Hungarian UFO

a.k.a. Varia Disk
Patented by I. Perdy 1983.
(plastic, same puzzle with different colors, 4 inches)

The four pegs, each composed of four quadrants, can be rotated. In addition, the top and bottom halves can rotate with respect to each other, causing two quadrants of each of the four pegs to be moved to the next peg. The goal is to match each quadrant of each peg with the color on that position of the body. Each of the eight colors appears on two of the quadrants. For a harder puzzle, the two copies of each color are marked with one or two dots, and the puzzle can be solved by making the markings match as well (one dot goes to the left and two dots to the right). A newer version of this puzzle was sold as the Tricky Disky.

Further reading:
Jaap's Page, from:
Peredy WO Patent, from: - patent no. WO83/01009