More projections in a friendly pdf: “An Album of Map Projections”[1], the one above is on page 190.

For a more festive example see Berghaus star projection on page 156.

[1]: https://pubs.usgs.gov/pp/1453/report.pdf (1989)

oh wow that's a lot like a maximally extended penrose diagram

I believe I have seen the same projection used in a mod for quake 3 for dramatically increased POV.