold with or without boundaries. Combinatorial pyramids are defined as stacks of successively reduced combinatorial maps. Such pyramids provide a rich framework which allows to encode fine properties of the objects (either shapes or partitions). Combinatorial pyramids have first been defined in 2D. This first work has latter been extended to pyramids of nD generalized combinatorial maps. Such pyramids allow to encode stacks of non orientable partitions but at the price of a twice bigger pyramid. These pyramids are also not designed to capture efficiently the properties connected with orientation. The present work presents our first result on the design of an nD pyramid of combinatorial maps.