Combinatorial maps define a general framework which allows to encode any subdivision of an nD quasi-manifold orientable and 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 encoded objects (either shape 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. Such pyramids are also not designed to capture efficiently the properties connected with the orientation of orientable objects. The present work presents our first result on the design of a nD pyramid of combinatorial maps.