How to tell whether a lens singlet is converging or diverging?

The center of a converging lens is generally thicker than its rim.
The center of a diverging lens is generally  thinner than its rim.
There are exceptions regarding meniscus lenses

Examples for converging lenses:

All convex-plano lenses, all plano-convex-lenses, alle biconvex lenses …

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… as well as all meniscus lenses with identical radiuses :

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Examples for diverging lenses:

All concave-plano lenses, all plano-concave lenses, all biconcave lenses

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