Cellular imaging with confocal fluorescence laser microscopy gave rise to many new insights into the cellular machinery. One interesting observation suggests that morphology of cell nucleus plays a key role for neutrophilic function, which is an essential part of the innate immune system of most mammals. Due to the increasing availability of high resolution 3D images coming from the microscope, machine learning becomes a promising tool for automatically discovering underlying hidden structures. Here, the major difficulty consists of selecting an appropriate representation for characterizing the morphology of cell nucleus. In this work we tackle this problem and propose a fully unsupervised mechanism for finding structure in high-throughput 3D image data. The key component of our approach is based on Generic Fourier Transform (GFT) for 2D images, which for 3D involves spherical coordinate transformation prior to fast Discrete Fourier Transformation. On top on GFT we apply dimensionality reduction with Principal Component Analysis, followed by generative cluster analysis with a Gaussian Mixture Model. We validate our new approach first on a synthetic 3D-MNIST dataset with random rotations, where quantitative and qualitative results confirm the applicability of the proposed pipeline for exploring shape space in a purely unsupervised manner. Then we apply our proposed technique to a new collected dataset of high resolution 3D images of neutrophile nuclei suggesting a clustering model with six significant clusters of morphological cell nuclei prototypes. We visualize differences in the cell shape clusters by providing prototypical examples of neutrophilic cell nuclei.