The latest issue of the newsletter from Wolfram Research (the folks who, among lots of other cool math-y things, bring us Mathematica and Mathworld [ http://mathworld.wolfram.com/]) has a link to an article in their "community" website with instructions for building two polyhedra from origami: "Spikey" (the Mathematica V1 logo, which "consisted of the spiked solid obtained from an icosahedron - the regular 20-faced solid that is one of the five Platonic solids - with regular tetrahedra (triangular pyramids) affixed to its faces.") and the Wolfram|Alpha logo (a rhombic hexecontahedron).
The newsletter is online here: http://msgcache.wolfram.com/wolfram-insider/2015/01/2015012017/COMM.html and the community article is here (with very nicely done photo-diagrams): http://community.wolfram.com/groups/-/m/t/413928 They both look like fun for the polyhedrally-minded out there. Anne