Convert HEALPix to cube map

Question

I'm looking for a way to convert fits file using the HEALPix projection to a cube map. I'm particularly interested in converting files from the Planck data release.

My question in pictures:

I have:

I want:

Answer 1

I found a workaround using a function from CMBView: http://code.google.com/p/cmbview/source/browse/src/Classes/CMBdata.m

Result: https://github.com/hannorein/planck_cmb_cubemaps