Dodecahedral Gnomonic Projections

Now, of course, most of you won't need me to tell you what these are, but for those of you who need a little refresher, one way to describe them is as a more accurate way to represent the Earth on a flat surface than stretching a rubber globe, with the added advantage that the flat shape can be made back up into something quite close to a sphere, in this case a regular dodecahedron. A regular dodecahedron – what an amazing word that is – it's a twelve (dodeca) faced (hedra) solid where all the sides are the same (regular).

Nick has always loved maps, and folding paper into solid shapes. As a boy, he used to draw maps of imaginary worlds, and, quite separately, used to work out how to arrange all the sides of complex boxes as a single, continuous shape on paper or card, including all the tabs needed to fold and glue it together. As a boy, he had no idea other boys his age we're doing this too. As a boy, he didn't have access to the World Wide Web, indeed, when he was a boy, the World Wide Web wasn't even a twinkle in Sir Tim Berners-Lee's eye.

Now, thanks to Sir Tim, we know there is a man in Brazil named Carlos Furuti, who may well have been playing with maps and folding paper at the same time Nick was. He – Mr Furuti – however, has taken this to an altogether higher level. He has assembled various computer programes, including some of his own, to create a number of Map fold-outs which may be printed, cut out, folded and stuck together to form pseudoglobes. (Follow the ‘fold-out’ link above for more on pseudoglobes.) We came across these when looking for a way to represent our round the world trip in 3D. Nick wrote to him asking for permission to digitally draw our route on one of his maps.

Now, Mr Furuti could have just said yes (or no) and left it at that, but he didn’t. He went several extra miles and took the co-ordinates for our route from our Google map, and made a special one-off version of one of his dodecahedron fold-outs just for us. He even spent part of his weekend creating it, and (so far) he hasn’t asked for a single centavo.

In this self-centred age, it’s all too easy to forget that there are good people out there, happy to do good things for other people.

Nice one, Mr F.

Happy folding.

Our 360 degrees in 360 days on a cut out and keep
dodecahedral gnomonic projection (PDF)
Copyright © Carlos Furuti 2012