Probably made in Hungary in the 1980's. (plastic, 3.5 inches)

Made by Tantrix, purchased 2007. (3 inches)

Rotate the hexagonal and square faces so that the edges match. Fairly easy to solve because by starting at one vertex where three faces meet, there are not many possibilities, and then you can start working your way around. The bottom face of the Hungarian version is plain black. The faces of the tantrix version ("The Rock") can also be snapped off and put on in different positions to make different puzzles.

The 1983 patent of Sasso describes a similar idea for a regular solid shape where pairs of opposite faces rotate together.

Further Reading
Sasso Patent, from: www.uspto.gov - patent no. 4,416,453