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:
Jaap's Page, from:
McFarren's Page, from:
Dry Erase Board Page, from:
Corbeck and Bandelow GB Patent, from: - patent no. GB2101491
Obermair DE Patgent, from: - patent no. DE3204033
Wikipedia Page, from: