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Foraminifera play an important role in oceanographic and paleoceanographic research. The test morphology and chemistry within species, as well as the presence or absence of certain species, are affected by environmental conditions. Classification of different species of foraminifera is a crucial yet tedious task for researchers. Deep-learning approaches can help with morphological studies and aid in species classification; however, they require large-scale datasets that are challenging to obtain and annotate because of the extremely small size and delicate handling of these microorganisms. In this work, we expand on an existing mathematical model for foraminifera shell growth to generate 3D synthetic models to aid in these studies. We define parameter spaces for the model which are intended to approximate seven randomly chosen foraminifera taxa. Along with providing an open-source code base to support other researchers in generating models and studying growth patterns, we further extend the synthetic data generation to include a rendering component that mimics two existing robotic imaging systems. We provide two use cases for our synthetic dataset. First, we show how orientation can affect the automated classification of different species and how incorporating aleatoric uncertainty indicators can help select the next views of the samples to significantly improve classification accuracy from 82% to 89%. Next, we show how a sparse set of synthetic 2D images can be used to extract 3D morphology of foraminifera using Neural Radiance Fields (NeRFs).