a.k.a. Bicube
Made by Mefferts, 2009.
(left: plastic 2.3 inches, red opposite white, yellow opposite orange, blue opposite green;
right: plastic 1+5/8", red opposite orange, green opposite blue, yellow opposite white)

The bandages restrict the way in which a Rubik's 3x3x3 cube can be mixed up, and the sequences to solve it are also restricted. Jaap's Page presents analysis and solution sequences. Here is what the other three sides look like:



Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/bandage.htm