Due to their potential for a variety of applications, digital building models are meanwhile well established in planning, construction and usage phases of modern building projects. Older stock buildings however frequently lack digital representations and creating these manually is a tedious and time-consuming endeavor. For this reason, as well as due to the increasing availability of mobile indoor mapping systems facilitating the straight-forward, accurate and time-efficient capture of building structures, the automated reconstruction of building models from indoor mapping data has arisen as an active field of research.In this context, many approaches rely on simplifying suppositions about the structure of buildings to be reconstructed like e.g. the well-known Manhattan World assumption. This however not only presupposes that a given building structure itself is compliant to this assumption but also that the respective indoor mapping dataset is aligned accordingly with the coordinate axes. Indoor mapping systems on the other hand typically initialize the coordinate system arbitrarily by the sensor pose at the beginning of the mapping process. Indoor mapping data thus need to be aligned with the coordinate axes as a necessary preprocessing step for many indoor reconstruction approaches, which is also frequently known as pose normalization. Even in the case of indoor reconstruction approaches that do not rely on the Manhattan World assumption, such an alignment can be beneficial as it prevents aliasing effects when using data structures like voxel grids or octrees. Furthermore, it can be useful in the context of coregistering multiple indoor mapping datasets, for the automated analysis of architectural structures as well as for stabilization and drift-reduction in indoor mapping applications.In this paper, we present a novel pose normalization method for indoor mapping point clouds and triangle meshes that is robust against large fractions of the indoor mapping geometries deviating from an ideal Manhattan World structure. In the case of building structures that contain multiple Manhattan World systems, the dominant Manhattan World structure supported by the largest fraction of geometries is determined and used for alignment. In a first step, a vertical alignment orienting a chosen axis to be orthogonal to horizontal floor and ceiling surfaces is conducted. Subsequently, a rotation around the resulting vertical axis is determined that aligns the dataset horizontally with the coordinate axes. The proposed method is evaluated quantitatively against several publicly available indoor mapping datasets. Our implementation of the proposed procedure along with code for reproducing the evaluation will be made available to the public upon acceptance for publication.