The discovery of the Batwing surface is usually attributed to Alan Schoen (NASA, famous for the Gyroid) in 2000. It was already know to Robert Corkery, an Australian scientist, several years before Alan Schoen published it. It is visible (in a non fully optimized b-spline version) in a 1993 article in the Multi-CAD magazine and was later described in detail, in a fully optimizd version in R. Corkery's PhD thesis (go to the end, in the chapter on the genus 25 minimal surface).
The name of the surface comes from the elementary patch that is used to build the minimal surface itself and which ressembles the shape of a bat wing. As the Gyroid, the surface is orientable (it's not related to Möebius strip).
This Batwing cubelet has been built using "Surface Evolver", the variational optimizer by Brakke. The resulting cubelet has been remeshed and worked out using Blender.