It’s not a wasp, a mantis or a fly. It doesn’t even have a stinger.

Wasp Mantidfly - Field Station

Mantisflies/mantidflies, family Mantispidae, are in the order Neuroptera (“nerve wings”), a very cool order that includes antlions and lacewings, plus owlflies and a few other dynamite groups. […] There are about 400 species in the mantidfly family – 13 in North America – and they’re most diverse just about anywhere south of Wisconsin. They’re not related to praying mantises and they’re not related to flies, either.

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Because they’re such good mimics, wasp mantisflies are probably overlooked frequently (especially by the BugLady). They come in five color phases, and each matches a Polistes (paper) wasp that’s found within its range. […] Batesian mimicry is mimicry wherein an animal that is edible disguises itself as something that is either noxious or harmful, benefiting from its doppelganger’s reputation.