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Flexibility is generally agreed to be a desirable feature of a Simple Temporal Network (STN). However, exactly what flexibility attempts to measure has varied, making it difficult to objectively evaluate flexibility metrics. Further, past metrics tend to lose information or exhibit other undesirable properties when aggregating the flexibility measures of individual events across an entire STN. Our work is driven by the realization that the solution space of an STN is a convex polyhedron whose geometric properties convey useful information about the STN. These geometric inspirations lead to measures of an STN solution space and also motivate a set of desiderata for general flexibility metrics. We also put forth two new geometrically-inspired flexibility metrics that have some theoretical advantages over existing metrics. Finally, we comprehensively evaluate both new and existing flexibility metrics against our proposed desiderata.