We present a flexible, polynomial-based approach to yield-surface representation that guarantees convexity by regularizing a faceted polytope of adjustable order. This mathematical formulation has been proposed earlier as a FACET method [1], however, with only limited fitting possibilities. It has recently shown, that the FACET yield surface can be expressed as a neural network [2]. This enables the use of machine learning and stochastic gradient methods for efficient calibration. A non-centro-symmetric formulation naturally captures strength differential effects, whereas a centro-symmetric version requires fewer parameters. We demonstrate the applicability of these formulations by calibrating of full-stress yield surfaces computed via a crystal plasticity model and comparing them to conventional Yld2004-18p predictions. The results highlight the versatility, fidelity and computational efficiency of the neural network-based FACET approach for accurately describing a wide range of yield behaviors.