Obviously I'm going to have to refrain from using fossil insects as ID challenges in future, or at least confiscate Adam Yates' copy of Grimaldi & Engel (2005) before I do so to stop him from identifying them so quickly*.
*Unless, of course, I cruelly exploit Grimaldi & Engel's neglect of Palaeozoic polyneopterans.
Ponopterix axelrodi is a member of the Jurassic to Cretaceous insect family Umenocoleidae from the Lower Cretaceous Crato Formation of Brazil. Umenocoleids were originally described in 1973 as beetles, which they resemble in having the front pair of wings hardened into a pair of elytra (wing covers). However, while elytra are only found in two orders among the Recent insect fauna (beetles and earwigs), umenocoleids represent a third independent origin of elytra and are in fact related to dictyopterans (the clade that includes cockroaches, mantids and termites). The retention of a short ovipositor in Umenocoleidae (visible in the specimen above at the very end of the abdomen) places them just outside crown Dictyoptera, though a position closer to polyphagoid cockroaches has also been suggested (which would imply more than one loss of the ovipositor among dictyopterans).
As Adam pointed out, umenocoleids differ from beetles in that wing venation is still marginally visible on the elytra (among crown-group beetles, the original venation has been completely obliterated) and in the presence of cerci (two tail-like appendages at the end of the abdomen, one on either side of the ovipositor in females; cerci are absent in paraneopteran and holometabolous insects). The anterior light patch at the base of the elytron in the specimen above is also present in another specimen of the same species illustrated in Grimaldi & Engel (2005), so this was the original colour pattern of the animal when it was alive*.
*Don't let the poor reputation of cockroaches put you off - many roaches are very attractive insects, boldly patterned in contrasting colours**.
**Just be careful of the desert cockroaches that walk around with their backsides pointed into the air. If they feel that a potential threat is approaching too close, they can fire a stream of foul-smelling liquid towards it from a pair of abdominal glands. Not pleasant.
Umenocoleids also inspire the one detail in Grimaldi & Engel (2005) that causes me to scream with frustration. In the caption to their photo of Ponopterix axelrodi, G & E make the remark, "Umenocoleid roaches are known from the Late Jurassic to Cretaceous, though a putative living species exist". A living umenocoleid? Tell me more! Unfortunately, Grimaldi and Engel provide no citation for this statement, and I have been unable to find any reference to a living umenocoleid anywhere else. I'm still holding out hope, though.
Bechly, G. 2007. 'Blattaria': cockroaches and roachoids. In The Crato Fossil Beds of Brazil: window into an ancient world (D. M. Martill, G. Bechly & R. F. Loveridge, eds). Cambridge University Press.
Grimaldi, D., & M. S. Engel. 2005. Evolution of the Insects. Cambridge University Press. 755 pp.