In response to the Sphere project, regular visitor Eric sent me links to his brother's flickr feed and website where he shows how he projects panoramic pictures onto for various 3D solids. Fantastic stuff!
I've followed the link from his site and downloaded the demo of Flexify which I'll be purchasing shortly.

With Flexify I can take their demo picture (above) and convert it so that it covers a variety of different 3D shapes from cubes through dodecahedrons (below) to the truncated isocahedron from the sphere project.

Cut out the net, glue it together. (You could right click the above picture, save it and print it out to try this at home) The result is this fascinating 3D projection.

So, next step, create some of my own panoramic pictures to stitch together and project. Thanks Eric!
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Comments
cpeep
Oooo, love these. I have a fascination with cubic projections. I made some based on the Fujimoto cube origami fold, but I cheated on the top and bottom--it's not a real projection.
http://extremecards.blogspot.com/2010/08/photo-cube.html
Carol
robives
Thanks for the link, I'll have to have a go with your Photo Cube idea. Nice!
cpeep
Have you seen the plaited polyhedra? They're interesting, too.
I created a globe using the icosahedron from here:
http://mathworld.wolfram.com/PlaitedPolyhedron.html
combined with a projection from here:
http://www.ngdc.noaa.gov/mgg/education.html
I just discovered that I re-invented the wheel as there is a globe on this site, darn.
http://www.hbmeyer.de/flechten/indexeng.htm
Carol
Nobledesign
That, as we say in Los Angeles, is majorly way cool!