a.k.a. Supernova
Patented by H. Corbeck and C. Bandelow 1982, G. Obermair 1982;
Left Tomy 1982, right Mefferts tiled version 2009.
(plastic, 2.75 inches between opposite faces)

Twelve sides, each a different color, can each be rotated. Jaap's Page gives a solution, mentions the relationship of this puzzle to Alexander's Star and Impossiball (see also Dogic), and has a discussion of a number of origins of this puzzle.

On opposite sides the Tomy version has:

red / green
blue / magenta
yellow / maroon
white (Tomy graphic in center) / orange ("MEGAMINX TOMY" in center)
dark purple / green
light blue / pink

On opposite sides the Meffert version has:

light blue / brown
green / light green
red / orange
white / yellow
purple / pink
blue / dark blue

Further reading:
Meffert's Page, from: http://www.mefferts.com/puzzles/megasol1.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/megaminx.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/mm/MegMin1.htm
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/megaminx/solution
Corbeck and Bandelow GB Patent, from: http://www.ipo.gov.uk - patent no. GB2101491
Obermair DE Patgent, from: www.epo.org - patent no. DE3204033
Wikipedia Page, from: http://en.wikipedia.org/wiki/Megaminx