The Cable & Wireless Giant Circle Map of 1945, photographed by iamdanw.
There’s a neater version at “Along What Dimension Is Cyberspace”, a post on what looks at a quick glance to be the fascinating (if slightly neglected) refractal site. (Again, thanks to Dan W for the pointer.)
It’s interesting comparing this decorative, slightly off-centred polar azimuthal map to the Pan Am route map, made just twenty years later, that I posted earlier. For example, the Empire and Dominions (as they then were) are shown in red, whereas Pan Am leaves the entire world off-white, and there’s far more labelling. Of course, both have the handy property of showing great circles (other than the Equator) as straight lines.